\r\n\tb) how a concentrated attention focus on screens (i.e., tablets and smartphones) could result in a total activity absorption and a flow experience; \r\n\tc) teens' preference for media social interaction appears to be closely associated with impaired modes of mood regulation; \r\n\td) the web activities as factors of externalized and/or internalized risks; \r\n\te) the implementation of health promotion interventions by Internet Apps; finally, \r\n\tf) the cross-cultural differences and similarities about teen approaches to the web around the world.
\r\n
\r\n\tThis book intends to provide the reader with an overview of studies with a research topic that is crucial today: the need to integrate teens' use of the web into the processes contributing to determine adolescents' developmental trajectories and Quality of Life.
",isbn:"978-1-83969-594-0",printIsbn:"978-1-83969-593-3",pdfIsbn:"978-1-83969-595-7",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"f005179bb7f6cd7c531a00cd8da18eaa",bookSignature:"Prof. Massimo Ingrassia and Prof. Loredana Benedetto",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10671.jpg",keywords:"Media Multitasking, Brain Development, Optimal-Experience Conditions, Digital Media Use, Mood Self-Regulation, Social Networking, Health Risk Behaviors, Internalizing/Externalizing Risk, Health Behaviors, Prevention, Cross-Cultural Research, Teen",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 25th 2021",dateEndSecondStepPublish:"March 24th 2021",dateEndThirdStepPublish:"May 23rd 2021",dateEndFourthStepPublish:"August 11th 2021",dateEndFifthStepPublish:"October 10th 2021",remainingDaysToSecondStep:"21 days",secondStepPassed:!1,currentStepOfPublishingProcess:2,editedByType:null,kuFlag:!1,biosketch:"Massimo Ingrassia is Director of the Post-graduate Advanced Studies in Palliative care and pain management for psychologists and a scientific advisor in research projects assessing psychological adjustment and therapeutic adherence in chronic illness. He was the author or co-author of several articles, and editor of the books on Parenting.",coeditorOneBiosketch:"Loredana Benedetto, Ph.D., is a psychologist and professor of Developmental and Educational Psychology at the Department of Clinical and Experimental Medicine, University of Messina. She was a scientific consultant for projects supporting families of the disabled and interventions in pediatric palliative care.",coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"193901",title:"Prof.",name:"Massimo",middleName:null,surname:"Ingrassia",slug:"massimo-ingrassia",fullName:"Massimo Ingrassia",profilePictureURL:"https://mts.intechopen.com/storage/users/193901/images/system/193901.png",biography:"Massimo Ingrassia, PsyD, is an Associate Professor of Developmental and Educational Psychology at Messina University, Italy, where he teaches graduate and postgraduate courses in Health Psychology. He is the Director of the postgraduate advanced studies in Palliative Care and Pain Management for Psychologists. His research interests include risk behaviors in adolescence and emerging adulthood, childhood development and digital technologies, pediatric palliative care and family resilience, and quality of life and chronic diseases. Dr. Ingrassia is also a scientific advisor for research projects assessing psychological adjustment and therapeutic adherence in chronic illness. He is the author or coauthor of several articles and books, including Growing Connected: Web’s Resources and Pitfalls",institutionString:"University of Messina",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"2",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"University of Messina",institutionURL:null,country:{name:"Italy"}}}],coeditorOne:{id:"193200",title:"Prof.",name:"Loredana",middleName:null,surname:"Benedetto",slug:"loredana-benedetto",fullName:"Loredana Benedetto",profilePictureURL:"https://mts.intechopen.com/storage/users/193200/images/system/193200.png",biography:"Loredana Benedetto, Ph.D., is a psychologist and Professor of Developmental and Educational Psychology at the Department of Clinical and Experimental Medicine, University of Messina, Italy. She teaches undergraduate and graduate courses in the areas of typical and atypical development, parent-child relationships, educational psychology, and family-based interventions. She has been a scientific consultant for projects supporting families of disabled children and interventions in pediatric palliative care. Her research interests focus on parenting assessment, self-efficacy and parental cognition, digital parenting and problematic use of the Internet in children, metacognition and childhood disorders, early intervention in autism and developmental disabilities, and behavioral parent training. She is the author or editor of several books, including Parenting: Empirical Advances and Intervention Resources (coedited with Massimo Ingrassia).",institutionString:"University of Messina",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"3",totalChapterViews:"0",totalEditedBooks:"2",institution:{name:"University of Messina",institutionURL:null,country:{name:"Italy"}}},coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"21",title:"Psychology",slug:"psychology"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"205697",firstName:"Kristina",lastName:"Kardum Cvitan",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/205697/images/5186_n.jpg",email:"kristina.k@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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1. Introduction
\n
In the last decades, timber is increasingly being used as building material as it represents a sustainable resource and is environmentally friendly and aesthetically pleasing when used both in new buildings and renovation. Using timber as building material leads to environmental benefits in terms of CO2 emissions. During the growth, the trees absorb CO2 by storing carbon and releasing oxygen in the atmosphere. When a tree is cut and processed into a building material, it delays the time when the carbon captured during the photosynthesis will be released back into the atmosphere. According to scientific studies and as shown in the Sixth Environmental Action Programme of the European Union, a cubic metre of wood used as construction material is equivalent to 1 ton of CO2 that is stored instead of being released into the atmosphere [1–3].
\n
Timber is also characterized by excellent properties such as lightness, low density, high strength-to-weight ratio, etc. These properties lead to the possibility to realize lightweight structures having excellent earthquake resistance, reduced cost of foundations, and the ease of transport and erection.
\n
Due to the aforementioned advantages nowadays, a significant increase in the volume of timber is used in building structures even in countries where there was weak tradition in construction of wooden structures (e.g. Italy, Spain, France, etc.). This growth has also been made possible by the availability on the market of a wide range of wooden products such as cross-laminated timber (CLT) and glue-laminated timber (GLT) elements. However, most of the timber used in these countries is imported from abroad. Using locally grown timber as building material would lead to economic, social and environmental benefits.
\n
Due to its organic nature, timber is not homogeneous; hence, it becomes of utmost importance to predict the base material quality and properties. The properties strongly depend on the growth condition and vary among different wood species [4]. International codes require the use of wood previously graded according to the current regulations in order to verify its reliability when used as structural material. Moreover, in Europe, structural timber shall be CE marked according to the European Construction Products Regulation (CPR) [5]. For these reasons, in the last 10 years, extensive researches have been carried out on locally grown timber species aiming at assessing the opportunity of a safe and economic use of these species as structural material.
\n
In Europe, the procedure for grading structural timber is defined by EN 14081-1 [6]. There are two systems for timber grading: machine and visual grading. Both the systems define grades to which characteristic values of strength, stiffness and density can be allocated according to EN 338 [7]. Characteristic values of strength, stiffness and density can be defined and measured according to EN 384 [8]. The two grading systems differ in (i) the property measured to define the grading criteria and (ii) the normative requirements.
\n
Visual and machine grading are based on defining visually and non-destructive parameters which are related to the three determining properties (density, stiffness, strength) based on relationships derived by means of destructive testing.
\n
Visual strength grading requires the non-destructive assessment of each piece of timber in order to define grading rules by means of visual features such as knots, rings width, slope of grain, warping, etc. Grading rules specify limits for all these features in order to assign each piece of timber into a grade. Then, based on the result of the destructive test, the grades are assigned to strength classes according to EN 338 [7]. Visual grading can be applied and implemented simply and without special measuring equipment.
\n
Machine strength grading is a process where a piece of timber is non-destructively sorted by a machine into grades by means of powerful predictors of the quality of the base material which are closely related to one or more of the grade determining properties. Machine grading can be applied quicker and with less risk of human error than visual grading.
\n
2. Visual strength grading
\n
In Europe, visual strength grading is performed according to EN 14081-1 [6] where minimum requirements for national visual stress grading standards are defined. Annex A sets the limitations for strength-reducing (knots, slope of grain, density and rate of growth, fissures), geometrical (wane, warp), biological (fungal and insect damage) and other (reaction wood) characteristics. The testing methods for determining the mechanical properties of sawn timber are specified in EN 408 [9]. The common strength class system is defined by EN 338 [7], while EN 1912 [10] sets up the assignment of species and visual grades derived from national standards to strength classes.
\n
In general, each European country has developed its own grading rules to define the methods for measuring properties and their limits.
\n
For coniferous sawn timber, as an example, the Italian Standard UNI 11035-2 [11] sets three grades (S1, S2 and S3), the Spanish Standard UNE 56544 [12] defines two grades (ME1 and ME2), while the German Standard DIN 4074-1 [13] establishes three grades (S13, S10, and S7).
\n
2.1. Strength-reducing parameters
\n
2.1.1. Knots
\n
Knots are caused by a branch embedded in the log. Knots are classified according to their shape, size and position in sawn timber [14]. Knots size is one of the main parameters for visual grading of sawn timber because it tends to cause a downgrading of the sawn timber due to its effect on warping and strength. Several studies have been carried out aiming at verifying the knots effects on the mechanical properties of sawn timber. For Portuguese Maritime Pine timber, the extensive presence of knots in the boards caused a rejection of 50% of sawn timber during the visual strength grading procedure and 44% of downgrading in visual strength grades [15]. In softwood, an increase in knots size from 25 to 75 mm can cause a decreasing in bending strength up to 50% [16]. Moreover, as reported by Olsson et al. [17] during fracture testing of 1000 pieces of timber, more than 90% of the failures were caused by knots.
\n
The criteria adopted in national standards for defining size of knots and their limitations are different. For example, the Italian Standard [11] defines the A and Ag parameters for knot and knot cluster, respectively. A signifies the ratio of the minimum knot diameter to the width of the cross section where the knot appears, while Ag denotes the ratio of the sum of the minimum diameters of the knots, comprised in a stretch of 150 mm, to the width of the cross section where the knot appears. According to the Spanish Standard [12], the limitation of the knots size depends on the type of knot (face, edge or margin knots): the knot diameter is defined as the distance between two straight lines tangent to the knot and parallel to the axis of the section. Additionally, the Spanish Standard [12] takes the knot cluster into consideration. The German Standard [13] defines a knot coefficient A in a simple way as the ratio of appropriate knot dimensions depending on the knot location to one of the cross-sectional dimensions. In the Polish Standard, as reported by Krzosek [18], the knot coefficient is given by a combination of two coefficients, tKAR and mKAR. tKAR coefficient is given by the ratio of the knot area in the weakest cross section to the cross-sectional area of the entire cross section. The parameter mKAR is the ratio of the cross-sectional area of the knots located in worse margin, namely closer to the corner of the cross section, to the area of the cross section. Figure 1 shows the knot measurements in accordance with the Spanish, German and Polish Standards.
Figure 1.
Knot coefficient according to different national standards.
\n
Comparisons of the results of visual strength grading rules applying the different national standards have been developed by researchers. Adell Almazán et al. [19] compared the results of Scots Pine visual strength grading according to the Spanish and German Standards and found a large difference. They stated that the most critical parameter was related to knot: 40% of the sawn timber pieces was rejected using the Spanish Standard, while only 5% of the sample was rejected following the indication of the German one. Krzosek [18] found irrelevant difference related to knot when applying the Polish and the German Standards on visual strength grading of Pinus sylvestris sawn timber. Stapel et al. [20] compared the results of visual strength grading of softwood sawn timber according to the German, Swiss, British, Danish and French Standards and pointed out several differences in the results caused by different rules of measuring knots and to an unequal number of visual grades in the standards.
\n
2.1.2. Slope of grain
\n
Slope of grain is a deviation of wood fibres from a line parallel to an edge of sawn timber. Slope of grain is expressed by the ratio between the deviation of grain length in millimetres (x) and the length over which the measurement is taken, in millimetres (y) as shown in Figure 2.
Figure 2.
Slope of grain measurement.
\n
Slope of grain is markedly depending upon wood species and is generally caused by two sources:
\n
slight bend of the tree: wood cells are arranged at a slight angle with respect to the axis of the stem during the growth of tree resulting in spiral grain;
manufacturing process: sawn timber cuts with a slight angle with respect to the axis of the stem.
\n
For visual grading, both forms of slope of grain shall be considered.
\n
Severe slope of grain results in twisting and warping of sawn timber. Furthermore, high values of slope of grain tend to decrease the mechanical parameters such as the strength of the sawn timber. Nevertheless, weak correlation between slope of grain and strength has been found by researchers probably due to the rather seldom occurrence of severe slope of grain [21].
\n
2.1.3. Density and rate of growth
\n
Density is one of the key mechanical properties of wood and represents the third grade determining property in the strength grading process. According to EN 384 [8], the density can be measured by following two methods:
\n
on specimens tested to failure: the density of each specimen shall be determined on a sawn timber piece cut out close to the fracture section and free from knots and resin pockets;
on specimens not tested to failure: the density of each specimen is determined from the ratio between the mass and volume of the test piece and divided by a coefficient equal to 1.05 in case of softwood to adjust to the density of the small defect-free pieces.
\n
As reported by Hanhijärvi et al. [21], several researches demonstrated that density is well correlated with strength properties in case of the defect-free wood specimens. In the case of structural timber, however, the density parameter has a very large variation and only low correlations have been found in the experimental programme where the density variation in the specimens is small.
\n
National standards specify methods of measurement of rate of growth. The Italian Standard defines the rate of growth as the average annual ring width, more specifically the ratio between a reference distance (l) and the number of annual rings (N) along the distance l. The distance l shall be identified as a straight line normal to the growth rings and either having a length of 75 mm or as the longest line normal to the growth rings. If the sawn timber contains the pith, l shall be taken outside a circle of 25 mm radius centred in the pith (Figure 3).
Figure 3.
Annual ring width measurement according to the Italian Standard.
\n
2.1.4. Fissures
\n
Different type of fissures can occur in wood due to natural event or seasoning conditions.
\n
Standing timber shows generally cracks or fissures, confined to the interior part of the trunk, due to a separation of fibres along the grain.
\n
Checks, splits and shakes (Figure 4) generally occur during the drying process: the change in moisture content causes a variation in the volume and the occurrence of internal stresses which cause the separation of the fibres [22].
Figure 4.
Fissures in sawn timber.
\n
Checks are fissures that occur along the grain and do not extend through the sawn timber from one face to the other, while splits are fissures that extend through the sawn timber from one face to another. Shakes are cracks caused by the separation of the fibres along the annual ring growth that occurs in standing or fallen tree, or during seasoning process.
\n
Limitation of fissures dimensions is given by grading national standards. Shakes are generally limited by grading national standards because they permit entrance of moisture, which may result in decay. For example, according to the Italian Standard, timber with shakes cannot be graded and must be rejected [23].
\n
2.2. Geometrical characteristics
\n
2.2.1. Wane
\n
Wane should be restricted in squared shape planks used in buildings. Although not primarily reducing strength and stiffness, nevertheless wane can influence the practical use and further processing of the sawn timber [24]. Wane can be particularly undesirable when nail plates or connectors are used or there is transverse compression. The current harmonized standards do not cover timber with non-rectangular cross section [25] although define limits for wanes.
\n
According to EN 1310 [14], the wane can be expressed either as a percentage of the total length of the board, measuring the length of the wane on one edge (and adding the different lengths if the plank shows more than one wane) or as a decimal fraction of the width of the edge reduced by the wane and the full width.
\n
Wane should not be greater than one-third of the full edge and/or face [6]. German Standard DIN 4074-1 [13] defines the wane parameter, k, as the ratio between the net and the full edge of the rectangular section; the maximum permitted values can vary with the visual strength class of timber, as illustrated in Table 1.
Visual strength classes
Wane parameter k
S7, S7k
≤1/4
S10, S10k
≤1/4
S13, S13k
≤1/5
Table 1.
Wane parameter values according to DIN 4074-1 [13].
\n
According to the Italian Standard UNI 11035-1 [26], the magnitude of the wane is expressed by the ratio (s) of the projection of the wane on one side to the side length itself. Its values should be limited to 1/3 for strength class S2 and S3; a reduced value of 1/4 is allowed for class S1 [11].
\n
As reported by Arriaga Martitegui et al. [27], the Spanish Standard suggests the measurements of the length of the wane and its dimensions on the edge and face of the sawn timber. The wane is evaluated as the ratio between the waneless dimension and the dimension of the rectangle into which the section fits. In length-wise direction, wane is determined as the ratio between its length and the total length of the sawn timber. Furthermore, according to Montero et al. [28], the Spanish Standard limits the maximum wane length to 1/3 of the length of the plank for Pinus sylvestris L. timber with thickness >70 mm. The relative dimension should also not be >1/3.
\n
Figure 5 shows the width of wane measurements according to EN 1310 [14], German [13], Italian [11] and Spanish [12] Standards. The limitations of wane size reported in national standards on visual strength grading lead to high number of rejected sawn timber. The major effect of wanes on timber elements is related to a reduction in the cross-sectional area and as a consequence a reduction in the total load-carrying capacity. The change of shape from square to circular cross section does not affect the bending strength if the area of the sections is the same [27].
Figure 5.
Width of the wane according to European visual strength grading standards (we = wane on edge, wf = wane on face).
\n
2.2.2. Warp
\n
Like wanes, warps can influence the practical use and further processing of the sawn timber and thus should be restricted. The maximum distortion (spring and bow) from the straight configuration should be referred to a length of 2 m and should be measured as in the following:
\n
for pieces up to a length of 2 m, with reference to a straight line, expressing the result in millimetres;
for pieces longer than 2 m, over a 2 m length, using a 2-m-long rigid straight edge applied against the piece symmetrically at the point of maximum distortion, visually estimated.
\n
The result is expressed in millimetres per 2 m (Figure 6).
Figure 6.
Spring and bow measurements.
\n
Cup is the maximum distortion along the width of the piece, expressed as a percentage of the width (Figure 7).
Figure 7.
Cup measurements.
\n
Twist represents the maximum distortion of the surface over a representative 2 m length and should be expressed in millimetres or as a percentage of the length of the piece (Figure 8).
Figure 8.
Twist measurement.
\n
According to EN 14081-1 [6], for both visual and machine graded structural timber, maximum warp over 2 m of length of the board should be limited to the values listed in Table 2.
Warp depends upon the moisture content of timber and can therefore change with time, and thus, limits in Table 2 should be considered only in case of dry grading. Longitudinal curvature in square section pieces may be assessed using the limits for bow [6].
\n
Sandberg [29] studied the influence of repeated cycles of wetting and drying in terms of warps on sawn timber of Pine and Spruce and stated that warp and the number of cracks increases if timber undergoes repeated cycles of wetting and drying.
\n
2.3. Biological characteristics
\n
Biological organisms such as fungi, bacteria and insects may attack and damage wood. Four critical elements must be present for the wood to be damaged by biological organisms: temperature, moisture, oxygen and a food source.
\n
Fungi require all the four critical elements to be present for attacking; however, the most important one is the presence of moisture in the form of free water. In general, an infection of fungi leads to a reduction in the wood structural integrity. Cross-sectional and mechanical strength reductions are the two principal consequences of the fungi infestation in wood elements: a 10% reduction in the section dimensions may lead up to 50% reduction in mechanical properties of wood. Impact strength, compression perpendicular and parallel to grain are the most affected mechanical properties. Moulds and staining fungi generally affect only the impact strength of wood and do not cause a reduction in the section dimensions. Soft and white rot fungi are most common in hardwoods such as Aspen, while brown rot fungi generally attack softwoods such as Pines, Firs and Spruces. These types of fungi cause degradation and affect the mechanical strength of wood [30].
\n
In general, the biotic decay caused by fungi or insect attacks leads to a reduction in the cross section of the wood elements. For this reason in case of grading new timber, the members subjected to a biotic decay must be rejected. Nevertheless, when grading timber members belonging to ancient and historical buildings, the presence of decayed elements is inevitable [23].
\n
2.4. Other characteristics
\n
Reaction wood is the term generally used for describing the abnormal tissue of wood, which is called compression wood in softwood and tension wood in hardwood. In general reaction, wood is characterized by higher density if compared to normal wood: 7% greater in tension wood and 35% greater in compression wood. Several defects, such as warps and surface checks, are caused by the presence of compression wood in timber elements during the drying process. Moreover, a brittle failure appears in timber containing compression wood [31, 32].
\n
The influence on the mechanical properties of both compression and tension wood compared to normal wood has been extensively studied: as reported by Wimmer and Johansson [33], compression wood is characterized by higher values of density and lower modulus of Young, bending and tensile strengths. Higher values of density, modulus of Young, bending strength and tensile strength are achieved in tension wood compared to normal wood.
\n
National visual strength grading rules limit the amount of compression wood in softwood elements, while no limits are indicated for tension wood in hardwood elements. The amount of reaction wood according to UNI 11035-1 [26] is given by the ratio between the sum of the widths of strips containing the reaction wood and the perimeter of the cross section as shown in Figure 9.
Figure 9.
Reaction wood measurement.
\n
3. Machine grading
\n
Machine grading has been commonly used in a number of countries for over 40 years. Like visual grading, the machine grading sorts the sawn timber into strength classes by means of some non-destructive measurements related to the mechanical properties. According to the European Standard EN 14081-1 [6], rectangular cross-sectional timber should be sorted into strength categories based on strength, stiffness and density, as well as some geometrical characteristics that should be limited because of their potential strength-reducing effects.
\n
The difference between machine grading and visual grading is that a machine can predicts the grade of timber by measuring some non-destructive properties, usually known as IPs (indicating properties). The IPs are measurements or combination of measurements taken by the grading machine that are closely related to one or more of the grade determining properties [34].
\n
Acceptance criteria are formulated in terms of intervals for the corresponding IP that have to be matched to qualify a piece of timber to a certain grade [35].
\n
These IPs are usually more powerful predictors of quality with respect to those measured by visual grading, and the grading can be done at a much faster rate with less risk of human error [25]. The oldest grading machines measured the modulus of elasticity of timber via non-destructive bending tests. Nowadays, new technologies and a great variety of IPs are used, with good correlations with the wood properties: for example, ultrasonic pulse velocity and longitudinal or flexural resonant frequency are measured in order to determine the dynamic modulus of elasticity, and X-ray analyses are performed to determine density and identify knots, etc.
\n
Two basic machine grading systems are provided by the European Standard EN 14081-2 [34]: the “output-controlled” and the “machine-controlled” methods.
\n
The “output-controlled” system was developed in North America. The control is based on statistical procedures assessed by means of destructive testing on specimens randomly selected from the daily production. Based on the correlation between the IP and the grade determining property (e.g. strength, stiffness), this method examines the output of the grading machine continuously by observing the values of the IPs which are measured by the grading machine non-destructively [36].
\n
In this way, machine settings are monitored and can be adjusted after each test in order to optimize the prediction of the properties of the graded timber material [37]. This implies that machine settings are strictly related to the quality of the wood, and the same type of machine could have non-identical performance.
\n
On the other hand, the output control system has been proved to be very expensive since a large amount of sawn material has to be assessed by destructive tests, and not all the data from these tests can be used for the recalibration of the grading machine [35].
\n
Thus, the “output-controlled” system is suitable in sawmills grading having production limited in sizes, species and grades because of the need of a continuous check of the grading process. The output control procedure currently requires only a verification of the bending strength and the bending stiffness. The measure of density is not required from the standardized control procedure [38, 39].
\n
The “machine-controlled” system was developed in Europe. Due to the large number of sizes, species and grades, it was not possible to carry out quality control tests on timber specimens taken from production [34]. Machine settings derived from the results of destructive testing programmes have been developed in order to have the same settings for the same machine types. Machine-controlled systems are not based on specific measurements, but on the capability of the machine to assign any piece of timber to a specific grade on the condition that the required characteristic values of the assigned grade have been satisfied [39]. For this reason, modern grading machines are based on non-destructive testing, contact-free measures or on their combination. Several authors demonstrated good correlations among non-destructive parameters and mechanical and stiffness properties of timber (ultrasounds measures or vibration methods) [39] or density (X-ray measures) [40–42]. Some models of grading machines incorporated a contact-free in-line moisture metre, so stiffness and density measures are automatically adjusted to the reference conditions (12%) [39].
\n
The effectiveness of a grading machine depends on the speed and on its capacity to subdivide the ungraded timber into sub-classes of graded timber in order to satisfy some predefined requirements [35]. The relationship between the IP and the three grade determining properties (density, stiffness and strength) varies with the wood species and with the region of provenience. Contrary to the output control system, the machine-controlled system is based on settings that are unique for grading region and wood species [25]. Thus, grading machines of the same type have the same settings if installed in the same region for grading the same wood species. However, both machine and output-controlled systems have revealed some problems and mainly related to the machine control strategy which is considered incapable to take into account the large scatter in the origin, sawing pattern and growth condition and other properties of the ungraded base material [35]. For this reason, both systems often require a further visual inspection in case of some strength-reducing characteristics were not automatically detected by the machine, for example, in the case of bending type machines, where the end of the pieces cannot be graded completely and a further visual inspection is necessary. EN 14081-1 [6] requires also some visual characteristics to be checked for each piece (warps, wane, fissures, insect damage, etc.).
\n
4. Visual strength grading of Sardinian Maritime Pine
\n
In this section, the results of an experimental programme aimed at identifying the visual strength grades of Sardinian timber are discussed and analysed.
\n
According to the National Forest Inventory (INSC) [43], one-fourth of Sardinia is covered by wood and about 5000 hectares are covered by conifers, in particular Stone Pine (Pinus pinea L.), Aleppo Pine (P. halepensis Mill.), Corsican Pine (P. nigra Arn.), Maritime Pine (P. pinaster Ait.) and Radiata Pine (P. pinaster D. Don) [1].
\n
Among the conifers, visual strength grading methodology applied to Sardinian Maritime Pine is reported and discussed. This species is quite widespread also in other Mediterranean regions such as the Iberian Peninsula, France, Corsica, etc. and is relatively fast growing.
\n
Three different growth regions, one located in the northern part, one in the centre and another in the southern part of Sardinia, were chosen in order to satisfy two requirements:
\n
density of population higher than 800 plants/ha;
stem bark size higher than 18 cm.
\n
The experimental programme was carried out on about 300 boards, 3.00 m long, 0.035 m thick and 0.125 m wide.
\n
Visual strength grading procedure according to UNI 11035-1 [26] was applied on boards after the drying process on a climate chamber at relative humidity of 65% and 20°C of temperature until constant weight was achieved.
\n
Table 3 gives a statistical summary of the most problematic geometrical and morphological parameters for visual strength grading and their values into the S1, S2, S3 and rejected (R) visual grades [11].
Parameter
S1
S2
S3
Rejected
Sample
Number [%]
5
18
30
47
Knot parameter
AV
0.18
0.25
0.32
0.4
St.Dev
0.06
0.07
0.16
0.14
CoV [%]
33.33
29.28
50.24
36.22
Knot cluster
AV
0.3
0.42
0.62
0.76
St.Dev
0.1
0.09
0.11
0.12
CoV [%]
33.33
21.55
18.62
16.10
Twist
AV [mm]
11.07
14.19
14.7
21.37
St.Dev [mm]
3.24
3.08
8.74
9.03
CoV [%]
29.29
21.7
59.53
42.25
Bow
AV [mm]
5.50
6.33
7.4
8.92
St.Dev [mm]
2.9
3.38
4.01
6.16
CoV [%]
57.75
53.37
54.30
69.02
Spring
AV [mm]
4.0
5.04
6.05
5.61
St.Dev [mm]
1.15
2.5
4.66
4.06
CoV [%]
28.87
49.63
77.01
72.42
AV, average; St.Dev, standard deviation; CoV, coefficient of variation.
Table 3.
Geometrical and morphological parameters.
\n
As shown in Table 3, about 50% of boards were rejected and could not be included into visual grades due to three parameters: knot, knot cluster and twist.
\n
Sardinian Maritime Pine timber is a low-quality wood: only 5% of the overall sample belongs to S1 visual grade, while about 45% of boards are divided into S2 and S3 visual grades.
\n
Maritime Pine boards are characterized by high scatter of all the geometrical and morphological parameters and by high values of knot, knot cluster and twist warping. Figure 10 shows the distribution of visual grades according to each of these parameters.
Figure 10.
Distribution of visual grades according to knot, knot cluster and twist parameters.
\n
Only about 10% of boards were rejected due to knot parameter, while more than 30% were rejected considering both knot cluster parameter and twist warping.
\n
The analysis of the visual grades distributions of knot and knot cluster parameters and twist warping highlights the low quality of wood: the boards that are included into the highest visual grade S1 are about 10% due to knot parameters, while more than 70% of boards are included into R and S3 grades.
\n
According to UNI 11035-2 [11], the boards were subdivided into visual grades, and then, they were tested to destruction in order to evaluate the characteristic values of density, modulus of elasticity and tensile strength and to determine which strength class is satisfied by the visual grades.
\n
Tensile tests were carried out in the worst sections of the boards for measuring the static elastic modulus of elasticity and the failure load according to EN 408 [9].
\n
Table 4 shows the statistical summary of the three keys parameters (density, modulus of elasticity in tension and tensile strength) used for determining the strength classes according to EN 338 [7].
Parameter
S1
S2
S3
Rejected
Density
[kg/m3]
520.10
506.69
501.19
504.95
St.Dev [kg/m3]
69.24
38.71
53.96
47.68
CoV [%]
13.31
7.64
10.77
9.44
Modulus of elasticity in tension
[N/mm2]
9208.50
8196.50
8584.16
4387.32
St.Dev [N/mm2]
1233.48
962.06
1480.95
1246.70
CoV [%]
20.09
17.39
25.56
22.02
Tensile strength
[N/mm2]
14.19
13.51
12.96
11.85
St.Dev [N/mm2]
3.08
4.20
3.26
3.17
CoV [%]
21.70
31.06
25.16
26.73
St.Dev = standard deviation; CoV = coefficient of variation.
Table 4.
Sardinian Maritime Pine: density, modulus of elasticity in tension and tensile strength.
\n
All the visual grades are characterized by high values of density and low values of both tensile strength and modulus of elasticity in tension. The boards belonging to R grade show similar values of density and tensile strength to S3 grade.
\n
The matrix of the strength class assignments is shown in Table 5.
Visual grades
Parameter
Tensile strength classes
A
T10
T11
T12
T13
T14
T28
T30
S1
Density
X
T11
Modulus of elasticity in tension
X
Tensile strength
X
S2
Density
X
T10
Modulus of elasticity in tension
X
Tensile strength
X
S3
Density
X
T10
Modulus of elasticity in tension
X
Tensile strength
X
R
Density
X
<T10
Modulus of elasticity in tension
Tensile strength
X
Table 5.
Sardinian Maritime Pine: matrix of the strength class assignments.
A = assigned tensile strength class.
\n
Several considerations can be made from the matrix of strength class assignments shown in Table 5:
\n
according to density, the high values of all the visual grades are confirmed by the T-strength class assignments: S1 grade corresponds to T30, while S2, S3 and R grades belong to T28 strength class;
the low values of modulus of elasticity cause a downgrade in the strength class assignments for all the visual grades;
the maximum T-class assignment according to tensile strength corresponds to T14 strength class, while T11 is achieved by the modulus of elasticity in tension.
\n
According to the three key parameters, both S2 and S3 Sardinian Maritime Pine timber visual grades can be assigned to T10 strength class, while S1 visual grade can be assigned to T11 strength class.
\n
Furthermore, the R-rejected class could be assigned to T10 class for tensile strength and density like the S3 and S2 visual grades. This suggests that the visual grading rule proposed in UNI 11035-1 [26] is too conservative regarding the limits of the defectiveness parameters, and a new proposal for visually grading of Sardinian Maritime Pine timber should be developed.
\n
5. Conclusions
\n
Maritime Pine is a very resinous, low strength conifer. Knots and warping are amongst the worst defects and are considered a disadvantage for structural uses because they markedly affect the strength and stiffness of timber.
\n
In addition, wood production is affected by several factors depending both on the growth area (altitude, wind, type of soil, rainfall, etc.) and on genetic factors which could result in a high variability of mechanical properties of the sawn timber [44]. For these reasons, several European countries have developed their own grading rules for locally grown species of timber based on the same criteria of the reference European Standard.
\n
Carballo et al. [45] visually graded according to the Spanish Standard [12], destructively tested Maritime Pine sawn timber from Galicia and stated that despite the high percentage of rejected board (37%), the base material exhibited a great structural capacity corresponding to C24 and C30 strength classes according to EN 338 [7].
\n
Morgado et al. [44] visually graded and destructively tested Maritime Pine poles from Portugal and compared test results with those obtained in similar researches. They stated that strength values obtained for Maritime Pine were significantly higher than those obtained from other species. Moreover, a proposal for visually grading Portuguese Maritime Pine roundwood was developed [46].
\n
Several researches demonstrated the suitability of low-quality wood for the production of structural elements [47, 48] like cross-laminated timber (CLT) panels because the lamination and system effect in CLT production reduce the influence of the defects (knots, warp, etc.) of the base material. Furthermore, as reported by Concu et al. [42], preliminary results on CLT panels made of Sardinian Maritime Pine wood confirmed that medium quality panels can be produced and used as horizontal and vertical elements in civil engineering structures.
\n
In conclusion, low-quality wood as Maritime Pine must be graded and classified into strength classes based on strength, stiffness and density before any use as a structural element. Grading rules for locally grown species should be drawn in order to minimize the negative effect of warping and other geometrical characteristics on strength class assignments.
\n',keywords:"timber structures, visual and machine grading, low-quality wood",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/53897.pdf",chapterXML:"https://mts.intechopen.com/source/xml/53897.xml",downloadPdfUrl:"/chapter/pdf-download/53897",previewPdfUrl:"/chapter/pdf-preview/53897",totalDownloads:2264,totalViews:878,totalCrossrefCites:2,totalDimensionsCites:4,hasAltmetrics:0,dateSubmitted:"June 13th 2016",dateReviewed:"December 1st 2016",datePrePublished:null,datePublished:"March 1st 2017",dateFinished:null,readingETA:"0",abstract:"Timber is a sustainable resource, environmentally friendly and aesthetically pleasing. Using locally grown timber as building material leads to economic, social and environmental benefits. Being an organic material, timber is not homogeneous; hence, it is crucial to predict the base material quality. International codes require the use of wood previously graded according to the current regulations in order to verify its reliability when used as structural material. An exhaustive analysis of the state of art of different methodologies and code requirements for structural timber grading is presented herein. Structural timber grading methods and their applicability to low-strength timber is analysed and discussed with reference to Maritime Pine locally grown in Sardinia (Italy). Several physical and morphological parameters such as density, the presence of knots, clusters of knots, grain deviation, warping, annual ring width and moisture content had to be measured. Moreover, mechanical parameters (tensile strength and modulus of elasticity in tension) were measured and analysed in order to identify the strength class of Sardinian Maritime Pine. The operational issues related to the application of the different methodologies and code requirements for structural grading of low-quality wood are also discussed and analysed.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/53897",risUrl:"/chapter/ris/53897",book:{slug:"wood-in-civil-engineering"},signatures:"Trulli Nicoletta, Monica Valdés, Barbara De Nicolo and Massimo\nFragiacomo",authors:[{id:"114603",title:"Prof.",name:"Barbara",middleName:null,surname:"De Nicolo",fullName:"Barbara De Nicolo",slug:"barbara-de-nicolo",email:"denicolo@unica.it",position:null,institution:{name:"University of Cagliari",institutionURL:null,country:{name:"Italy"}}},{id:"193575",title:"Ph.D.",name:"Nicoletta",middleName:null,surname:"Trulli",fullName:"Nicoletta Trulli",slug:"nicoletta-trulli",email:"nicolettatrulli@hotmail.it",position:null,institution:null},{id:"193742",title:"Dr.",name:"Monica",middleName:null,surname:"Valdes",fullName:"Monica Valdes",slug:"monica-valdes",email:"m.valdes@unica.it",position:null,institution:null},{id:"193743",title:"Prof.",name:"Massimo",middleName:null,surname:"Fragiacomo",fullName:"Massimo Fragiacomo",slug:"massimo-fragiacomo",email:"massimo.fragiacomo@univaq.it",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Visual strength grading",level:"1"},{id:"sec_2_2",title:"2.1. Strength-reducing parameters",level:"2"},{id:"sec_2_3",title:"2.1.1. Knots",level:"3"},{id:"sec_3_3",title:"2.1.2. Slope of grain",level:"3"},{id:"sec_4_3",title:"2.1.3. Density and rate of growth",level:"3"},{id:"sec_5_3",title:"2.1.4. Fissures",level:"3"},{id:"sec_7_2",title:"2.2. Geometrical characteristics",level:"2"},{id:"sec_7_3",title:"Table 1.",level:"3"},{id:"sec_8_3",title:"Table 2.",level:"3"},{id:"sec_10_2",title:"2.3. Biological characteristics",level:"2"},{id:"sec_11_2",title:"2.4. Other characteristics",level:"2"},{id:"sec_13",title:"3. Machine grading",level:"1"},{id:"sec_14",title:"4. Visual strength grading of Sardinian Maritime Pine",level:"1"},{id:"sec_15",title:"5. Conclusions",level:"1"}],chapterReferences:[{id:"B1",body:'Fragiacomo M., Riu R., Scotti R. Can structural timber foster short procurement chains within Mediterranean forests? 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In: Conference COST E53; 29–30th October; Delft, The Netherlands. 2008.'},{id:"B40",body:'Nocetti M., Bacher M., Brunetti M., Crivellaro A., van der Kuilen J.W.G. Machine grading of Italian structural timber: preliminary results of different wood species. In: WCTE 2010: World Conference on Timber Engineering; 20-24th June; Trentino, Italy. 2010.'},{id:"B41",body:'Concu G., De Nicolo B., Trulli N., Valdés M., Fragiacomo M. Strength class prediction of Sardinia grown timber by means of non destructive parameters. Advanced Materials Research. Trans Tech Publications. Switzerland. 2013; 778:191–198. doi:10.4028/www.scientific.net/AMR.778.191'},{id:"B42",body:'Concu G., De Nicolo B., Valdés M., Fragiacomo M., Menis A., Trulli N. Experimental grading of locally grown timber to be used as structural material. In: Chang, Al Bahar, Zhao, editors. Advances in Civil Building Materials. CEBM 2012: 2nd International Conference on Civil Engineering and Building Materials; 17–18th November 2012; Hong Kong. London: Taylor and Francis Group; 2013. pp. 189–193. ISBN: 978-0-415-64342-9.'},{id:"B43",body:'Gasparin P., Tabacchi G., editors. INFC 2005: L’Inventario Nazionale delle Foreste e dei serbatoi forestali di Carbonio. Secondo inventario forestale nazionale italiano. Metodi e risultati. Ministero delle Politiche Agricole, Alimentari e Forestali; Corpo Forestale dello Stato. Consiglio per la Ricerca e la Sperimentazione in Agricoltura, Unità di ricerca per il Monitoraggio e la Pianificazione Forestale. Bologna: Il Sole 24 ore Edagricole; 2011. 653 p. ISBN-10: 8850653948. (in Italian).'},{id:"B44",body:'Morgado T.F.M., Rodrigues J.N.A., Saporiti J., Dias A.M.P.G. Grading and testing of Maritime pine and larch roundwood. In: Conference COST E53; 29-30th October; Delft, The Netherlands.2008.'},{id:"B45",body:'Carballo J., Hermoso E., Fernández-Golfín J.I. Mechanical properties of structural maritime pine sawn timber from Galicia [Spain] (Pinus pinaster Ait. ssp. atlantica). Investigación agraria. Sistemas y recursos forestales. 2009;18(2):152–158. doi:10.5424/fs/2009182-01058'},{id:"B46",body:'Morgado T.F.M., Saporiti Machado J., Dias A.M.P.G., Cruz H., Rodrigues J.N.A. Grading and Testing of Maritime Pine Roundwood. In: WCTE 2010: World Conference on Timber Engineering; 20–24th June; Trentino, Italy. 2010.'},{id:"B47",body:'Smith R.E. Interlocking Cross-Laminated Timber: alternative use of waste wood in design and construction. In: Building Technology Educators\' Society, editor. BTES Conference 2011—Convergence and Confluence; 4–7th August; Toronto, Ontario, Canada.'},{id:"B48",body:'Negri M., Gravić I., Marra M., Fellin M., Ceccotti A. Using low quality timber for X-Lam: raw material characterisation and structural performance of walls under semi-dynamic testing. In: WCTE 2012: World Conference on Timber Engineering; 16–19th July; Auckland, New Zealand. 2012.'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Trulli Nicoletta",address:"ntrulli@unica.it",affiliation:'
Department of Civil Engineering, Environmental and Architecture, University of Cagliari, Cagliari, Italy
Department of Civil, Construction-Architecture and Environmental Engineering, University of L’Aquila, Italy
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1. Introduction
In multiple-input multiple-output (MIMO) communication systems, both the transmitters and receivers are equipped with several antennas which will help in achieving high gains in spectral, power, and energy efficiency compared to conventional single-input single-output (SISO) systems where both the transmitters and receivers have only one antenna each. As a matter of fact, the MIMO systems have the ability to turn multipath propagation and multipath delay spread into a benefit for the receiver. The key advantage of MIMO systems is the many orders of magnitude of the signal-to-noise ratio (SNR) at no extra bandwidth. However, a non-negligible software and hardware processing complexity is added at both sides (transmitter and receiver). Present wireless communication standards including Wi-Fi standards like IEEE 802.11n/ac, long-term evolution (LTE), and WiMAX are considering MIMO technology as a key element. Moreover, in the next generation of wireless technology systems (i.e., 5G), massive MIMO is emerging as a new research field in which base stations are equipped with 100 or more antennas. At the receiver side, designing reliable and energy-efficient MIMO detectors is a very challenging task, because of the complexity of the implementation of the signal detection due to the interfering sub-streams. The signal detection problem refers to finding the most probable transmitted symbols based on the perfect channel state information (CSI) available at the receiver and the received signal.
The hardware implementation of massive MIMO detector is of particular interest to deal with 5G wireless technology. Optimal massive detectors such as the maximum likelihood detector (MLD) or the sphere decoding (SD) are considered infeasible given their high computational complexity. Hence, low computational complexity algorithm achieving near-optimal performance is required; many existing detection algorithms like zero forcing (ZF), minimum mean-square error (MMSE), and successive interference cancelation (SIC) are used to deal with massive MIMO detection. In [1, 2], the authors presented surveys on various MIMO and massive MIMO detection techniques from algorithmic viewpoints. Although many classical massive MIMO detectors have been proposed in the literature, herein, new recent algorithms based on the application of machine learning, geometrical techniques, and bioinspired methods are presented and discussed.
In this chapter, we propose an overview of the SDM detection algorithms. We specifically stress out the different paradigms that are used to solve the detection problem and compare all of them. Thus, we describe the most well-known and promising MIMO detectors, as well as some unusual-yet-interesting ones. Section 2 presents the framework and the assumptions that are used in the remainder section. Section 3 introduces the maximum likelihood (ML) optimal detector, and then Section 4 describes the linear ones. Section 5 details algorithms based on the interference cancelation, and Section 6 discusses the one based on tree-search. Finally, Section 7 highlights unusual-yet-interesting detectors before Section 8 concludes the chapter. Figure 1 provides an overview of all the detectors described in this chapter as a tree mind map.
Figure 1.
Tree mind map of the detectors described in this chapter and the number or the corresponding section.
2. Introduction to MIMO detection algorithms
In the SDM framework, data streams are transmitted at the same time and at the same frequency, and the receiver relies on spatial consideration to distinguish the streams. Herein, we assume that the MIMO transmitter does not use any spatial coding and that all data streams are independent. To give the reader a unified mathematical description through this chapter, we adopt the following notation: scalars, vectors, and matrices are denoted by lower-case, bold-face lower-case, and bold-face higher-case letters, respectively. We call vi the ith coefficient of the vector v, and Hij is the element of the ith row and jth column in the H matrix.
In the linear input–output MIMO model where data are transmitted as the symbols of a constellation Φ, the received vector y∈CM is the result of the emitted symbols x∈ΦN propagated through the channel H and added to an additive noise w. This model leads to the following equation:
y=Hx+wE1
and the MIMO detection problem then refers to the combinatorial optimization problem:
argminx∈ΦN∥y−Hx∥2.E2
Assuming a circularly symmetric Gaussian noise, solving Eq. (2) is equivalent to searching the most probable emitted symbol vector based on the signal on each receive antennas and the channel state. Even if ∥y−Hx∥2 is a convex function with respect to x, the detection problem is not a convex optimization problem due to the discrete feasible solution set ΦN. As a result, a special algorithm has to be used, and this chapter will describe the most common ones.
Let us start by outlining the traditional assumptions that we will use in the present chapter. Although many constellation types could be used in MIMO systems, we limit the discussion to the square quadrature amplitude modulations (QAMs) that are most commonly investigated. Besides, the channel is considered memoryless, linear, and flat and with a block fading1. In this chapter, we assume that channel state information (CSI) is correctly estimated at the receiver side but not at the transmitter side. The impact of imperfect CSI at the receiver on the performance of detection algorithms is not addressed in the present chapter. Some known training symbols are sent from the transmitter, based on which the receiver estimates the channel before proceeding to the detection of the transmitted data symbols.
The channel matrix is modeled as a complex matrix H∈CMN. In that case, the element Hij refers to the complex channel gain between the jth transmit antenna to the ith receive antenna. Many channel models can fit in this framework, and we stick to the most popular one: the uncorrelated Rayleigh fading channel [3, 4]. The uncorrelated channel model provides a good approximation of propagating environments with rich scattering where the signals between the transmitter and the receiver experience many different paths and no strong line of sight between the transmitter and the receiver. This situation occurs, for instance, in urban and indoor conditions. In these conditions, each receiver antenna receives a sum of a large number of signal paths, and the channel transfer functions can be modeled as the realization of a circularly symmetric normal distribution.
3. Maximum likelihood detector
Obtaining the optimal result requires, in the most straightforward approach, the use of the ML detector that solves Eq. (2) using an exhaustive search. Even if this method gives the best result since all x∈ΦN are evaluated, it is not suitable for real implementation. Indeed, the number of vectors to be tested grows exponentially with the number of transmit antenna and the constellation size. Thus, the computational cost of evaluating Eq. (2) requires an unrealistic quantity of resources to detect the transmitted vector x. That is why a variety of detection algorithm has been developed throughout the past year to achieve the same detection performance of ML detectors while having a tractable complexity.
From a computational theory perspective, the detection problem is an instance of the closest lattice-point search (CLPS) problem with a specified lattice [5]. It has been proved that regardless of the preprocessing on the lattice (i.e., the channel matrix), the problem is always NP-hard [5]. The NP-hardness implies that it is not possible, at the moment, to find any detector that is sure to have both an optimal performance and a polynomial complexity2. For that reason, all the following detectors have suboptimal performance (which can be very close to optimal) or a non-polynomial worst-case complexity (which can be polynomial is the average case).
4. Linear detectors
4.1 Zero forcing (ZF) detector
Linear detectors are the most simple algorithms to solve the detection problem. The most basic one is the ZF algorithm that follows a two-step process. First, the ZF detector solves Eq. (2) transforming the constraint from x∈ΦN to x∈CN such that the problem become an easy-to-solve convex optimization with a known mathematical solution:
x0=H+yE3
with H+=HHH−1HH being the left Moore-Penrose pseudoinverse. Then, the constraint on x is reintroduced by quantizing the vector accordingly to the constellation in use. This quantization should lead to a good estimation as after the application of the detection matrix TZF=H+, Eq. (1) becomes
TZF.y=x+H+wE4
highlighting that all the interference are canceled. The previous equation is also the proof that the ZF detector is the optimal linear one regarding the signal-to-interference ratio (SIR) criteria. Indeed, one can see that the vector TZF.y contains each stream independently plus some noise but without any interference.
4.2 Minimum mean-square error (MMSE) detector
By only focusing on the interference, the ZF detector performance suffers from not taking the noise into account. Indeed, if the noise level is known to the receiver, a Bayesian estimator including this information can provide a better detection. A linear Bayesian estimator minimizing the mean-square error can be derived using the orthogonality principle [6] leading to
TMMSE=HHH+2σ2I−1HHE5
with σ2 being the noise variance per real direction. The detector based on this detection matrix, followed by the quantization, is called the minimum mean-square error (MMSE), and it is known to maximize the signal-to-noise-plus-interference ratio (SINR). When the signal-to-noise ratio (SNR) is low (i.e., σ2 is high), the MMSE detector provides better results, jointly minimizing the interference and the noise. Otherwise, when σ2 is very low, the corrective term becomes negligible, and the ZF and MMSE detectors overlap.
5. Interference cancellation detectors
To improve further the performance, it is necessary to drop the linear detector approach and look for more elaborate decoding algorithms. Historically, the first nonlinear detector type is still based on the principle of canceling signal interference. This concept leads to two approaches: an iterative one named successive interference cancelation (SIC) and a simultaneous version named parallel interference cancelation (PIC).
The SIC detectors opt for a two-step iterative process: first, a decision is taken on the first position x1, and then assuming that the decision was right, the detector corrects y by removing the interference that would have been generated by x1. Then, SIC detectors repeat this process on the next x’s entry until the whole vector is received.
Even if the performance is better than with the linear detectors, the SIC process is very prone to error, given that the assumption at an iteration has an impact on all the following ones. For this reason, the simple SIC detector has quickly been replaced by a variant seeking for an optimal iteration order [7]. This variant called ordered successive interference cancelation (OSIC) aims to make the first assumption on the position that leads to the better SNR or SINR.
To select the best symbol to detect at each iteration, the OSIC detector computes the post-SNR or post-SINR for each symbol, assuming that the kth element is canceled using the detection matrix T. Most of the time, the detection matrix is chosen to be TZF or TMMSE optionally updated after each iteration. When using the SNR criterion, the value of the kth post-SNR is computed as in [7, 8].
SNRk=<xk2>ΦTkhk2σ2∥Tk∥2E6
with Tk being the kth row of T, hk the kth column of H, and <xk2>Φ the expected value over the constellation set. The latter term is the average signal power of the kth data stream that can be computed, assuming that each symbol is equiprobable, as
<xk2>Φ=1φ∑x∈Φxk2E7
with φ the number of symbols in constellation Φ.
When using the SINR criterion, the post-SINR expression becomes slightly more complex as the post-processed power of each other channel appears in the expression
SINRk=<xk2>ΦTkhk2∑l≠k<xl2>ΦTlhl2+σ2∥Tk∥2.E8
For clarity sake, Figure 2 sums up the OSIC detection algorithm introducing a process t:H↦T to build a detection matrix from a channel one. This process is most of the time the Moore-Penrose pseudoinverse or the process described in Eq. (5). We also denote by D the set of the symbol index to be decoded and by ← the affectation. One must note that an instruction is optional and may be skipped. If this instruction is applied, performance is increased by canceling the interference in the post-criterion computation and so is the complexity.
The main drawback of the OSIC algorithm is that the number of iterations grows linearly with the number of antennas. The number of stage becomes an issue for large MIMO system since each stage adds a reception delay. For that reason, a detector capable of canceling the interference for all antennas at once was developed.
The first application of such an algorithm to SDM systems dates from the early 2000s, and it is based on a few basic steps summed up in Figure 3 as published in [9]. The main point of the PIC algorithm is to start by using a simple detector with poor performance, most of the time a linear one, and cancel the interference on all antennas at once based on the assumption. If better performance is required, it is possible to iterate the last three instructions as many times as needed by using the new detected symbol as the new assumption.
Figure 3.
PIC algorithm outline as published in [9].
Simultaneously, the iterative reception techniques developed for turbo codes and single-input single-output channels are adapted to MIMO systems. The goal is to receive a coded message by alternating between soft-input soft-output detector and decoder. Each algorithm uses a priori information from the other to improve its performance [10]. This method leads to one of the current most accomplished version of the PIC family: a soft-input soft-output detector to be used in iterative decoding with any message coding [11].
This version adds several improvements to the basic algorithm described in Figure 3. First, it uses the soft symbols from [12] that are defined as the expected value of the symbols knowing the a priori. The reliability of a soft symbol is computed as its variance. Then, the parallel cancelation (see the third instruction in Figure 3) is performed using the soft symbols in place of the rough estimation. Finally, a last MMSE filtering is performed before the computation of the log-likelihood ratios (LLRs). Further reductions in complexity are also used, such as the max-log approximation [10, 13, 14] or the channel Gram matrix [15]. Thanks to all of these improvements, an application-specific integrated circuit (ASIC) is reported to achieve a throughput greater than 750 Mb/s with good BER performance [11].
5.3 Selecting between SIC and PIC detectors
The key idea to select between SIC and PIC detectors is to compare the relative quality of data streams. As stated earlier, SIC algorithms guess the best data stream and then process the other one based on this assumption. This process makes the SIC algorithms very prone to error propagation. Indeed, if an assumption is wrong, the error has consequences on all the data streams to be detected. Hence, SIC detectors should be used when there is a net ranking in the quality of each data stream. A basic scenario for this would be a MIMO system receiving data from several users with different channel qualities.
On the contrary, PIC detectors process all the data streams at once so that they are more resilient to interstream error propagation. However, the parallel computations assume that every data stream is as reliable as the other. Due to this assumption, a poor-quality data stream propagates its error to the whole system. For that reason, PIC detectors are well suited when all data streams have the same quality level.
6. Tree-search-based detectors
Tree-search-based detectors are the current most investigated algorithms. They use a different framework than the linear and the interference cancelation detector. As the name suggests, the tree-search detector interprets the detection problem from Eq. (2) as the search for the best path in a tree. Tree-search-based detectors can either be optimal with a non-polynomial yet small complexity or quasi-optimal yet not optimal with a polynomial convexity.
Figure 4 gives an example of the tree interpretation for a constellation with four symbols and two data streams. In this configuration, solving the detection problem is equivalent to find two symbols in the set Φ=s1s2s3s4 that minimize the objective function. This process can be seen as finding the path in the tree that leads to the best objective function. The first tree level corresponds to the first symbol and so on for each level.
Figure 4.
Tree view of the detection problem: Example for Φ=s1s2s3s4 and two data streams.
In this paradigm, the exhaustive search detector described in Section 3 computes the objective function for each leaf node and then selects the best path. Tree-search-based detectors search for the best leaf without trying every path. This leads to three enumeration paradigms: depth-first, breadth-first, and best-first. These paradigms will be detailed after the description of the preprocessing used by all the variants.
6.1 Preprocessing using QR decomposition
All tree-search-based detectors use the same preprocessing. Let be H=QR the QR decomposition of the channel matrix with Q a unitary matrix and R an upper triangular one. The decomposition is computed only once per coherence block leading to a negligible overhead of the complexity per received symbol. Using the QR decomposition, we have
∥y−Hx∥=∥y−QRx∥=∥QHy−QHQRx∥E9
as unitary matrices act as isometries. Thus, by exploiting the property of unitary matrices QH=Q−1, this norm can be rewritten as
∥y−Hx∥=∥y˜−Rx∥E10
with y˜≜QHy. Computing y˜ is the only overhead in complexity that is required on a symbol basis as it cannot be preprocessed for the whole coherence block.
The point of this QR preprocessing is that the triangularity of R allows to compute the objective function iteratively. Indeed, we can introduce for all k∈1…N,dk≜y˜k−Rxk with Rxk being the kth coefficient of the product Rx. Given this definition, the objective function is written as
∥y˜−Rx∥2=∑k=1ndk2.E11
Moreover, the triangularity of R gives
∀k∈1…N,Rxk=∑j=1nRkjxj=∑j=knRkjxjE12
that leads to
∀k∈1…N,dk=y˜k−∑j=knRkjxj.E13
With this expression, it is clear that we can compute partial estimations of the objective function and dk coefficients while the symbol vector is built. Indeed, starting from the last component, Eq. (13) is fully evaluated for the jth position as soon as a hypothesis is made on xj. Thus, it is possible to add a new operand in Eq. (11) and to have an idea of how promising the partial symbol vector is. The partial objective function from Eq. (11) is traditionally called the partial Euclidean distance (PED).
The depth-first paradigm is the oldest one, and it is commonly known in the communication field as the sphere decoding (SD). SD is the transposition of the mathematical Fincke-Pohst algorithm in the telecommunication field [16]. The basic principle of this algorithm is to define an upper-bound for the objective function named the radius r2 and then to use it to prune paths as early as possible. Reintroducing x0 from Eq. (3), the upper-bound constraint gives
∥y−Hx∥2=∥Hx0−x∥≤r2.E14
This inequality highlights that constraining the objective function may be interpreted as looking for solution no so far from x0. As stated in Eq. (4), the only deviation from x0 is due to the noise so that the choice of r must be adapted to the SNR. Thus, if the SNR is high, the radius can be small, while in the contrary scenario, the radius should be increased so that there is at least one vector x satisfying the constraint from Eq. (14).
In the remainder of this section, we assume that r2 is adequately chosen and that there is at least a solution. As stated in Section 6.1, the QR decomposition allows us to compute a PED at each level. As the PED is a sum of squares, it can only increase during the decoding process. Thus, if at some point, a PED violates the constraint from Eq. (14), then all the vectors build upon this partial solution are bound to be infeasible. From a tree-search perspective, this means that if a node already breaks the constraint, all its children will do the same. Thus, all paths starting from this node can be pruned without performance loss.
The SD is referred to as a depth-first detector as starting from the root node, it goes as depth as possible until it reaches a leaf or violates Eq. (14). If a leaf is reached, it is compared to the best leaf so far and saved if it is the new best leaf. If Eq. (14) is violated, the SD algorithm backtracks and explores a new path. When all paths are either completed or pruned, the result is the best leaf reached.
The Schnorr-Euchner (SE) enumeration is another depth-first enumeration known to perform better by using a lattice reduction method [17, 18]. The basic idea is to explore the node’s children by the increasing order of their PED. This is particularly useful when using the radius reduction technique that sets an infinite r2 at the beginning and then updates it to the best objective function for a leaf encounter so far.
The SD algorithm and its SE version are optimal as they ensure to find the exact solution of the detection problem. Indeed, the best leaf is obviously the best leaf among all the completed paths, and the pruned paths cannot lead to a better point due to their already worst PED. The NP-hardness argument detailed in Section 3 implies that SD has a non-polynomial worst-case complexity. Moreover, SD expected complexity is also non-polynomial even if the exponential growth is slow enough to compete with polynomial detectors under certain circumstances [19].
A very efficient soft-input soft-output depth-first algorithm is the single tree-search sphere decoding (STS-SD) [20]. To produce its soft-output, it uses the max-log approximation [10, 13, 14] and makes some changes on the pruning criterion. The max-log approximation avoids the computation of the exact LLRs by claiming that
Li≈12σ2minx∈χi0∥y−Hx∥2−minx∈χi1∥y−Hx∥2E15
where χik=x∈ΦN:bi=k is the set of all symbols with the ith bit set to k. Thus, to compute the max-log approximation, one must know the objective function of the best leaf (i.e., one of the minimum in Eq. (15)) but also the objective function of each best counter-hypotheses (the other minimum). A path should then be pruned only if its PED is greater than the current radius r2 and if this path cannot lead to a better counter-hypothesis. This can be implemented by adding another radius called the hypothetical radius constraint.
One of the most advanced ASIC-implemented depth-first reported so far uses a two-dimensional Schnorr-Euchner enumeration. This implementation reaches a throughput higher than 600 Mb/s for the soft-output version and exceeds 1.2 Gb/s for the hard-output one while keeping an excellent energy efficiency [21]. The high throughput is achieved by using several SD cores in parallel to decode several vectors simultaneously.
6.3 Breadth-first tree-search detectors: K-best and M-algorithm
Breadth-first detectors drop out of optimality for better implementability. Indeed, they address the two main issues of the depth-first paradigm: the unpredictable complexity that depends on the SNR through r2 and the depth-and-backtrack enumeration that prevents the use of hardware pipelines. Breadth-first detectors achieve this goal by removing the pruning criterion and always keep the same number of paths instead. At each level, the detector compares all the current paths’ PED and keeps only the best ones. This number is traditionally called K for the K-best algorithm [22] or M for the M-algorithm [23]. A recent work mixed this approach with the upper-bound radius from death-first to prune even more path per level and reduce the complexity further [24]. This method converges to the breadth-first if all PED are always under the upper-bound, but if some PEDs overgrow, it can reduce the number of surviving paths.
The restricted number of surviving paths induces that the right one can be pruned early if its PED has grown too quickly in the early levels. This is the reason for the optimality loss. Then, some detectors implement a post-detection SNR criterion to reorder the tree levels such that the most certain one is at the top. Thus, the right path is less likely to be pruned by mistake in the early stages. Thanks to this reordering, the K-best algorithm performs very well yet, not optimally in a mathematical sense.
From a hardware implementation perspective, breadth-first tree-search detectors are very efficient. They do not require any backtrack so that an expanded node can be safely deleted as it will never be revisited. Moreover, the number of visited nodes per level is fixed. Thus, ASIC can embed the exact amount of resources required. These two characteristics allow the construction of efficient hardware pipelines that substantially increase the throughput. K-best can achieve at least the same throughput as depth-first without the need for parallel cores. Hard-output implementations exceeding 2.5 Gb/s are reported using the breadth-first paradigm [25]. Another study focused on energy efficiency designed a breadth-first variant that can handle both the channel noise and the hardware noise generated by the voltage over the scaling method in memories [26].
Breadth-first detectors can provide soft-output using the max-log approximation and a list. This list approach is used by several detectors, including some other tree-search algorithm and detectors from other families. The point of this approach is to produce a list Γ of point associated with their objective function and to approximate Eq. (15) as
Li≈12σ2minx∈Γ∩χi0∥y−Hx∥2−minx∈Γ∩χi1∥y−Hx∥2.E16
For most breadth-first algorithms, Γ is the list of all completed paths [22, 25].
6.4 Best-first tree-search detector: fast descent tree-search and parallel tree-search
Best-first detectors are also sometimes called metric-first. The basic idea besides this enumeration is to not favor depth or breadth over each other. Instead, the node with the best PED is expanded, regardless of its level. The best-first algorithm keeps a node pool with nodes to be expanded. First, the pool is initialized with the root node. Then, at each iteration, the node with the lower PED is popped out from the pool, and all its children are computed and pushed in the pool unless they are leaves. If they are, a comparison with the best leaf so far allows us to keep track of the best result. When a leaf is reached, its objective function may be used as an upper-bound to prune the pool for each node with a PED higher than the new reference. The detection ends when the pool is empty.
This simple method quickly overfills the pool as several nodes are added when only one is popped out. Rather than providing a huge pool to contain all the nodes, improvement is to convert the φ-ary tree (with φ the constellation size) to a first-child next-sibling binary tree [27]. This method is called the modified best-first algorithm (MBF). With this variant, the only nodes added in the pool after an expansion are the best child and the best yet-to-visit siblings. Then, the growth rate of the pool size is controlled. However, this method struggles to provide a full path solution quickly as the popped out node is the one with the lower PED that is often close to the root. To solve this issue, a variant implementation called MBF fast descent (MBF-FD) changes the expansion rule. When a node is expanded, the process goes through the best child until reaching a leaf, pushing in all best siblings along the way [28].
Recently, a best-first algorithm ASIC is reported to reach 800 Mb/s in a soft-input soft-output framework [29]. The modified algorithm, called cross-level parallel tree-search, splits the pool node into several pools, one per level. At each iteration, a node from each pool in popped out expanded using the best-child/best-sibling framework, and the new nodes are pushed in the according pool. Moreover, the presented detector prune nodes in each pool using the upper-bound to keep only the one that can improve the result or the counter-hypothesis (see Section 6.2 for details). The slit pool helps the parallelization process so that this algorithm variant is very suitable for hardware implementation.
7. Other unusual detectors: bioinspired and geometrical detectors
7.1 Deep neural MIMO detection: learning to detect
The rise of deep learning leads to the search for an efficient neural network to solve the detection problem such as DetNet [30]. This network is inspired by the projected gradient descent algorithm that is a major option to solve convex optimization. It is trained for both static channel (H is fixed) and on a time-varying channel (the same condition as previously). As the errors are sometimes unavoidable due to a bad channel realization, the loss function should not be the objective function. Thus, the DetNet designers opt for a
∑k=1Llogk∥x−xk∥∥x−xZF∥E17
with xZF the result of ZF detection and xk the detected symbol of the kth layer. Then, the normalization with the ZF result avoids over-penalizing the situation with bad H realization. Moreover, the logarithm weights the result from each layer to give more credit to the final ones.
7.2 Bioinspired detectors
The most studied bioinspired decoders fall into two categories: ant colony optimizations (ACO) and particle swarm optimizations (PSO) that include the firefly algorithm (FA). These techniques are often very complex compared to the previously described algorithms, but they claim to be resilient to challenging conditions. Bioinspired algorithms should be able to decode messages with imperfect CSI, or the data streams are correlated.
ACO-based detectors simulate several ants that choose a path randomly to follow with a nonuniform probability function [31]. Each antenna is processed independently. At each iteration, an ant selects the symbol s∈Φ with the probability
ps=τsαηsβ∑s∈ΦτsαηsβE18
with τs the pheromone level on the path, ηs an image of the objective function, most of the time through a log-sigmoid function, and αβ the two parameters that balance the relative importance of each term. After each iteration, the pheromone level is updated according to the following principle: the better the objective function the ant achieves, the more pheromone it dropped off. Thus, the ant selects more often the path that seems more promising regarding the objective function and the previous runs while preserving some chance of exploring a new path.
FA-based detectors simulate several fireflies that try to find the best mating partner. The objective function determines the attractiveness of a firefly. Then a firefly goes toward more attractive congeners biased with a random influence to promote exploration [32]. Some FA variant implements a memory effect that makes it even closer to a PSO-based algorithm [33]. This framework is applied to MIMO detection using the QR decomposition described in Section 6.1. The FA represents each symbol to decode as a nest containing as many fireflies as the constellation size. Thus, the fireflies have to select a partner in each nest from the last symbol to the first based on the biased attractiveness. When the firefly population searched all the nests, the best path represents the decoded symbol vector. FA-based detectors can be related to tree-search-based algorithm with a randomness exploration and a fixed number of path allowed.
7.3 Geometrical detectors
Geometrical detectors are based on a two-step process: an exploration to find a small set of promising solutions and an exploitation to improve this set at a small cost. It follows the traditional approach in nonconvex optimization to perform simple descents that can be stuck in local optimums from several starting points. Geometrical detectors use a real-valued model and the singular value decomposition (SVD) rather than the QR one [34]. Let us rewrite the objective function by introducing the SVD of H=UDVT with U and V two orthogonal matrices and D the diagonal matrix containing the singular values λi:1≤i≤n in ascending order.
Consequently, the objective function can be rewritten as
∥y−Hx∥2=VTx−x0TDUTUDVTx−x0E19
using x0 from Eq. (3). As the vectors of V, named vi:1≤i≤n, constitute a basis, we can define αi:1≤i≤n the coordinates of x−x0 on this basis. Using the orthogonality of U and V and the diagonality of D, Eq. (19) leads to
∥y−Hx∥2=∑i=1nαi2λi2.E20
Let Δi be the straight line passing through x0 and directed by vi. One can note that Eq. (20) highlights that the objective function grows more slowly along the first Δi rather than along the last ones so that promising points must be around these first straight lines. Then the solution is most likely to be found along this line. The geometrical exploration step is then performed, selecting some points near the first Δi. Then a straightforward descent algorithm is performed by looking for the best point in the close neighborhood until convergence.
A soft-output version of this algorithm is possible using the max-log approximation and the list approach detailed in [35], Section 5.2. A field-programmable gate array (FPGA) implementation has recently been proposed. This groundwork points out that geometrical detectors may achieve good performance in the future yet being far from mature at that point [36].
8. Conclusions and summary
MIMO detection is a well-studied problem that has been tackled from several perspectives. The mathematical interpretation, as a combinatorial optimization problem, leads to the optimal and linear detectors. From the signal processing perspective, detecting a signal means improving the SNR or SINR so that the direct answer is to cancel the interference and to remove the noise. From an algorithmic perspective, the detection problem is the search for the best path in a weighted tree that relies on some well-known algorithms. Other sources of inspiration, such as nature or geometry, provide some interesting perspectives. These paradigms and the associated detectors are summed up in Table 1, and we compare all of them according to the BER-complexity trade-off.
Detector
BER
Complexity
Comment
ML
Optimal
Dramatically complex
ZF
Very poor
Very simple
Best linear detector regarding SNR criterion
MMSE
Poor
Simple
Best linear detector regarding SINR criterion
SIC/OSIC
Good
Rather complex
Best when there is a clear ranking in the quality of each data stream
PIC
Good
Rather complex
Best when all data streams have the same quality level
Depth-first
Optimal
Very complex
Breadth-first
Good
Rather complex
Possible trade-off between BER and complexity via the number of surviving paths
Best-first
Good
Less complex
Deep neural
Good
Rather complex
Possible trade-off between BER and complexity via the number of layers
Bioinspired
Good
Very complex
Resilient to imperfect CSI and channel correlation
Geometrical
Rather good
Rather complex
Possible trade-off between BER and complexity via the number of descents
Table 1.
Summary of all detectors described in this chapter.
All these perspectives shed a different light on the problem, leading to fruitful experimentation. Indeed, some methods take inspiration from others to keep on improving. Therefore, some improvement axes remain open, for instance, the permanent decrease of complexity with equal performance, the development for efficient hardware implementations, or the optimization of the interaction with decoders to exploit channel codings better.
Conflict of interest
The authors declare no conflict of interest but to research and publish in this area, in particular on geometrical detectors.
Nomenclature
Memoryless
the channel outputs only depend on its state and its inputs.
Linear
Flat
Block fading
the channel states vary slow enough to be considered constant over many symbols named coherence block.
ACO
ASIC
application-specific integrated circuit
CDMA
code-division multiple access
CLPS
closest lattice-point search
CSI
channel state information
FA
firefly algorithm
FPGA
field-programmable gate array
LLR
log-likelihood ratio
MBF
modified best-first
MBF-FD
modified best-first fast descent
ML
maximum likelihood
MMSE
minimum mean-square error
OSIC
ordered successive interference cancelation
PED
partial Euclidean distance
PIC
parallel interference cancelation
PSO
particle swarm optimization
QAM
quadrature amplitude modulation
SD
sphere decoding
SE
Schnorr-Euchner
SDM
space-division multiplexing
SIC
successive interference cancelation
SIR
signal-to-interference ratio
SINR
signal-to-noise-plus-interference ratio
SNR
signal-to-noise ratio
SVD
singular value decomposition
ZF
zero forcing
\n',keywords:"MIMO systems, MIMO detectors, space-division multiplexing, SDM-MIMO, linear detection, interference cancelation, tree-search",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/72718.pdf",chapterXML:"https://mts.intechopen.com/source/xml/72718.xml",downloadPdfUrl:"/chapter/pdf-download/72718",previewPdfUrl:"/chapter/pdf-preview/72718",totalDownloads:242,totalViews:0,totalCrossrefCites:1,dateSubmitted:"February 28th 2020",dateReviewed:"June 1st 2020",datePrePublished:"July 3rd 2020",datePublished:"September 23rd 2020",dateFinished:null,readingETA:"0",abstract:"Multiple-input multiple-output (MIMO) systems entered most major standards in the past decades, including IEEE 802.11n (Wi-Fi) and long-term evolution (LTE). Moreover, MIMO techniques will be used for 5G by increasing the number of antennas at the base station end. MIMO systems enable spatial multiplexing, which has the potential of increasing the capacity of the communication channel linearly with the minimum of the number of antennas installed at both sides without sacrificing any additional bandwidth or power. To handle the space-division multiplexing (SDM), receivers have to implement new algorithms to exploit the spatial information in order to distinguish the transmitted data streams. This chapter provides an overview of the most well-known and promising MIMO detectors, as well as some unusual-yet-interesting ones. We focus on the description of the different paradigms to highlight the different approaches that have been studied. For each paradigm, we describe the mathematical framework and give the underlying philosophy. When hardware implementations are available in the literature, we provide the results reported and give the according references.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/72718",risUrl:"/chapter/ris/72718",signatures:"Bastien Trotobas, Amor Nafkha and Yves Louët",book:{id:"9882",title:"Advanced Radio Frequency Antennas for Modern Communication and Medical Systems",subtitle:null,fullTitle:"Advanced Radio Frequency Antennas for Modern Communication and Medical Systems",slug:"advanced-radio-frequency-antennas-for-modern-communication-and-medical-systems",publishedDate:"September 23rd 2020",bookSignature:"Albert Sabban",coverURL:"https://cdn.intechopen.com/books/images_new/9882.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"16889",title:"Dr.",name:"Albert",middleName:null,surname:"Sabban",slug:"albert-sabban",fullName:"Albert Sabban"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"30907",title:"Dr.",name:"Amor",middleName:null,surname:"Nafkha",fullName:"Amor Nafkha",slug:"amor-nafkha",email:"amor.nafkha@supelec.fr",position:null,institution:{name:"Supélec",institutionURL:null,country:{name:"France"}}},{id:"319464",title:"Dr.",name:"Bastien",middleName:null,surname:"Trotobas",fullName:"Bastien Trotobas",slug:"bastien-trotobas",email:"bastien.trotobas@centralesupelec.fr",position:null,institution:{name:"CentraleSupélec",institutionURL:null,country:{name:"France"}}},{id:"319465",title:"Prof.",name:"Yves",middleName:null,surname:"Louet",fullName:"Yves Louet",slug:"yves-louet",email:"Yves.louet@centralesupelec.fr",position:null,institution:{name:"CentraleSupélec",institutionURL:null,country:{name:"France"}}}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Introduction to MIMO detection algorithms",level:"1"},{id:"sec_3",title:"3. Maximum likelihood detector",level:"1"},{id:"sec_4",title:"4. Linear detectors",level:"1"},{id:"sec_4_2",title:"4.1 Zero forcing (ZF) detector",level:"2"},{id:"sec_5_2",title:"4.2 Minimum mean-square error (MMSE) detector",level:"2"},{id:"sec_7",title:"5. Interference cancellation detectors",level:"1"},{id:"sec_7_2",title:"5.1 Successive interference cancellation (SIC) detector",level:"2"},{id:"sec_8_2",title:"5.2 Parallel interference cancellation (PIC) detector",level:"2"},{id:"sec_9_2",title:"5.3 Selecting between SIC and PIC detectors",level:"2"},{id:"sec_11",title:"6. Tree-search-based detectors",level:"1"},{id:"sec_11_2",title:"6.1 Preprocessing using QR decomposition",level:"2"},{id:"sec_12_2",title:"6.2 Depth-first tree-search detection: sphere decoding",level:"2"},{id:"sec_13_2",title:"6.3 Breadth-first tree-search detectors: K-best and M-algorithm",level:"2"},{id:"sec_14_2",title:"6.4 Best-first tree-search detector: fast descent tree-search and parallel tree-search",level:"2"},{id:"sec_16",title:"7. Other unusual detectors: bioinspired and geometrical detectors",level:"1"},{id:"sec_16_2",title:"7.1 Deep neural MIMO detection: learning to detect",level:"2"},{id:"sec_17_2",title:"7.2 Bioinspired detectors",level:"2"},{id:"sec_18_2",title:"7.3 Geometrical detectors",level:"2"},{id:"sec_20",title:"8. Conclusions and summary",level:"1"},{id:"sec_24",title:"Conflict of interest",level:"1"},{id:"sec_23",title:"Nomenclature",level:"1"}],chapterReferences:[{id:"B1",body:'Yang S, Hanzo L. Fifty years of MIMO detection: The road to large-scale MIMOs. 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Improved methods for calculating vectors of short length in a lattice, including a complexity analysis. Mathematics of Computation. 1985;44(170):463-471'},{id:"B17",body:'Schnorr CP, Euchner M. Lattice basis reduction: Improved practical algorithms and solving subset sum problems. Mathematical Programming. 1994;66(1–3):181-199'},{id:"B18",body:'Agrell E, Eriksson T, Vardy A, Zeger K. Closest point search in lattices. IEEE Transactions on Information Theory. 2002;48(8):2201-2214'},{id:"B19",body:'Jalden J, Ottersten B. On the complexity of sphere decoding in digital communications. IEEE Transactions on Signal Processing. 2005;53(4):1474-1484'},{id:"B20",body:'Studer C, Bolcskei H. Soft–input soft–output single tree-search sphere decoding. IEEE Transactions on Information Theory. 2010;56(10):4827-4842'},{id:"B21",body:'Chuang PIJ, Sachdev M, Gaudet VC. VLSI implementation of high-throughput, low-energy, configurable MIMO detector. 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