Multi User MIMO Communication: Basic Aspects, Benefits and Challenges

The explosive growth of Multiple Input Multiple Output (MIMO) systems has permitted for high data rate and a wide variety of applications. Some of the technologies which rely on these systems are IEEE 802.11, Third Generation (3G) and Long Term Evolution (LTE) ones. Recent advances in wireless communication systems have contributed to the design of multi-user scenarios with MIMO communication. These communication systems are referred as multi-user MIMOs. Such systems are intended for the development of new generations of wireless mobile radio systems for future cellular radio standards. This chapter provides an insight into multi-user MIMO systems. We firstly present some of the main aspects of the MIMO communication. We introduce the basic concepts of MIMO communication as well as MIMO channel modeling. Thereafter, we evaluate the MIMO system performances. Then, we concentrate our analysis on the multi-user MIMO systems and we provide the reader a conceptual understanding with the multi-user MIMO technology. To do so, we present the communication system model for such emerging technology and we give some examples which describe the recent advances for multi-user MIMO systems. Finally, we introduce linear precoding techniques which could be exploited in multi-user MIMO systems in order to suppress inter-user interference.


Introduction
The explosive growth of Multiple Input Multiple Output (MIMO) systems has permitted for high data rate and a wide variety of applications. Some of the technologies which rely on these systems are IEEE 802.11, Third Generation (3G) and Long Term Evolution (LTE) ones. Recent advances in wireless communication systems have contributed to the design of multi-user scenarios with MIMO communication. These communication systems are referred as multi-user MIMOs. Such systems are intended for the development of new generations of wireless mobile radio systems for future cellular radio standards. This chapter provides an insight into multi-user MIMO systems. We firstly present some of the main aspects of the MIMO communication. We introduce the basic concepts of MIMO communication as well as MIMO channel modeling. Thereafter, we evaluate the MIMO system performances. Then, we concentrate our analysis on the multi-user MIMO systems and we provide the reader a conceptual understanding with the multi-user MIMO technology. To do so, we present the communication system model for such emerging technology and we give some examples which describe the recent advances for multi-user MIMO systems. Finally, we introduce linear precoding techniques which could be exploited in multi-user MIMO systems in order to suppress inter-user interference.

An historical overview
The main historical events which make the MIMO systems [2] [3] are summarized as follows: • In 1984, Jack Winters at Bell Laboratories wrote a patent on wireless communications using multiple antennas. Jack Winters in [4] presented a study of the fundamental limits on the data rate of multiple antenna systems in a Rayleigh fading environment.
• In 1993, Arogyaswami Paulraj and Thomas Kailath proposed the concept of spatial multiplexing using MIMO.
• Several articles which focused on MIMO concept were published in the period from 1986 to 1995 [5]. This was followed by the work of Greg Raleigh and Gerard Joseph Foschini in 1996 which invented new approaches involving space time coding techniques. These approaches were proved to increase the spectral efficiency of MIMO systems.
• In 1999, Thomas L. Marzetta and Bertrand M. Hochwald published an article [6] which provides a rigorous study on the MIMO Rayleigh fading link taking into consideration information theory aspects.
• The first commercial MIMO

Fundamentals of MIMO system
MIMO system model is depicted in Figure 1. We present a communication system with N T transmit antennas and N R receive antennas. Antennas Tx 1 , . . . , Tx N T respectively send signals x 1 , . . . , x N T to receive antennas Rx 1 , . . . , Rx N R . Each receive antenna combines the incoming signals which coherently add up. The received signals at antennas Rx 1 , , . . . , Rx N R are respectively denoted by y 1 , . . . , y N R . We express the received signal at antenna Tx q ; q = 1, . . . , N R as: The flat fading MIMO channel model is described by the input-output relationship as: • H is the (N R × N T ) complex channel matrix given by: . . , N R is the complex channel gain which links transmit antenna Tx p to receive antenna Rx q .
The continuous time delay MIMO channel model of the (N R × N T ) MIMO channel H associated with time delay τ and noise signal b(t) is expressed as: • y(t) is the spatio-temporel output signal.

MIMO channel modeling
Several MIMO channel models [7] have been proposed in literature. These models mainly fall into two categories as depicted in Figure 2. • Geometry-based Stochastic Channel Models (GSCMs) have an immediate relation with the physical characteristics of the propagation channel. These models suppose that clusters of scatterers are distributed around the transmitter and the receiver. The scatterers locations are defined according to a random fashion that follows a particular probability distribution. Scatterers result in discrete channel paths and can involve statistical characterizations of several propagation parameters such as delay spread, angular spread, spatial correlation and cross polarization discrimination. We distinguish two possible schemes which are the Double Bounce Geometry-based Stochastic Channel Models (DB-GSCMs) and the Single Bounce Geometry-based Stochastic Channel Models (SB-GSCMs). That is when a single bounce of scatterers is placed around the transmit antennas or receive antennas.

Analytical models
The second class of MIMO channel models includes analytical models which are based on the statistical properties obtained through measurement (Distribution of Direction of Departure  1. When no Channel State Information (CSI) is available at the transmitter, the power is equally split between the N T transmit antennas, the instantaneous channel capacity is then given by: γ denotes the Signal to Noise Ratio (SNR).
2. When CSI is available at the receiver, Singular Value Decomposition (SVD) is used to derive the MIMO channel capacity which is given by: is the rank of the channel matrix H 3. When CSI is available at both the transmitter and the receiver, the channel capacity is computed by performing the water-filling algorithm. The instantaneous channel capacity is then: • a + = max(a, 0) • λ H,p is the p − th singular value of the channel matrix H • µ is a constant scalar which satisfies the total power constraint We consider the case where CSI is available at the receiver, the simulated ergodic MIMO capacity is depicted in Figure 3. For a MIMO system with two transmit antennas, numerical results show that ergodic capacity linearly increases with the number of antennas. Plotted curves are presented for different levels of the SNR. The use of additional antennas improves the performances of the communication system. Moreover, MIMO system takes advantage of multipath propagation. The performances of MIMO system are observed in the following in terms of the Bit Error Rate (BER). We consider a MIMO system with various receive antennas, the BER is evaluated for communication systems with Rayleigh fading MIMO channel and additive gaussian noise. At the receive side, the Maximum Ratio Combining (MRC) technique is performed. According to Figure 4, it is obvious that MIMO technology allows for a significant improvement of the BER. Once the MIMO technology is presented, we introduce in the following multi-user MIMO systems.

Multi-user MIMO system
The growth in MIMO technology has led to the emergence of new communication systems. We are particularly interested in this chapter in multi-user MIMO (MU-MIMO) ones [11]. MU-MIMO [12] system is often considered in literature as an extension of Space-Division Multiple Access (SDMA). This technology supports multiple connections on a single conventional channel where different users are identified by spatial signatures. SDMA uses spatial multiplexing and enables for higher data rate. This could be achieved by using multiple paths as different channels for carrying data. Another benefit of using the SDMA technique in cellular networks is to mitigate the effect of interference coming from adjacent cells.   Table 1 summarizes the main features of both SU-MIMO and MU-MIMO systems [13]. In contrast to MU-MIMO systems where one base station could communicate with multiple users, base station only communicate with a single user in the case of SU-MIMO systems. In addition, MU-MIMO systems are intended to employ multiple receivers so that to improve the rate of communication while keeping the same level of reliability. These systems are able to achieve the overall multiplexing gain obtained as the minimum value between the number of antennas at base stations and the number of antennas at users. The fact that multiple users could simultaneously communicate over the same spectrum improves the system performance. Nevertheless, MU-MIMO networks are exposed to strong co-channel interference which is not the case for SU-MIMO ones. In order to solve the problem of interference in MU-MIMO systems, several approaches have been proposed for interference management [14] [15]. Some of these approaches are based on beamforming technique [31]. Moreover, in contrast to SU-MIMO systems, MU-MIMO systems require perfect CSI in   order to achieve high throughput and to improve the multiplexing gain [16]. Finally, the performances of MU-MIMO and SU-MIMO systems in terms of throughput depend on the SNR level. In fact, at low SNRs, SU-MIMO performs better. However, at high SNRs level, MU-MIMO provides better performances.  users transmit signals to the base station. However, in the case of downlink communication, base station transmits signals to users. A representation of these systems is depicted in Figure  6. We assume that the base station is equipped with N antennas. Case of DL-MU-MIMO, the base station attempts to transmit signals to K users U 1 ,. . . ,U K which are respectively equipped with antennas of numbers M 1 , . . . , M K . For notations, if antenna k acts like a receiving antenna, it is denoted by Rx k . Otherwise, it is denoted by Tx k .

UL-MU-MIMO
Let X k (M k × 1), the transmit signal vector of user U k ; k = 1, . . . , K. We assume that data streams associated to user U k ; k = 1, . . . , K are zero mean white random vectors where : E{X k X k * } = I M k ; k = 1, . . . , K E denotes the expected value operator. The complex channel matrix relating user U k ; k = 1, . . . , K to the base station, H k is of dimension (N × M k ). In presence of additive noise signal b(N × 1), the received signal vector at the base station, y(N × 1) is expressed in the slow fading model by: The noise signal vector is a zero mean white Gaussian variable with variance σ 2 b . The uplink scenario should satisfy two constraints: • It should be as many receive antennas at the base station as the total number of users antennas.
• Each user should have as many transmit antennas as the number of data streams.
In Figure 7, the block diagram for the UL-MU-MIMO includes a joint linear precoder and decoder. Linear precoders associated to users U 1 , . . . , U K will be respectively denoted by An estimate of the transmitted signal vectors denoted by Y k ; k = 1, . . . , K are obtained by using the linear decoders G 1 , . . . , G K . The decoding process is such that :

DL-MU-MIMO
DL-MU-MIMO communication model assumes that K users are simultaneously receiving signals from the base station. The transmitted signal vector x(N × 1) is expressed as the sum of signals intended to users U 1 , . . . , U K : The channel matrix between user U k ; k = 1, . . . , K and the base station is denoted by H k (M k × N). At each user, received signal vector of dimension (M k × 1); k = 1, . . . , K is given by: B k ; k = 1, . . . , K is an additive noise signal vector of size (M k × 1). Equation (11) could be also written: The second term of the sum in equation (13) represents the interference signal coming from multiple users. Processing techniques such as beamforming should be introduced in the block diagram of the MU-MIMO system for mitigating the effect of users interference and improving the performances of the communication system.

Fields of application
MU-MIMO technology finds its applications in many areas and is nowadays exploited in many evolving technologies wich are described in the following.

3GPP LTE: 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) is one of the next generation cellular networks which exploit the MU-MIMO technology.
Thanks to this technology, available radio spectrum 3GPP LTE networks could achieve higher spectral efficiencies than existing 3G networks [18] [19].

Capacity region of multi-user MIMO system
There is no closed form for the channel capacity of multi-user MIMO systems. For this purpose, the performances of such systems will be analyzed in terms of the capacity region. This metric [23] could be defined in the usual Shannon sense as the highest rates that can be achieved with arbitrarily small error probability. Firstly, the capacity [24] needs to be evaluated for each user. Then, the capacity region is determined as the entire region for which maximum achievable rates are reached. The evaluation of the capacity region is strongly related to some constraints and should be determined according to the performed communication scenario. We address the following scenarios :

Capacity region of UL-MU-MIMO with single antenna users
We consider the UL-MU-MIMO with N multiple antenna BS and K single antenna users. The performed communication scheme is depicted in Figure 9. The equivalent MIMO channel for the presented communication model is given by: H k (N × 1); k = 1, . . . , K represents the Single Input Multiple Output (SIMO) channel between user U k ; k = 1, . . . , K and the BS. Case of two users (i.e. K=2), the capacity region is defined as the set of rates (R 1 , R 2 ) associated to users U 1 and U 2 . We consider the notations: • P 1 : average power constraint on user U 1 • P 2 : average power constraint on user U 2 • N 0 : noise signal power The capacity region [25] is evaluated by determining the individual rate constraint for each user. Assuming that user U 1 has the entire channel, an upper bound of the maximum achievable rate is given by : · indicates the Frobenius norm. Similarly, an upper bound for the maximum achievable rate for user U 2 is: Finally, the sum rate constraint which is obtained when both users are acting as two transmit antennas of a single user has an upper bound expressed as : The capacity region for the UL-MU-MIMO is presented in Figure 10 where two users with single antennas are considered.

Figure 10. Capacity region of UL-MU-MIMO for two single antenna users
Case of K users, the capacity region is determined as a function of several constraints and K! corner points are determined for evaluating the boundary of the capacity region. For rates R 1 , . . . , R K respectively associated to users U 1 , . . . , U K , the sum rate is determined for an optimal receiver [25] as:

Capacity region of UL-MU-MIMO with multiple antenna users
The capacity region could be obtained for the generalized case where the base station has N antennas and user U k ; k = 1, . . . , K is equipped with multiple antennas of number M k > 1. An upper bound of the maximum achievable rate for user U k is given by : • H k (N × M k ) links the N antenna base station to the M k antenna user; k = 1, . . . , K.
• D k (M k × M k ) is a diagonal matrix formed by the power allocated at transmit antennas at user U k .
The sum rate constraint of UL-MU-MIMO with multiple antennas users is expressed as :

DL-MU-MIMO with multiple antenna users and single antenna BS
In the case of downlink scenario, the upper bounds of the users rates are analogously determined as the uplink scenario. Nevertheless, the effect of interference could not be neglected. In fact, for the scenario with two multiple antenna users U 1 and U 2 and one antenna base station, the upper bounds of the rates achievable by users U 1 and U 2 become: and Here, the signal of user U 2 is considered as interference for user U 1 .

Precoding techniques
The DL-MU-MIMO system uses precoding techniques which are usually linear.

Zero Forcing and Block Diagonalization methods
Popular low-complexity techniques include both Zero Forcing (ZF) and Block Diagonalization (BD) [27][28] methods. Algorithms for the ZF as well as BD methods are presented in [29]. The aim of these solutions is to improve the sum rate capacity of the communication system under a given power constraint. These performances could be achieved by canceling inter-user interference. Zero Forcing Dirty Paper Coding (DPC) [30] represents a famous technique for data precoding where the channel is subject to interference which is assumed to be known at the transmitter. The precoding matrix is equal to the conjugate transpose of the upper triangular matrix obtained via the QR decomposition of the channel matrix.

MU-MIMO with Block Diagonalization precoding
We consider a communication system model with a broadcast MIMO channel where the transmitter is a base station equipped with N antennas and the receiver consists of K users U k ; k = 1 . . . K (See figure 6(b)). The received signal at user U k ; k = 1 . . . K with dimension (M k × 1) is expressed as : • H k (M k × N) is the channel matrix between user U k and the base station

is the additive noise signal vector
We assume in the following that users U 1 , . . . U K have the same number of antennas which will be denoted by M. Block Diagonalization strategy defines a set of precoding matrices V BD (k) (N × M) associated to users U 1 , . . . , U K . These matrices form an orthonormal basis such that: and the Block Diagonalization algorithm achieves : The aim of these conditions is to eliminate multi-user interference so that to maximize the achievable throughput. The performance of downlink communication scenarios with precoding techniques depends on the SNR level. In fact, it has been shown in [27] that SU-MIMO achieves better performances than MU-MIMO at low SNRs. However, the BD MU-MIMO achieves better performances at high SNRs. As such, switching between SU-MIMO and MU-MIMO is optimal for obtaining better total rates over users.

MU-MIMO with Zero Forcing precoding
Case of Zero Forcing strategy, each transmitted symbol to the l − th antenna (among M antennas of user U k ) is precoded by a vector which is orthogonal to the columns of H j , j = k but not orthogonal to the l − th column of H k [26].

Beamforming for linear precoding
Beamforming paradigms represent another class of linear precoding for MU-MIMO systems. For the communication model with beamforming (Figure 12), we consider a MU-MIMO system with K multiple antenna users U 1 , . . . , U K at the receive side which are respectively equipped with M 1 , . . . , M K antennas. At the transmit side, a multiple antenna base station with N antennas transmits data signals x 1 , . . . , x K to users U 1 , . . . , U K .

Vt BF Vr
Transmit side Receive side The received signal vector at user U k ; k = 1, . . . , K is expressed as : where: • H k (M k × N) is the complex channel matrix between receiver U k and the transmit base station.
• B k (M k × 1) is an additive noise signal vector.
• Vt BF (k) (N × 1) is the transmit beamforming vector of index k. The transmit beamforming matrix is : At the receive side, beamforming vectors are denoted by Vr The resulting signal at user U k is: The conjoint receive-transmit beamforming weights are obtained by maximizing the sum rate of the MU-MIMO system expressed as: SI NR (k) ; k = 1, . . . , K is the Single Interference Noise Ratio (SINR) [31] associated to user U k . The SINR is determined as the ratio of the received strength for the desired signal to the strength of undesired signal obtained as the sum of noise and interference signal. For unit signal noise variance, the SINR for user U k is given by : Beamforming weights at the receiver are determined so that to suppress inter-user interference such as [32]: C (k) is the covariance matrix of H k . · 2 stands for the 2-norm operator.

Conclusion
This chapter presents a basic introduction to the fundamentals of multi-user MIMO communication. MU-MIMO is considered as an enhanced form of MIMO technology. Such technology has been a topic of extensive research since the last three decades. The attractive features of MIMO systems have shown that the use of multiple antennas at both the ends of the communication link significantly improves the spectral efficiency of the communication system as well as the reliability of the communication link.
In multiuser channels and cellular systems, MIMO is offered for MU-MIMO communication to allow for spatial sharing of the channel by several users.
Nowadays, it has been a great deal with MU-MIMO systems. Several approaches are adopted and different scenarios may be considered. Throughout this chapter, we have presented possible configurations associated with MU-MIMO with particular emphasis on the fundamental differences between SU-MIMO and MU-MIMO. Througout this chapter, we have presented precoding techniques used within MU-MIMO systems for efficient transmission and interference cancelation. Among the existing techniques, we have introduced ZF and BD methods. Of particular interest, we have described the linear beamforming algorithms.
The design of multi-user MIMO systems is attractive for the research field as well for the industrial one and the field of application is extensively growing.