Open access peer-reviewed chapter - ONLINE FIRST

Steered Beam Adaptive Antenna Arrays

By Amin H. Al Ka’bi

Submitted: February 17th 2021Reviewed: August 27th 2021Published: September 23rd 2021

DOI: 10.5772/intechopen.100168

Downloaded: 32

Abstract

In this chapter, the performance of steered beam adaptive arrays is presented with its corresponding analytical expressions. Computer simulations are used to illustrate the performance of the array under various operating conditions. In this chapter, we ignore the presence of mutual coupling between the array elements. The principal system elements of the adaptive array consist of an array of sensors (antennas), a pattern-forming network, and an adaptive pattern control unit or adaptive processor that adjusts the variable weights in the pattern-forming network. The adaptive pattern control unit may furthermore be conveniently subdivided into a signal processor unit and an adaptive control algorithm. The manner in which these elements are actually implemented depends on the propagation medium in which the array is to operate, the frequency spectrum of interest, and the user’s knowledge of the operational signal environment.

Keywords

  • antennas
  • adaptive arrays
  • steered beam
  • electromagnetic waves
  • pointing errors

1. Introduction

Antenna systems can be classified as omnidirectional, directional, phased array, or adaptive array. An omnidirectional antenna (also called isotropic antenna) has equal gain in all directions. On the other hand, directional antennas have more gain in certain directions and less in others. A phased array antenna uses an array of antenna elements and combines the signals received on these elements with appropriate phase shifts to form the output of the array. The direction of the maximum gain (main beam) can be controlled by adjusting the phase between the elements of the array. For the case of narrow-band signals, which is considered here, the term adaptive antenna is used when the weights (magnitudes/gains and phases) of the signals induced on the array elements are regularly updated before combining, in order to control the radiation pattern of the array dynamically according to the requirements of the system [1, 2, 3].

In an optimal adaptive antenna array system, the gain and phase of each antenna element are adjusted to achieve the optimal performance of the array in some sense. For example, one basis for adjusting the gain and phase of each element is to obtain maximum output signal-to-interference-plus-noise ratio (SINR) by canceling undesired interferences while receiving the desired signal. Such an arrangement is referred to as optimal combining in the mobile communication literature [2, 4].

Desired signal tracking with an adaptive array can be accomplished in various ways. One can either supply a reference signal in the feedback loop of the array and use an adaptive algorithm such as the least mean squares algorithm (LMS); or one can inject steering weights into the feedback loops based on the prior knowledge of the arrival angle of the desired signal and use optimal combining to adjust the weights of the array; or as a third approach, blind adaptation can be used which is similar to LMS but it does not require a reference signal. The second approach is vastly simpler than the first one since no reference signal is required at all. The only difficulty with this approach is that the designer must know the arrival angle of the desired signal accurately [5]. In many situations, however, the angle of arrival of the desired signal is known to some degree of accuracy. The disadvantages of the third approach lie in the fact that the blind adaptation is too slow and/or complex in the mobile environment, because fading and movement may introduce sudden large variations in levels of desired signals and interferers, which complicate the blind adaptation process.

This chapter focuses on the second approach, and in particular optimal combining steered beam adaptive arrays. Such arrays typically aim to maximize the SINR. The achieved SINRdepends largely on the “pointing error” in steering the main beam of the array toward the direction of the desired signal [5, 6, 7]. Therefore, the effect of pointing error will be discussed extensively, and it will be considered as one of the assessment criteria of the array performance.

Here are some basic concepts and considerations related to beam formation using antenna arrays mounted on base stations:

  1. Formation of multiple beams: The antenna array is used to form multiple static beams to cover the whole cell site. This is the simplest configuration but leads to waste in transmitted power.

  2. Formation of adaptive beams: The array is used to find the location of each mobile, and beams are formed to cover different mobiles or groups of mobiles by tracking their locations adaptively.

  3. Formation of nulls: In general, an N-element antenna array has N− 1 degrees of freedom; that is, it can null out N −1 interference signals. By forming nulls in the antenna pattern toward interfering mobiles, the co-channel interference can be reduced in two ways. In the transmit mode, less energy is transmitted from the base toward these mobiles, reducing the interference from the base to them. In the receiving mode, formation of nulls reduces the contribution from these mobiles at the base. Consequently, SINRcan be improved and thus, the capacity of the communication system can be increased. Moreover, nulling of interferers can allow for low-power transmitters to coexist with high-power transmitters without a substantial decrease in performance [8]. If the number of interferers exceeds the number of array elements, the array tends to form a radiation pattern such that the output SINRis maximized. In this case, the interference signals are not perfectly nulled, and the performance of the array is significantly affected, as will be discussed in Section 2 [9, 10, 11, 12].

It is assumed that the elements of the adaptive array are short dipoles (such that their individual radiation patterns are very close to isotropic antennas) and arranged in vertical positions with their beams that are formed in a broadside direction. The array elements are spatially arranged in such a way to provide sufficient coverage over the expected range of directions of the desired signal. The type and the arrangement of the elements set significant limitations on the maximum capability of the array system, in terms of its capability to detect the desired signal and to null the interference signals with acceptable SINR[13, 14].

The individual output of each antenna element is fed to the pattern-forming network shown in Figure 1, where outputs are weighted by complex weights (amplifiers/attenuators and phase shifters), and then added to generate the overall output of the array. The values of the weights (which are determined by the adaptive signal processor based on the available information and the physical arrangement of the individual isotropic sensor elements) determine the overall array beam sensitivity pattern.

Figure 1.

Block diagram of an adaptive antenna array system.

The steered beam adaptive arrays are based on the concept of maximizing the desired-to-undesired (interference plus thermal white noise) signal ratio at the output of the array [1, 2, 3, 5, 9]. Conceivably, this leads to placing nulls in the directions of the interference and noise while placing a maximum gain in the direction of the desired signal.

Advertisement

2. Signal model

The steered beam adaptive arrays are based on the concept of maximizing the desired-to-undesired (interference plus thermal white noise) signal ratio at the output of the array [2, 3]. Conceivably, this leads to placing nulls in the directions of the interference and noise while placing a maximum gain in the direction of the desired signal.

Consider the N-element adaptive array shown in Figure 1, receiving complex analytic signals1 where the ithcomplex analytic signal is denoted by x¯itand the ithcomplex weight is denoted by wi. We define the signal vector,

X=x¯1tx¯2tx¯3tx¯NtE1

This signal vector can be split into a desired signal term, an interference term, and a thermal noise term,

X=Xd+XI+XnE2

The output signal of the array may be split in a similar way,

S¯ot=XTw=S¯dt+S¯It,+S¯ntE3

The desired signal power, interference power, and noise power at the output of the array are then given as

Pd=E{S¯dt2E4
PI=E{S¯It2E5
Pn=E{S¯nt2E6

where E{.} denotes expectation with respect to time. The steering vector adaptive array is based on the concept of maximizing the ratio of the desired signal power Pdto the undesired signals powers Pu=PI+Pn; that is, to adjust the weights so that the quantity

SINR=PdPu=PdPI+PnE7

is maximized. In his paper [3], Applebaum proved that the feedback loop shown in Figure 2 maximizes the output SINRof the array. More details on this are given in the next section.

Figure 2.

Feedback loop of the steering vector adaptive array [3].

In Figure 2, it should be noted that the N-element array has Nfeedback loops, where w0jis the jthcomponent of the steering vector w¯0, and kis the feedback loop gain. In the absence of any incoming signals, the weight vector wis a scalar complex-valued multiple of w¯0. In this case, the array has a pattern determined by w¯0, and this pattern is called the quiescent pattern of the array [2, 3]. w¯0can be chosen to obtain a desired pattern from the array (i.e., it can be determined by the user’s knowledge of the arrival angle of the desired signal). Because the vector w¯0steers the main beam of the quiescent antenna pattern, it is usually called the steering vector. This steering vector is vulnerable to errors. One kind of error is the pointing error, which is studied extensively in this research in order to mitigate its effect on the performance of the adaptive array.

Advertisement

3. Problem formulation

Figure 3 shows a linear N-isotropic element adaptive array with inter-element separation distances y1,y2,y3,,yN1, which, in general, may be nonuniform. Here, we consider the case of one desired signal and Minterference signals, lying in the same 2-D plane containing the linear array.

Figure 3.

N-elements adaptive array with nonuniform spacings.

The received signal from the ithelement (which is assumed to be a complex random process) is multiplied by a complex weight wiand summed with the other N− 1 output signals to produce the array output S¯ot. Using the feedback loop configuration of Figure 2, the steady-state weight vector that maximizes the output SINRis given by [2, 3]:

w=w1w2w3wNT=I+kΦTw¯0E8

where, Φ=EXXTis the covariance matrix of the received signal, and w¯0=w10w20w3wN0Tis the steering vector of the array [1], Iis the identity matrix, kis the feedback loop gain, Tdenotes transpose, * denotes complex conjugate, E{.} denotes the expectation, and Xis the received signal vector as defined in Eq. (1). The received signal of the jthelement is given by the following:

x¯jt=S¯djt+i=1MS¯Iijt+S¯njt,j=1,2,,NE9

where S¯djtis the signal induced on the jthelement due to the desired signal, S¯Iijtis the signal induced on the jthelement due to the ithinterference signal, Mis the number of interference signals, and S¯njtis the white thermal noise at the jthelement, which has zero mean and is uncorrelated with other thermal noise signals such that

ES¯nitS¯njt=σ2δijE10

where σ2is the variance of the thermal white noise, and δijis the Kronecker delta function. In this array, uniform plane waves are assumed to be incident on the sensors of the array, and the medium is assumed to be linear and its only effect on the signals is a time delay. Hence, the desired signals S¯d1t,S¯d2t,.,S¯dNtdiffer by an inter-element propagation time

Tdp=ypcsinθdE11

where cdenotes the velocity of light, θdis the arrival angle of the desired signal, ypis the inter-element spacing between the pthelement and the p+1thelement, and Tdpdenotes the propagation time between the pthelement and the p+1thelement. Hence

S¯djt=S¯d1tp=1j1Tdp.γd,j=1,2,,NE12

where γd=expjωcp=1j1Tdp, and ωcis the center frequency of the power spectral density of the desired signal. Similarly, S¯Iijtis given by the following:

S¯Iijt=S¯Ii1tp=1j1TIip.γI,j=1,2,,NE13

where γI=expjωcp=1j1TIip, idenotes the ithinterference signal, jdenotes the jthsensor element of the array, and

TIpi=ypcsinθIiE14

where θIiis the arrival angle of the ithinterference signal. The desired and the interference signals are assumed to have zero mean, and are stationary and statistically independent from each other and the thermal noise. This applies in many cases, especially in narrowband-faded signals, with different Directions of Arrival (DOA’s).

Using these results in Eq. (8), together with the initial steering vector w¯0, a signal component-based expression for the steady-state weight vector of the array can be determined.

With the aim of obtaining a complete signal component-based expression for the steady-state weight vector wof Eq. (8), we now focus on the steering vector w¯0. The steering vector w¯0is chosen to provide a beam maximum of the quiescent pattern in a given direction θmax. It can be noted that a CW signal from an angle θmaxwill produce a signal vector:

X=1el1sinθmaxel1+l1sinθmaxei=1N1lisinθmax.ejωctE15

where ωcis the center frequency of the power spectral density of the desired signal and β=2πλis the wave number of the desired signal. The output of the array for such a signal would be

S¯ot=XTwE16

so that

S¯ot=w1w2ejμ1+w3ejμ2++wNejμN1.ejωctE17

where μi=j=1iljβsinθmax.

The quiescent pattern of the array will have a maximum on this signal if

w1=w2ejμ1=w3ejμ2==wNejμN1E18

Therefore, for a given θmaxand according to the phased array theory, w¯0should be chosen as

w¯0=ejμN1ejμ2ejμ11TE19

Using this w¯0, the steady-state weight vector wmay then be calculated from Eq. (8), that is, w=I+kΦTw¯0. Here, it should be noted that the difference between θmaxand the actual direction of the desired signal θdis called the pointing error (θper) of the main beam of the array.

The signals S¯dtand S¯I1t,S¯I2t,S¯I3t,.,S¯IN1tare defined such that the normalized autocorrelations in Eqs. (20) and (21) could be found; thus, they are each assumed to be a wide sense stationary random process with flat band-limited power spectral density centered atωc.

Using Eq. (7), the steady-state weight vector wmay then be calculated from Eq. (1). The output power of the desired signal can be written as

Pd=Sdn=1NwN2+i=1N1m=2N2RewNwmρdij],form>nE20

where ρdijis the normalized autocorrelation between the desired signals coming from the ithand jthantenna elements. The output power of the ithinterference signal is [5]:

PIi=SIin=1NwN2+i=1N1m=2N2RewNwmρIipj],form>nE21

and the output power of the thermal noise is given by the following:

Pn=σ2n=1NwN2E22

From Pd,i=1MPIi,and Pn, the output SINRcan be computed as

SINR=10log(Pd/(i=1MPIi+PnE23

which can be used as a measure of the performance of the adaptive array in the sequel. The radiation/sensitivity pattern of the array can be calculated from

Eθ=20logw1+w2ejμ1+w3ejμ2++wNejμN1E24

where μi=j=1iyjβsinθ.Now, all of the equations needed to compute the output SINR as a function of the input signal-to-noise ratio (SNR), input interference-to-noise ratios, arrival angles of the desired and interference signals, and bandwidths of the desired and interference signals are readily available. MATLAB application is used to simulate the operation of the array.

Advertisement

4. Performance of the array

In this section, the performance of steered beam adaptive array with uniform inter-element spacing of (λ/2) will be studied with respect to various operating conditions,2 including pointing error, feedback loop gain, input SNR/element, input INR/element, and DOAs and bandwidths of the desired and interference signals.

Consider first the case where there is no interference. Figure 4 shows the output SINR of a three-element array as a function of pointing error (θperr), which is the difference between the DOA of the desired signal (θd) and the direction of the main beam of the array (θmax). Several curves are shown for different input SNR’s/element. The curves are computed for feedback loop gain K = 0.1, and zero desired signal bandwidth (Bd= 0).

Figure 4.

Output SINR vs.θperr. Three-element array,θd=0o, K = 0.1, andBd= 0. No interference.

From Figure 5, it can be seen that the sensitivity of the array to pointing errors increases with increasing SNR. For example, if SNR = 5 dB, the array provides output SINR > 5B if the pointing error margin lies within ±15o, but for SNR = 40 dB, the array output exceeds 5 dB only if the pointing error lies within ±0.8o. The explanation of this behavior is illustrated in Figure 5, where typical radiation patterns are plotted using Eq. (24), under the same conditions as in Figure 4.

Figure 5.

Radiation patterns of three-element array. K = 0.1, with different SNR’s. No interference. (a) Pointing error (θperr=θdθmax)=0o. (b) Pointing error (error (θperr=θdθmax)=5o.

In Figure 5(a), the pointing error θperr=θdθmax)=0o, and in Figure 5(b), θperr=5o. For θperr=0o, it can be seen that as the SNRincreases, the overall radiation pattern magnitude is reduced. As the pattern amplitude drops, both the desired signal power and the thermal noise power drop in proportion. Hence, the output SINRremains relatively unaffected by this change in pattern amplitude. For θperr=5o, the pattern behavior is quite different. Here, it can be seen that as the SNRincreases, the array increasingly suppresses the desired signal. Since it can do this without lowering the overall pattern amplitude, the result is to reduce the desired signal power without reducing the thermal noise power. This accounts for the behavior seen in Figure 4. However, in most system designs, achieving maximum gain is not the most important objective. What matters most is achieving SINRat the output of the array that exceeds a certain threshold.

The effect of increasing the number of array elements is depicted in Figure 6. When comparing the curves in this figure with those in Figure 4, it can be seen that the five-element array is more sensitive to pointing errors than the three-element array. For example, when SNR = 5 dB, the array provides output SINR > 5 dB, as long as 9oθperr9o.

Figure 6.

OutputSINRvs. pointing error. Five-element array,θd=0o, K = 0.1. No interference.

The explanation of this behavior lies in the fact that the directivity of the array increases by increasing the number of its elements, as illustrated in Figure 7. Here, the 3-dB beamwidth of the main beam for the five-element array is less than that of the three-element array.

Figure 7.

Normalized radiation patterns of three- and five-element arrays.θd=0o, pointing error (θperr=θdθmax)=0o(K = 0.1). No interference.

A different perspective on these results may be gained by plotting the output SINRas a function of input SNR. Figure 8 shows several curves for the three-element array with different values of pointing error (θperr). This figure shows that the beam-pointing error that can be tolerated is essentially a matter of dynamic range. For example, if θperr=5o, the output SINRis greater than 5 dB only for 1dBSNR19dB, whereas if θperr=0.1o, the output SINR > 5 dB for 0dBSNR56dB. Therefore, the greater the desired signal dynamic range we wish to accommodate, the less pointing error θperrwe should have.

Figure 8.

Output SINR vs. input SNR/element. Three-element array.θd=0o, K = 0.1, with different values of pointing error (θperr=θdθmax). No interference.

Until now, we assumed that the feedback loop gains of the array K = 0.1. However, the effect of Kon the performance of the array is illustrated in Figure 9.

Figure 9.

Output SINR vs. feedback loop gain (K). Three-element array,θd=0o, and SNR = 30 dB, with different values of pointing error (θperr=θdθmax). (a) No interference. (b) One 40-dB INR interference signal @30o.

In Figure 9(a) where interference does not exist, the output SINRdeteriorates rapidly by increasing Kbecause the array tends to suppress the desired signal more, which results in more sensitivity to pointing errors.

On the other hand, when interference exists, Figure 9(b) shows that low values of K, as well as high values of K, have a negative effect on the performance. This is due to the capability of the array to effectively decrease null interference signals by decreasing K. From Figure 9, it can be concluded that the most appropriate value for the feedback loop gain is 00.1K0.1. In this chapter, we used K = 0.1 as a representative value.

In Figure 4, we presented the performance of the array in the absence of interference signals. Now consider the case when interference is present. The equivalent results of Figure 4 are presented in Figure 10, where one interference signal is incident at θI=10owith INR = 30 dB and zero bandwidth BI=0.

Figure 10.

Output SINR vs. pointing error. Three-element array,θd=0o, K = 0.1. One 30-dB INR interference signal @θI=10o,BI=0.

These curves differ from those in Figure 4 in several respects. First, for SNR < 10 dB, θperrhas less effect on the SINR(except for θperr=θI) than it did with no interference. Second, for higher SNRs, the SINRagain becomes sensitive to θperr, but much less than that without interference. For example, in Figure 10 with SNR = 30 dB, SINR > 5 dB for 8.25oθperr3.75o, whereas in Figure 4, SNR = 30 dB yields SINR > 5 dB only for 2.55oθperr2.55o. The reason for this difference is that, in general, with the presence of interference, the array uses its degrees of freedom to form nulls toward the interference. Therefore, the array cannot null the desired signal, as it could without interference.

For further illustration of the performance of the array, Figure 11 shows the output SINRfor different DOAs of the desired signal. In this figure, it can be seen that the SINRdecreases as the DOA of the desired signal gets closer to the DOA of the interference signal. This is because, as expected, the desired signal is increasingly suppressed by the null formed toward the interference signal.

Figure 11.

Output SINR vs. direction of the main beamθmax. Three-element array, K = 0.1. One 30-dB INR interference signal atθI=10o. SNR = 30 dB with DOAs ofθd=10o,5o,0o,5o,10o,15o.Bd=0,BI=0.

The corresponding results for different DOAs of the interference signal can be seen in Figure 12. Again, the SINRdrops as the interference DOA gets closer to the DOA of the desired signal. Figure 13 provides extra explanation for these results: the depth of the null toward the interference signal decreases as the DOA of the interference signal gets closer to the DOA of the desired signal. Therefore, more interference power appears at the output of the array.

Figure 12.

Output SINR vs. pointing errorθmax. Three-element array,θd=0o,K = 0.1,Bd=0,BI=0. One 30-dBINRinterference signal with DOA @θI=5o,10o,15o.

Figure 13.

Normalized radiation patterns for three-element array.θd=0o, pointing error (θperr=θdθmax)=0o,Bd=0,BI=0. One 30-dBINRinterference signal with DOA atθI=5o,15o.

Figure 14 depicts the output SINRvs. the DOA of the interference signal for different values of INR, and Figure 15 depicts the output SINRvs. the INRof the interference signal with different DOAs. Here, the pointing error θperr=0o.

Figure 14.

OutputSINRvs. DOA of the interference signal. Three-element array,θd=θmax=0o, SNR = 30 dB, K = 0.1, andBd=0,BI=0.

Figure 15.

OutputSINRvs. interference-to-noise ratio (INR). Three-element array,θd=θmax=0o. SNR = 30 dB, K = 0.1, andBd=0,BI=0, with different DOAs of the interference signal (θI).

From these two figures, it can be seen that for the case of θperr=0o, the output SINRdecreases as the interference signal gets closer to the desired signal (Figure 14) and as its INRincreases (Figure 15). It can be noticed that the interference signal is more effectively nulled when its DOA is far away from the DOA of the desired signal. When θperr0o, we get the similar curves as in Figures 14 and 15 (not shown here), but with lower output SINR. The reason is that the complex weights for forming a radiation pattern are selected for the center frequency.

Figure 16 shows the output SINRversus the input SNRfor several values of pointing error θperr, taking into consideration the effect of the interference signal bandwidth (BI). Here, it can be seen that the output SINRdecreases by increasing the interference bandwidth (BI), due to the decreased efficiency in the null formation toward the interference.

Figure 16.

Output SINR vs. input SNR/element. Three-element array, K = 0.1, andBd=0, with different values of pointing error (θperr=θdθmax). One 30-dB INR interference signal with DOA@30owith different bandwidths (BI).

By comparing Figure 16 with Figure 8 (where the interference is absent), it can be seen that the performance of the array has been enhanced in the interference case in terms of the dynamic range of the desired signal that can be accommodated for a given θperr. For example, for θperr=1oand BI=0, the interference-free case provides output SINR greater than 5 dB only for 1dBSNR34.2dB, whereas in the presence of interference, the output SINR > 5 dB for 1dBSNR43.5dB.

The interference bandwidth BIdecreases with a decreasing INR. This can be concluded from the comparison between Figures 16 and 17, where the effect of BIis insignificant in the latter case.

Figure 17.

Output SINR vs. input SNR/element. Three-element array, K = 0.1, andBd=0, with different values of pointing error (θperr=θdθmax). One 5-dBINRinterference signal with DOA@30oand bandwidths (0%BI20%).

The effect of the interference signal bandwidth and its INRis further explained in Figure 18. Here, it can be seen that the effect of the bandwidth of the interference signal is more significant when its INRis higher.

Figure 18.

Output SINR vs. interference signal bandwidth (BI). Three-element array, K = 0.1, andBd=0, pointing error (θperr=θdθmax). One interference signal with DOA@30oand different INRs.

In contrast, for low INRs (<5 dB), the effect of the interference bandwidth is unnoticeable. Additionally, the interference bandwidth has more impact on the output SINRas its DOA gets closer to the DOA of the desired signal. This is illustrated in Figure 19 for the case of θperr=0o. The effect of the interference bandwidth BIon the depth of the nulls formed toward the interference signals is explained in Figures 20 and 21.

Figure 19.

Output SINR vs. interference signal bandwidth (BI). Three-element array, K = 0.1, andBd=0, pointing error (θperr=θdθmax). One interference signal with INR = 30 dB and different DOAs.

Figure 20.

Radiation patterns of a three-element array with different interference bandwidthsBI. Input SNR = 10 dB,Bd=0, K = 0.1, pointing error (θperr=θdθmax). Two interference signals with identical bandwidths, INR’s = 30 dB at30oand50o.

Figure 21.

Null depths formed by three-element array @30oand50oas a function of the interference bandwidth. Input SNR = 10 dB,Bd=0, K = 0.1, pointing error (θperr=θdθmax). Two interference signals with identical bandwidths, INR’s = 30 dB at30oand50o.

Figure 20 shows that the depth of the null formed at 30ohas a depth of –61 dB when the bandwidth of the interference signals is 0%, while it gets shallower (–48 dB) when the bandwidth of the interference signals increases (20% of the carrier frequency). This also applies to the null formed at 50o, but with less change in the depth (as explained in Figure 19).

For more explanation, Figure 21 illustrates the depths of the two nulls (formed at 30oand50o), as a function of the interference signals bandwidth. For simplicity, we assumed here that the two bandwidths are identical. It can be seen that the nulls get shallower as the bandwidth of the interference signals increases and the close the DOA of the interference signal to the DOA of the desired signal, the more change in the null depth occurs.

As previously discussed, the N-element steered beam adaptive arrays have N− 1 degrees of freedom. Hence, they have the capability of efficiently nulling up to N− 1 interference signals. However, if more than N− 1 interference signals are incident on the array, the array cannot form nulls toward the interference signals. Instead, it tries to form a radiation pattern such that the output SINRis maximized. This is shown in Figure 22 where 6 and 12 30-dB interference signals are incident on a seven-element uniformly spaced array with uniform spacings of (λ/2).

Figure 22.

Radiation patterns for the seven-element uniformly spaced adaptive array with a different number of interference signals with INR’s = 30 dB. SNR = 20 dB with pointing error (θperr)=0o.

As observed in Figure 22, in the case of the six interference signals with DOAs of 60o,50,40o,45o,30o,20o,30o, and 60o, we can see that the array has effectively nulled these signals, while in the case of the twelve interference signals with DOAs of 20o,30o,60o,45o,10o,10o,20o,30o,45o,50o,60o, and 75o, the array could not form nulls toward these signals, but it arranged the radiation pattern in such a way that the least amount of interference power is allowed (e.g., by forming a null between two close interference signals).

However, the presence of a large number of interference signals adds more interference power to the array output, which lowers the output SINR. This is illustrated in Figure 23, where the output SINRfor the six effectively nulled interference signals is very close to the situation where interference signals do not exist. Clearly, both of these cases show much better performance of the adaptive array when 12 interference signals are present. Significantly, the array has more sensitivity to pointing errors in the absence of interference signals. This explains the enhancement of the output SINRfor θperras the input SNRincreases.

Figure 23.

Performance of the seven-element uniformly spaced adaptive array with a different number of interference signals and pointing errors. INR’s = 30 dB. SNR = 20 dB.

Advertisement

5. Conclusions

In this chapter, we have presented and discussed the analytical formulation of the steered beam adaptive array, and we have studied the performance of the uniformly spaced steered beam adaptive array from several perspectives. It is found that by increasing the number of array elements, its directivity increases and as a result, its sensitivity to pointing errors increases as well. We also found that the greater the desired signal dynamic range (in terms of input SNR/element), we wish to accommodate, the less pointing error we should have. This also applies when the input SNR/element of the desired signal increases.

It has been found also that low values (<0.001) and high values (>0.2) of the feedback loop gain of the array have a negative effect on the performance of the array. Therefore, moderate values of feedback loop gain are preferred. It is assumed that the bandwidth of the feedback loop is large enough to accommodate the processed signals; otherwise, the adaptation process would behave erroneously.

The effect of the interference signals on the array is less if their INRs and bandwidths have low values. Additionally, it has been found that if the DOA of the interference is far away from the DOA of the desired signal, its effect is less pronounced. Moreover, it is shown that if the number of the interference signals is less than the degrees of freedom of the array, the effect on the performance is less noticeable, whereas, when the number of interferers exceeds the degrees of freedom of the array, the output SINRis significantly affected.

Notes

  • Complex analytic signals correspond to real passband signals, as a result of complex baseband signal processing.
  • The nonuniformly spaced adaptive arrays will be studied in the next chapters.

DOWNLOAD FOR FREE

chapter PDF

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

How to cite and reference

Link to this chapter Copy to clipboard

Cite this chapter Copy to clipboard

Amin H. Al Ka’bi (September 23rd 2021). Steered Beam Adaptive Antenna Arrays [Online First], IntechOpen, DOI: 10.5772/intechopen.100168. Available from:

chapter statistics

32total chapter downloads

More statistics for editors and authors

Login to your personal dashboard for more detailed statistics on your publications.

Access personal reporting

We are IntechOpen, the world's leading publisher of Open Access books. Built by scientists, for scientists. Our readership spans scientists, professors, researchers, librarians, and students, as well as business professionals. We share our knowledge and peer-reveiwed research papers with libraries, scientific and engineering societies, and also work with corporate R&D departments and government entities.

More About Us