# Antenna Selection Techniques In Mimo Systems Computer Science Essay

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The greatest favour of MIMO systems is that more satisfactory performance can be easily achieved without using additional transmit power or extension of the bandwidth. However, its main disadvantage is that additionally high-cost radio frequency (RF) modules are an essential necessity as multiple antennas are deployed. In general, RF modules include components like low noise amplifier (LNA), frequency down-converter and analog-to-digital converter (ADC). In an effort to reduce the cost associated with the multiple RF modules, antenna selection techniques can be used to employ a smaller number of RF modules than the number of transmit antennas. This paper gives the performance evaluation of various antenna selection techniques in MIMO systems.

Keywords- MIMO, antenna, RF, LNA, ADC

## I.INTRODUCTION

The MIMO systems are the one which are basically having multiple antenna elements at both the transmitter and receiver side. The main practical applications of MIMO systems are diversity combining, beam forming and spatial multiplexing. MIMO technology in association with the turbo coding play a vital role in wireless communication. There is always a great assurance that MIMO technology brings out a significant improvement and increase in the system capacity. A MIMO system takes good advantage of the spatial diversity scheme that is obtained by spatially separated antennas in a dense multipath scattering environment. In a number of different ways, MIMO systems may be successfully implemented in reality to obtain either a diversity gain to combat signal fading or to obtain either a capacity gain. In a much generalized manner, MIMO technique aims to improve the power efficiency by maximizing spatial diversity. Such techniques include delay diversity, space-time block codes [1],[2] and space-time trellis codes[3].

MIMO systems have the ability to exploit rather than combat, multipath propagation. The separability of the MIMO channel relies on the presence of rich multipath, which makes the channel spatially selective. Thus, MIMO effectively exploits multipath. In contrast, some smart antenna systems perform better in the LoS case, and their optimization criteria are based on the DoA/DoD. Although some smart antenna systems generate good results in the non-LOS channel, they mitigate multipath rather than exploit it.

The maximum spatial diversity obtained for a non-frequency-selective fading MIMO channel is proportional to the product of the numbers of receive and transmit antennas. In the uncorrelated Rayleigh fading channel, the MIMO channel capacity or the throughput limit always grows linearly with the number of transmit or receive antennas, whichever is smaller. According to the analysis and simulation performed in [4], MIMO can provide a spectral efficiency as high as 20-40 bits/s/Hz. MIMO and OFDM are commonly thought to be the key techniques for next-generation wireless LAN and 4G mobile communications. MIMO-OFDM is used in IEEE 802.11n, IEEE 802.16m, and LTE.

The efficient use of multiple antennas at the transmitter and receiver side for wireless communication systems has gained and attracted an overwhelming interest during the past two decades both in academia and industry. Multiple antennas can be utilized for the successful achievement of a multiplexing gain, a diversity gain, or an antenna gain, thus increasing the quality of bit rate, the error performance, or the signal-to-noise-plus-interference ratio of wireless systems, respectively. Without a very large number of yearly publications, the field of multiple-antenna systems, often called multiple-input multiple-output (MIMO) systems, has evolved rapidly and has drastically brought a great revolution in technology. To date, there are many papers on the performance limits of MIMO systems which have evolved rapidly in a very short span of time.

It is essential for the MIMO systems to provide a good quality of service and in order to guarantee it, not only high bit rates are required, but also a good error performance rate should be achieved. However, the disruptive characteristics of wireless channels mainly caused by multipath signal propagation and fading effects, make it challenging to accomplish both of these goals at the same time. In particular, given a fixed bandwidth, there is always a fundamental tradeoff between bandwidth efficiency (high bit rates) and power efficiency (small error rates).

The conventional single-antenna transmission technique which aims at an optimal wireless system performance operates in the time domain and/or in the frequency domain. In particular, channel coding is typically employed, so as to overcome the detrimental effects of multipath fading. However, with regard to the ever-growing demands of wireless services, the time is now ripe for evolving the antenna part of the radio system. In fact, when utilizing multiple antennas, the previously unused spatial domain can be exploited. The great potential of using multiple antennas for wireless communications has only become apparent during the last decade.

## II. mimo system model

The narrowband MIMO systems with Nt transmit and Nr receive antennas have a channel that can be described by an Nr x Nt matrix B= [bij], where bij represents the channel transfer function from the jth transmitter to the ith receiver. H is modelled as a random matrix characterized by an uncorrelated or correlated Rayleigh fading channel, or an uncorrelated or correlated Ricean fading channel.

Assuming that each transmit antenna has energy for each input symbol as Es/Nt, Es being the total energy transmitted from all antennas per input symbol, the received signal at antenna j is given by

(1)

where njâ€™s are the i.i.d additive zero mean circularly symmetric complex Gaussian variables(ZMCSCG) with two-sided PSD No/2, and bij is the flat fading channel gain from transmit antenna i to receive antenna j, bji being also a ZMCSCG variable in the non-LOS case.

In matrix form, we have

(2)

where s, an Nr-dimensional vector, corresponds to the output signals at the receiver antennas, x is an Nt-dimensional vector, whose elements xj denotes the signal transmitted from the jth transmitter and n is the additive ZMCSCG noise vector with covariance matrix Rw at the receive antennas. The SNR at each receive antenna is Es/No.

MIMO implementation relies on the rich scattering about the transmitter and receiver antennas. Insufficient scattering frequently occurs when the channel is approximately LOS, or when beam forming or directional antennas are used for interference reduction or long-range transmission.

For space-time codeword of block length Nst, Nst receive vector symbols in the codeword can be stacked together in a matrix form and be processed together. For the frequency-selective channel, the channel B can be represented as B(l), l=0,1,.......,L-1, where L is the maximum channel length; in this case, multiple continuous received vector samples can be stacked to solve H(l), l=0,1,.....L-1.

## III.SPATIAL CORRELATION AND MIMO CHANNEL MODEL

For a MIMO system, the elements of B are usually assumed to be statistically independent of one another. This assumption is not always accurate, since correlation may exist due to the propagation environment (such as the presence of LOS component), the polarization of antenna elements, and the spacing between antenna elements. The fading correlation associated with B can be decomposed into two independent components

(3)

where Rr and Rt are called receive correlation and transmit correlation matrices, respectively, Bw is a matrix with independent Gaussian elements and unity variance, and the superscript Â½ denotes the Hermitian square root of a matrix. Rr determines the correlation between the rows of H, independent of the transmit antennas. Similarly, Rt determines the covariance of the columns of H, independent of the receive antennas. This model is widely used in MIMO implementation, and it has been adopted by IEEE 802.11n and IEEE 802.20 as a MIMO channel model.

The correlation matrices Rr and Rt can be measured, or be computed by assuming the scattering distribution around the receive and transmit antennas. For uniform linear arrays at the transmitter and receiver, the correlation matrices Rr and Rt can be calculated according to two different methods in[5, 6]. From [6], we have

1 .......

1 ....... .

1 .......

. . . (3)

## . .

...... 1

where N is equal to Nr or Nt, corresponding to the receive or transmit antenna array, and is the fading correlation between the two adjacent receive or transmit antenna elements, which can be approximated by

(4)

with being the angular spread and s the inter-element distance. Note that for small r(s), the higher-order terms are negligible and the correlation matrices take the form of triagonal matrices.

In practical cases, the degenerate channel phenomena called keyholes may arise, where the antenna elements at both the transmitter and receiver have very low correlation, yet the channel matrix B has only a single degree of freedom, yielding a single mode of communication [7,8,9,10]. This phenomenon is very similar to the case when rich-scattering transmit and receive antennas are separated by a screen with the wave passing through the keyhole. This model also applies for indoor propagation through hallways, narrow tunnels or waveguides. Relay channels in the amplify-and-forward mode can be treated as keyhole channels. Thus, low correlation is not a guarantee for achieving high capacity. For outdoor environments, roof edge diffraction is perceived as a keyhole by a vertical base array, whereas the keyhole effect may be avoided by employing a horizontally oriented transmitter array [11]. Instantaneous SNR and outage capacity distributions of spatially correlated keyhole MIMO channels have been investigated in [12].

A double-scattering MIMO channel model that includes both the fading correlation and rank deficiency was introduced in [13]. The multi keyhole channel is analysed in [12]. For a large number of antennas, the capacity of a multi keyhole channel is a normally distributed sum of the capacities of single keyhole channels.

The correlation between antennas is typically not a problem for MIMO systems with well designed antennas. This is due to the fact that even for the worst case the correlation rarely exceeds 0.7, and this yields a degradation of less than 1 dB with MRC [14] and even less with the MMSE combiner. The capacity achievable with isotropic inputs is lowered by antenna correlation, while for non isotropic inputs correlation may not be detrimental [15]. For example, transmit correlation may be advantageous for small SNR and for Nt>Nr [15].

The impact of channel correlation on the capacity of a MIMO system is negligible when the two-element array beamwidth, defined as, d being the inter-element distance and then the mean DoA, is smaller than the angular spread of the incoming multipath signals [5]. Fully correlated fading destroys diversity gain, but array gain is retained. LOS components stabilizes the link, improving the SER performance, but it reduces the MIMO system capacity [ 16].

3GPP/3GPP2 have defined a cross-polarized channel model for MIMO systems [17]. The 3GPP cross-polarized channel model neglects the elevation spectrum. A composite channel impulse model for the cross-polarized channel that takes into account both the azimuth and elevation spectrums has been proposed in [18], based on which closed-form expressions for the spatial correlation have been derived and the impact of the various factors on the mutual information of the system has also been studied.

## IV. ANTENNA SELECTION TECHNIQUES

The advantage of MIMO systems is that better performance can be achieved without using additional transmit power or bandwidth extension. However, its main drawback is that additionally high-cost RF modules are required as multiple antennas are employed. In general, RF modules include low noise amplifier (LNA), frequency down-converter and analog-to-digital converter (ADC). In an effort to reduce the cost associated with the multiple RF modules, antenna selection techniques can be used to employ a smaller number of RF modules than the number of transmit antennas. The diagram below illustrates the end-to-end configurations of the antenna selection in which only Q RF modules are used to support NT transmit antennas (Q < NT). Note that Q RF modules are selectively mapped to Q of NT transmit antennas.

Since Q antennas are used among NT transmit antennas, the effective channel can now be represented by Q columns of .Let denote the index of the ith selected column, i=1,2,â€¦..,Q. Then, the corresponding effective channel will be modeled by NR Q matrix, which is denoted by . Let denote the space-time-coded or spatially-multiplexed stream that is mapped into Q selected antennas. Then, the received signal y is represented as

(5)

Where is the additive noise vector. The channel capacity of the system in the above equation will depend on which transmit antennas are chosen as well as the number of transmit antennas that are chosen. In the following subsections we will discuss how the channel capacity can be improved by the antenna selection technique.

A.OPTIMUM ANTENNA SELECTION TECHNIQUE

Step 1:A set of Q transmit antennas must be selected out of NT transmit antennas so as to maximize the channel capacity. When the total transmitted power is limited by P, the channel capacity of the system using Q selected transmit antennas is considered expressed in terms of bps/Hz.

(6)

where is expressed as a QQ covariance matrix. In this case if equal power is being allocated to all selected transmit antennas then ,yields the channel capacity for the given .

Step 2:The optimal selection of P antennas for all possible antenna combinations is considered. In order to maximize the system capacity, one must choose the antenna with the highest capacity, that is,

(7)

where A represents a set of all possible antenna combinations with Q selected antennas.

Step 3:It is considered that = that is, considering all possible antenna combinations in equation 7 may involve the enormous complexity, especially when NT is very large. Therefore some methods of reducing the complexity need to be developed. In this paper this particular issue is solved. The figures 2,3,4,5 shows the channel capacity with antenna selection for NT=4 and NR=4 as the number of the selected antennas varies by Q= 1,2,3,4. It is clear that the channel capacity increases in proportion to the number of the selected antennas. When the SNR is less than 10 dB, the selection of three antennas is enough to warrant the channel capacity as much as the use of all four antennas.

Fig 1., Channel capacity with optimal antenna selection NT=NR=Q=1.

Fig 2., Channel capacity with optimal antenna selection

NT=NR=Q=2.

Fig 3., Channel capacity with optimal antenna selection NT=NR=Q=3.

Fig 4., Channel capacity with optimal antennan selection NT=NR=Q=4.

B. COMPLEXITY-REDUCED ANTENNA SELECTION:

The optimal antenna selection in equation (7) may involve too much complexity depending on the total number of available transmit antennas. In order to reduce its complexity, we may need to resort to the sub-optimal method. For example, additional antenna can be selected in ascending order of increasing the channel capacity. More specifically, one antenna with the highest capacity is first selected as

(8)

Step 1: Given the first selected antenna, the second antenna is selected such that the channel capacity is maximized, that is,

(9)

Step 2:After the nth iteration which provides {, the capacity with an additional antenna, say antenna I can be updated . The additional antenna (n+1)th antenna is the one that maximizes the channel capacity and is given by

(10)

Step 3: This process continues until all Q antennas are selected and it is taken into consideration that the matrix inversion is required for all in the course of the selection process.

Step 4: Meanwhile the same process can be implemented by deleting the antenna in descending order of decreasing channel capacity also .It is also considered that the complexity of selection method in descending order is higher than that in ascending order.

From the performance perspective, however, the selection method in descending order outperforms that in ascending order when 1<Q<NT. This is due to the fact that the selection method in descending order considers all correlations between the column vectors on the original channel gain before choosing the first antenna to delete. When Q=NT-1, the selection method in descending order produces the same antenna index set as the optimal antenna selection method produces equation (7). When Q=1, however, the selection method in ascending order produces the same antenna index as the optimal antenna selection method in Equation(7) and achieves better performance than any other selection methods. In general , however,all these methods are just suboptimal, except for the above two special cases.

The channel capacities with two suboptimal selection methods is computed by using the program below where sel_ant=1,2.,,,,,,,NT-1 is used for setting the number of selected antennas, and variable sel_method=0 or 1 indicates whether selection is done in ascending or descending order. The figure shows the channel capacity with the selection method in descending order for various numbers of selected antennas with NT=4 and NR=4.Comparing the curves with those in the previous one we can almost achieve the same channel capacity as the optimal antenna selection method in equation (7).

Fig 5., Channel capacity with sub optimal antenna selection NT=NR=Q=1.

Fig 6., Channel capacity with sub optimal antenna selection NT=NR=Q=2.

Fig 7., Channel capacity with sub optimal antenna selection NT=NR=Q=3.

Fig 8., Channel capacity with sub optimal antenna selection NT=NR=Q=4.

C.ANTENNA SELECTION FOR OSTBC

In the previous technique, channel capacity has been used as a design criterion for antenna selection. Error performance can also be used as another design criterion.

Step 1:Transmit anennas can be selected so as to minimize the error probability.

Step 2:Let denote the pairwise error probability when a space-time codeword Ci is transmitted but Cj is decoded for the given channel ji.

Step 3: For an effective channel with Q columns of B chosen, an upper bound for the pairwise error probability for orthogonal STBC(OSTBC) is given initially.

Step 4: The Q transmit antennas can be selected to minimize the upper band equivalently and the antennas corresponding to high column norms are selected for minimizing the error rate.

Step 5. The average SNR on the receiver side with Q selected antennas is considered. The simulation shows that BER performance with Q=2 and NT=4. It is also observed that the further diversity gain has been achieved without using additional RF modules on the transmitter side. It is also interesting to compare the results in Fig 12.4 with those in Fig.12.10, which demonstrate that the antenna selection method provides more gain over the precoding method.

Fig 9., BER performance of Alamouti STBC scheme with antenna selection : Q =2 and N = 4.

CONCLUSION

Thus the main practical applications of MIMO systems are diversity combining, beam forming and spatial multiplexing. MIMO technology in association with the turbo coding play a vital role in wireless communication. There is always a great assurance that MIMO technology brings out a significant improvement and increase in the system capacity. Thus the performance evaluation of various antenna selection techniques in MIMO systems like optimal antenna selection technique, complexity reduced optimal antenna selection technique and antenna selection for OSTBC techniques are implemented successfully.

Acknowledgment

The author wishes to acknowledge the department of Electronics and Communication Engineering, Bannari Amman Institute of Technology, Sathyamangalam, Tamil Nadu, India for their consistent patronage.