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Novel closed-form expressions are derived for the performance analysis of a multiple-input multiple-output (MIMO) system in Rayleigh fading using transmit antenna selection (TAS) at the transmitter and maximal ratio combining (MRC) at the receiver. Receive antennas are assumed to be arbitrarily correlated, as no restriction is imposed on the correlation matrix. General exact and asymptotic expressions to evaluate the bit error rate (BER) of different modulation schemes are presented for uncoded transmission, and a closed-form expression is presented for the channel capacity. It is demonstrated that channel capacity may improve due to correlation at the receive antennas if the transmit array size is large enough as a result of a higher signal variability and the antenna selection performed at the transmitter. Monte Carlo simulations have been carried out to validate the analysis, showing an excellent agreement with the theoretical results.

Multiple-input multiple-output (MIMO) systems use multiple antennas at both the transmit and receive ends to improve the performance of wireless links. Among the different possible MIMO schemes, TAS/MRC, employing transmit antenna selection at the transmitter and maximal ratio combining at the receiver, has been proposed as a means to provide full diversity gain and reduce implementation complexity [

Several works have analyzed the performance of TAS/MRC systems in different fading conditions in the last decade; however, most previous works assume uncorrelated antennas at both the transmit and receive ends [

In this work, we study a TAS/MRC system in semicorrelated Rayleigh fading channels where transmit antennas are assumed to be independent and receive antennas are considered to be arbitrarily correlated. No restriction is imposed on the correlation matrix of the receive array, as arbitrary correlation is considered between any pair of receive antennas, thereby allowing the multiplicity of the receive correlation matrix eigenvalues to be arbitrary. We derive closed-form expressions for the pdf and CDF of the signal-to-noise ratio (SNR) as well as for the BER of different modulation schemes for uncoded transmission. In order to provide insight into the impact of the different system parameters on performance, a simple and compact asymptotic expression of the BER for the high SNR regime is also derived and it is shown that correlation results in an increased BER for high values of the SNR. We also develop an expression for the ergodic capacity and, by studying the derivative of capacity with respect to correlation, we demonstrate that the presence of correlation may increase channel capacity if the number of transmit antennas is high enough. This beneficial impact of correlation on capacity has also been observed in multiuser MIMO schemes (see [

Let us consider a wireless system with

Simplified system model.

For MRC combining, it is known that, when the transmit antenna

Using partial fraction expansion, (

From (

The unconditional instantaneous output SNR per symbol will be

Using the multinomial theorem [

The pdf of the output SNR can therefore be written in compact form by differentiating (

The average BER depends on the fading distribution and the modulation technique and can be obtained by averaging the conditional error probability (CEP), that is, the error rate under AWGN, over the output SNR. Alternatively, the average error rate can be expressed in terms of the CDF of the output SNR as

For the sake of compactness, in order to compute the BER of the considered modulations, we will use the following expression for the CEP [

Taking the derivative of the CEP, we can write

An exact expression of the average BER for the considered modulations can be obtained by introducing (

Although the error rate expression (

It can be observed in (

The ergodic capacity of the channel

When MRC is performed at the receiver and there is a single transmit antenna, it is known that correlation has a detrimental effect on capacity [

In order to simplify our analysis, let us consider the case of constant correlation, denoted as

A general treatment of (

In order to study the effect of correlation on capacity, we calculate the derivative of capacity with respect to

To study the monotonicity of capacity, the capacity derivative given in (

Derivative of ergodic capacity versus correlation coefficient

Derivative of ergodic capacity versus average SNR per branch for low correlation (

In this section, numerical results are presented for the BER as well as for the channel capacity of the analyzed TAS/MRC scheme. Monte Carlo simulations have also been carried out showing an excellent agreement with the analytical results.

Figure

Average BER versus average SNR per receive antenna with BPSK modulation for

Figures

Ergodic capacity versus constant correlation parameter

Ergodic capacity versus constant correlation parameter

Probability density function of output SNR for a given transmit antenna (

Figure

Ergodic capacity versus average SNR per receive antenna;

We have presented novel closed-form expressions for the pdf and CDF of the output SNR of TAS/MRC systems in Rayleigh fading with arbitrarily correlated receive antennas. Additionally, a novel closed-form expression has been derived for the average BER under several modulation techniques, and the corresponding asymptotic expression is also presented. Our results show that antenna correlation has always a detrimental impact on BER except for very low average SNR per receive antenna. We have also studied the impact of correlation on ergodic capacity and we have shown that correlation may have a beneficial impact on ergodic capacity of TAS/MRC systems due to the antenna selection performed at the transmitter, as a higher variability of the output signal increases the probability that a transmit antenna in good fading conditions is selected for transmission. As a consequence, the capacity will increase as receive antenna correlation increases if the number of transmit antennas is high enough.

We will follow the framework provided in [

First, let us consider that a single transmit antenna

The pdf of the random variable

When transmit antenna selection is performed, the CDF of the output SNR at the origin can thus be written as

Note that (

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work has been supported by European FEDER funds and the Spanish Ministry of Economy and Competitiveness (Grant TEC2009-13763-C02-01).