Performance Analysis of Maximal-Ratio Transmission/Receive Antenna Selection in Nakagami- $m$ Fading Channels With Channel Estimation Errors and Feedback Delay

This paper focuses on multi-antenna systems that employ both maximal-ratio transmission and receive antenna selection (MRT&RAS) in independent and identically distributed Nakagami-
$m$
flat-fading channels with channel estimation errors (CEE) [or feedback quantization errors (FQE)] and feedback delay (FD). Useful statistics of the postprocessing signal-to-noise ratio (SNR) such as the probability density function, cumulative distribution function, moment-generating function, and
$n$
th-order moments are presented. To examine the capacity and the error performances of the MRT&RAS scheme, ergodic capacity, outage probability, and bit error rates/symbol error rates (BERs/SERs) for binary and
$M$
-ary modulations are analyzed. Exact analytical expressions for all the performance metrics are separately derived for practical situations that consist of CEE (or FQE) and FD, as well as ideal estimation and feedback conditions. By considering approximations for the statistics of the postprocessing SNR, it is shown that, at high SNRs, the investigated system achieves full-diversity orders in the ideal case, whereas it keeps maintaining receive diversity at practical impairments. The performance superiority of the MRT&RAS scheme to other diversity schemes is also shown by numerical comparisons. In addition, analytical performance results related to the outage probability and BERs/SERs are validated by Monte Carlo simulations.