Unified Performance Analysis of Transmit Antenna Selection with OSTBC and Imperfect CSI over Nakagami-m Fading Channels

A unified error analysis of multi-Antenna systems with orthogonal space-Time block coding (OSTBC) using transmit antenna selection (TAS) over Nakagami-m channels in the presence of feedback delay and channel estimation error is presented, where the number of transmit antennas is arbitrarily selected. For imperfect channel state information (CSI), the Nakagami-m channel is modeled as the sum of Nakagami-\hat{m} channel and independent Gaussian channel error. By this model, accurate and closed-form approximate bit error rate (BER) expressions of TAS-OSTBC for M-Ary quadrature amplitude modulation and M-Ary phase-shift keying are derived by using the moment generating function of received SNR. With the approximate BER formula, the number of antennas to be selected for transmission can be adapted by minimizing the BER of the system with imperfect CSI. The diversity and coding gains of TAS-OSTBC with K receive antennas and M antennas selected from N transmit antennas for transmission are analyzed at high SNR. For noninteger mK, the upper and lower bounds of the diversity gain for different CSI and estimation error scenarios are derived. But for integer mK, the results indicate that the upper and lower bounds are equal achieving the full diversity order of mKN for perfect CSI, zero diversity order and partial diversity order of mMK for estimation error variance being fixed and being a decreasing function of average SNR, respectively. The coding gain is affected by M, N , K, Nakagami parameter m, code rate, modulation, and channel correlation coefficients. Simulation results verify the validity of the theoretical analysis and effectiveness of the adaptive antenna selection scheme.