Performance Bounds for Combined Channel Coding and Space-Time Block Coding with Receive Antenna Selection

This paper studies the performance of the concatenation of an outer channel code with an orthogonal space-time block code (STBC), where the outer code can be a convolutional code (CC) or a trellis-coded modulation (TCM) code. In particular, we derive upper bounds on the bit error rate (BER) for this concatenation scheme with receive antenna selection. In our analysis, we assume that 1) the receiver uses only L out of the available M receive antennas, where, typically, L <= M, 2) the selected antennas are those that maximize the instantaneous received signal-to-noise ratio (SNR), 3) the channel state information is perfectly known at the receiver, 4) the underlying channel is fully interleaved, and 5) the underlying orthogonal STBC is full-rate. We derive an explicit upper bound on the BER for the above concatenation scheme for any N, M and L, where N denotes the number of transmit antennas. We show that the diversity order, with antenna selection, is the same as that of the full complexity system, whereas the deterioration in SNR is upper bounded by 10 log(10) (M/L) dB. We also derive a tighter upper bound on the BER for the Alamouti scheme when the receiver uses the best antenna, i.e., L = 1. These upper bounds can be extended in a straightforward manner to other types of outer codes and fading channels, including fast, block and slow fading channels. Finally, we present simulation results that validate our analysis.