Understanding the Ber-performance of Space-time Block Codes

In this paper we show that in the case of general Space-Time Block Codes (STBC) not only the Pairwise Error Probabilities (PEPs) between nearest neighboring code words have to be considered to evaluate the total Bit Error Ratio (BER) performance of the STBC. It turns out that code word pairs differing in a rather large large number of positions typically lead to rank deficient Distance Matrices (DMs) causing a severe diversity loss and thus deteriorate the total BER performance in Rayleigh fading wireless Multiple InputMultiple Output (MIMO) channels especially at high Signal to Noise Ratio (SNR) levels. In the special case of orthogonal codes from the Generalized Complex Orthogonal Design (GCOD), nearest neighbor code word errors dominate the BER-curve and no diversity loss at high SNR occurs.