Decoupling of the received signals and performance analysis for pre-coding orthogonal STBC systems

Starting from three transmit antennas and N_r receive antennas (3Tx-N_r Rx, generally defined as MIMO) system employing orthogonal space-time block coding (STBC-MIMO), the paper analyzes the solution procedure of complex orthogonal weighting channel matrix (OWCM) and decoupling method of the signals received for the resulting pre-coding system, and concludes an algorithm process using computer simulation to generate the complex OWCM. Employing the orthogonal OWEM, we can decouple easily received signals at receiver terminals. Utilizing such decoupled received signals, the paper provides a normal expression of the average output signal-noise-ratio (SNR) for the interest systems. Taking a sample of precoding 2Tx-1Rx STBC system, in the three cases of channel gain x₁ and x₂ are uncorrelated, order statistics x₁gesx₂, and the 2 out of 3 transmit antennas with x₁gesx₂gesx₃, respectively, the three exact closed-form bit error rate (BER) expressions are presented. According to these analytical BER expressions, 4 sets of curves are presented to illustrate the performance results. Except the case of x₁ and x₂ are uncorrelated / no order statistic, the numerical results show that perfect power allocation for transmit antennas selected can effectively enhance system bit error performance. Meanwhile, increasing transmit antennas power related to the best channel can improve obviously system error performance. But if k=W₁/W₂ is enough large, the BER performance improvement is not obvious, this conclusion makes guidance function for the MIMO systems of using pre-coding STBC technique.