Analysis of diversity order and performance for phase hop diversity in rayleigh fading channel

In this paper, the performance of phase hop diversity in multiple input multiple output (MIMO) wireless system is researched. We get the diversity order of the phase hop diversity (PHD) according to the definition of diversity order and discuss the diversity order in different cases. Although diversity order is an important parameter to evaluate the performance of a communication system using diversity, but the diversity order can only be the performance of the PHD when the SNR (signal-to-noise ratio) is higher, so we consider the performance of PHD when the SNR is lower too. Furthermore, we get the up bound for performance of the (PHD) when the channel state information (CSI) is known and not known at transmitter, respectively, by transforming the problem of cost function of the PEP (pairwise error probability) into a maximum the determinant of a matrix. At last, the problem is resolved by using the maximum trace with constraint.