Harmonic mean of squared product distances: a new criterion to design codes for independent fading channels

A new performance criterion which is called harmonic mean of squared product distances (HMSPD) to design codes for an independent fading channel is proposed. The bound on symbol error probability due to HMSPD criterion is shown to be tighter than the one due to the popular minimum product distance (MPD) criterion. HMSPD criterion is applied to obtain the optimum pre-rotating matrices for a BPSK transmission over a fast fading channel. The optimum 2/spl times/2 pre-rotating matrix is derived analytically and a new ad-hoc method is proposed to do numerical optimization for rotation matrices of higher dimensions. The BER performance of the codes designed using them is compared with that of the one designed based on the MPD criterion. The HMSPD criterion gives a slightly better performance.