This paper proposes performance improvement schemes for non-coherent multiple-input multiple-output (MIMO) communication systems employing per transmit antenna differential mapping (PADM). PADM is one form of differential space-time coding (DSTC), which generates an independent differentially encoded sequence for each of the multiple transmit antennas by means of space-time coding and mapping. The features of the proposed schemes are as follows: 1) it employs an asymmetric space-time mapping instead of the conventional symmetric space-time mapping in order to lower the required signal to noise power ratio (SNR) for maintaining the bit error rate (BER) performance; 2) it employs an analytically derived branch metric criterion based on channel prediction for per-survivor processing (PSP) in order to track fast time-varying channels. Finally, computer simulation results confirm that the proposed schemes improve the required SNR by around 1dB and can track at the maximum Doppler frequency normalized by symbol rate of 5%.