A method for performance comparison of generator matrices in wireless communication

Space-Time Trellis Code (STTC) is a wireless communication system that can provide both diversity and coding gain. Since Tarokh discovered STTC in 1998, a considerable effort has been done to improve the performance of the original STTC. One way of achieving enhancement is by focusing on the generator matrix G. The generator matrix G represents the encoder structure for STTC. Having a generator matrix G of higher quality implies a better STTC transmission system. Until now, researchers have only concentrated on STTC of different states in analysing the performance of generator matrix G. No effort has been made on different generator matrices G of similar state. It is because no algorithm available to produce a wide variety of generator matrices G with diverse minimum determinants. Hence, the performance of generator matrices G of similar state with different minimum determinant (MD) is to be analysed. A number of generator matrices G with minimum determinant of four (4), eight (8) and sixteen (16) of the same state have been successfully produced. A method was developed via coding to simulate and analyse the behaviour of different generator matrices G of similar state with different minimum determinant over a flat Rayleigh fading for a 4-PSK scheme in wireless communication system. The method will define the parameters and generator matrices G as well as establish the trellis diagram and generate the state diagram. The mapped output at the receiver will be used to evaluate the/performance of generator matrices G in terms of Bit Error Rate (BER) output against Signal-to-Noise Ratio (SNR). This research provides an early analysis of how the generator matrices G of varying minimum determinant would behave when the signal transmission is established in a similar state of trellis. From this research, it is found that generator matrices G with minimum determinant of sixteen (16) has achieved a better performance relative to the generator matrices G with minimum determinant of eight (8). However at certain extent, increasing the minimum determinant will merely give an insignificant contribution to the improvement of the performance when only one receive ntenna is used and this was shown by the performance of generator matrices G with minimum determinant of four (4). They achieve a better performance relative to the generator matrix G with minimum determinant of sixteen (16). This research can be used as a platform for future studies that employing multiple receive antennas.

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