Asymptotic analysis of precoded OFDM with hierarchical modulation

This paper investigates the bit error rate (BER) performance of hierarchically modulated precoded Orthogonal Frequency Division Multiplexing (OFDM). We consider a low priority stream modulated on top of a high priority stream with a constellation ratio a and analyze the resulting BER performance. Since the BER depends in a complex way on the particular precoding matrix used, it is difficult for one to gain direct insight into the performance of the hierarchically modulated system. We overcome this difficulty by resorting to the framework of large system analysis [1] in order to derive the asymptotic expression of the BER of the Minimum Mean Squared Error (MMSE) receiver. Assuming that the entries of the precoding matrix are independent and identically distributed (i.i.d) random variables, we derive the limit BER for the 4QAM and the 16QAM low priority stream cases. The limit BER is obtained by assuming that the number of OFDM sub-carriers and the number of OFDM symbols tend to infinity at the same rate. We show that the limit BER is independent of the particular realizations of the precoding matrix. Simulation results show that the asymptotic expression perfectly matches the empirical results obtained for FFT sizes as low as 256 in different channel conditions. We then use the asymptotic expression to gain useful insights into the effect of the different configuration parameters on the system performance.