Maximum a-Posteriori Equalizer for Sparse Walsh Hadamard Modulation

Several waveforms have been recently proposed in the literature as alternatives to orthogonal frequency division multiplexing (OFDM) for frequency selective channels. However, in order to achieve a superior performance, it is necessary to employ iterative equalization. In this paper, we consider the sparse Walsh-Hadamard (SWH) waveform with maximum a-Posterior (MAP) equalization. We show that the inherent structure of the SWH matrix allows a significant reduction in the number of multiplications required for the MAP equalizer implementation. The proposed solutions is compared with the zero padding single carrier (ZP-SC) with MAP equalization. We show that SWH with MAP equalization achieves a good trade-off performance vs complexity compared with ZP-SC. In particular, for 16-QAM under the Proakis C channel, ZP-SC is not even feasible while SWH with MAP equalization has manageable complexity.