Application of the Joint Fast Walsh Hadamard-Inverse Fast Fourier Transform in a LDPC Coded OFDM Wireless Communication System: Performance and Complexity Analysis

An efficient low complexity T transform which combines the Walsh Hadamard Transform and Discrete Fourier Transform (DFT) into a single fast orthonormal unitary transform is considered for the application in low density parity check coded orthogonal frequency division multiplexing (LDPC-OFDM) across additive white Gaussian noise channel model and multipath fading channel models. The T-transform is developed through the sparse matrices factorization method using Kronecker product scheme. T-transform based COFDM system, which is capable of reducing peak to average power ratio (PAPR) of the transmitted symbols and improving the bit error rate (BER) performance at a reasonable reduced complexity. Several signaling formats such as Quadrature phase shift keying and 16- ary Quadrature amplitude modulation (16-QAM) are considered. A T COFDM system is described which could provide an alternative to DFT-COFDM system, and is therefore a better alternative to balance the transform complexity, PAPR reduction and system performance. Simulation results are used to examine and compare the complexity, PAR and the BER performance of T-OFDM system and DFT-OFDM system. Numerical results show that the T-COFDM system outperforms the DFT-COFDM based in the multipath channel models.