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In this paper, we propose two groups of recursive codes, namely the Hadamard recursive carrier interferometry (HRCI) codes and diagonal recursive carrier interferometry (DRCI) codes, to simultaneously reduce the peak-to-average power ratio (PAPR) and suppress the phase noises and residual carrier frequency offset (RCFO) for high-speed orthogonal frequency division multiplexing (OFDM) systems. We exploit the recursion property of the Hadamard and diagonal matrices to constitute the proposed HRCI code and DRCI code using the carrier interferometry (CI) code, and present the system model in details to spread OFDM symbols in the frequency domain. Then, we prove that both HRCI and DRCI generation matrices keep their invertibility during the recursions. As a direct result of the new code design, the phase intervals are enlarged and the signals are shifted in the time domain, thus both the PAPR and the phase noises are reduced, and the RCFO can be mitigated. Moreover, the enlarged phase intervals enable the transceiver blocks including the channel estimator, which estimate the phase noise based on the received signals, to improve the performance. Furthermore, we present the expressions for the HRCI and DRCI embedded transmitted and received signals, and derive the analytical signal-to-interference-plus-noise ratio (SINR) expressions for bit error rate (BER) performance analysis. Then, we analyze the effects of presented codes on the phase differences and provide the computational complexity analysis. Numerical simulations verify the effectiveness of our theoretical analysis of SINR. Additionally, under different parameter settings, which consider the working conditions of practical systems, we demonstrate that the presented robust HRCI and DRCI coded OFDM systems can suppress the PAPR satisfactorily and better BER performances can be achieved by the recursive CI-aided spread OFDM systems with phase noise rejection and RCFO compensation when compared with counterpart systems.

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Recursive Carrier Interferometry Aided High Data Rate OFDM Systems With PAPR Suppression, Phase Noise Rejection, and Carrier Frequency Offsets Compensation