Low-Complexity Joint-MMSE GFDM Receiver

Generalized frequency division multiplexing (GFDM) is one of the new waveforms with several attractive features such as lower out of band radiation, higher spectral efficiency, and better immunity to carrier frequency offset errors as compared with orthogonal frequency division multiplexing. However, it requires receivers with high computational complexity. Among different linear receiver structures, the joint minimum mean square error (joint-MMSE) receiver for GFDM achieves the best bit-error-rate (BER) performance, but it is the most computationally complex linear receiver. In this paper, we present a novel low complexity joint-MMSE receiver. We derive the closed-form expression for the joint-MMSE receiver filter by harnessing circulant properties of the matrices involved in the demodulation process. Amidst different operations involved in the receiver processing, inversion of a positive definite circulant-plus-diagonal matrix is found to be the costliest. Two low-complexity algorithms for the inversion of a positive definite circulant-plus-diagonal matrix are developed to design the low complexity receiver. We also propose a low complexity bias correction to improve BER performance. Our proposed receiver achieves a log-linear order of complexity without any noticeable loss in BER performance.