Linear WDE for performance enhancement of MIMO-OFDM system in the presence of Co-CFO

The Discrete Walsh Hadamard Transform (DWHT) has emerged as an efficient alternative to the Discrete Fourier Transform (DFT) for Orthogonal Frequency Division Multiplexing (OFDM) implementations, particularly in handling channel impairments. In this article, we proposed an efficient Joint Low Complexity Regularized Zero Forcing-Wavelet Domain Equalizer (JLCRLZF-WDE) to replace the traditional Frequency Domain Equalizer (FDE) in DWHT-OFDM systems. Unlike FDE, which requires additional DFT and Inverse DFT (IDFT) computations, the proposed JLCRLZF-WDE directly operates in the Walsh domain, effectively mitigating the computational overhead. The derivation of the proposed JLCRLZF-WDE equations take the effect of the channel, Co-Carrier Frequency Offset (Co-CFO), as well as the noise into account. During the derivation of the system model equations, we assume a Multiple-Input-Multiple-Output (MIMO)-OFDM communication system through a Rayleigh fading channel. The Bit Error Rate (BER) performance and computational complexity of the proposed and the conventional algorithms are compared, indicating the significance of the proposed algorithm. Simulation results confirm the superiority of the proposed equalizer, demonstrating a 23.68%–28.4% reduction in computational complexity compared to Minimum Mean Square Error (LMMSE)-FDE based on DFT, while maintaining comparable BER performance at various MIMO configuration. Furthermore, at a BER of 10⁻⁴, the JLCRLZF-WDE achieves performance parity with conventional Walsh domain LMMSE equalizers, whereas other equalizers require an additional Signal-to-Noise Ratio (SNR) of 3.06 dB to achieve the same performance.