Abstract
Signal processing is a core technique in wireless communication and is important for the progress of sixth-generation (6G) systems. The linear processing has been widely applied and remains effective in standard scenarios. However, its performance is limited when signals exhibit statistical asymmetries. Widely linear processing (WLP) could systematically address these limitations. WLP could utilise pseudo-covariance and extended second-order statistics, which give more flexibility and higher robustness. This thesis studies WLP methods for equalisation and precoding in wireless systems. The main contributions are set out below.</p><p> </p><p> First, a widely linear post-distortion method is developed for satellite communications. Conventional approaches usually aim to mitigate hardware and channel impairments. The proposed method shows that hardware and channel impairments can instead be exploited to improve performance, which also addresses nonlinear distortions. Furthermore, traditional WLP relies on expected second-order statistics. This work instead employs instantaneous statistics, extending the applicability of WLP to a broader range of signals.</p><p> </p><p> Second, a precoding scheme based on WLP is proposed for multiple-input multiple-output (MIMO) downlink transmission. Conventional WLP is restricted to signals that are already improper. The proposed scheme introduces impropriety by transmitting conjugate-augmented symbols. This increases statistical diversity and improves mutual information (MI), enabling more efficient use of the available transmission resources.</p><p> </p><p> Third, a joint transceiver framework is introduced, which jointly optimises the WLP precoding and equalisation in MIMO systems. This joint design enhances the coordination between transmitter and receiver. Simulation results show that the joint framework yields an MI gain of up to 3 dB over conventional linear methods. The improvements remain consistent across different modulation schemes and antenna configurations.</p><p> </p><p> These contributions establish WLP as an effective framework for modern communication systems and highlight its potential to enhance the efficiency, adaptability, and robustness of future wireless networks. The work documented in this thesis goes beyond the state-of-the-art and makes valuable contributions to the field of widely linear processing.