Optimal receive filter design under similarity constraint in coloured noise

This study considers the design of optimal receive filter under similarity constraint in coloured noise and compares it with signal design methods and conventional schemes. Similarity constraint restricts the sought-after filter to be close to the transmit waveform to control the output sequence envelope, avoiding potential risks of poor range solution and high sidelobes of whitening filter (WF) in severe coloured noise. The detailed solution to this constrained optimisation problem is provided. Then, the authors compare the filter design (FD) with the schemes of conventional or designing signal based on the matched/whitening filter. Five schemes are analysed on their performances of output signal-to-noise ratio, sequence control and requirements for practical applications. The merits of five schemes are concluded. In simulations, comparison between the designed filter and whitening filter illustrates the necessity of similarity constraint. FD under similarity constraint is regarded as a robust scheme for output sequence envelope control, easy to implement for coloured noise suppression.