Improved Demodulation of Phase Shift Keyed Signals Using Wavelet Thresholding

Abstract

In this study the use of wavelet transform-based techniques to de-noise Phase Shift Keyed (PSK) signals is investigated. Specifically, Binary Phase Shift Keyed (BPSK), Quadrature Phase Shift Keyed (QPSK) and 8-PSK signals are considered in the presence of Additive White Gaussian Noise (AWGN). Wavelet-domain decomposition of the received signals is carried out via the Discrete Wavelet Transform (DWT). The Haar, Daubechies5, Coiflet5 and Symmlet4 wavelets are used, along with both hard-and soft-thresholding techniques. The improvements realized by matched filter-based demodulation in conjunction with the use of wavelet thresholding techniques are shown by Bit Error Rate (BER) curves for each of the three modulation schemes. It has been found that by using appropriate wavelets and wavelet thresholding methods improvements in BER of over three orders of magnitude are achievable within the range of bit energy-to-noise spectral density ratios ( ) b 0 E N from -5 dB to 8 dB.Index Terms-Phase shift keying, wavelet transforms, matched filters, noise.

A Study on Performance Analysis for Error Probability in SWSK Systems

“…Let the signal processing functions of the high pass filters and the low pass filters be denoted by the operators H and G. Now let {h(k)} be a square-summable sequence of coefficients which defines the linear operator H, and similarly {g(k)} for G. The relationship between the mother wavelet, the scaling function and the filter coefficients are defined as [7] …”

“…Recently some attempts have been made to apply the wavelet transform in digital communication [6] [7]. Reference [8] provides the modulation scheme which uses the mother wavelet instead of the carrier frequency such as phase shift keying.…”

Performance analyses of communications receivers employing wavelet-domain minimum mean-squared error equalizers

“…ECENTY there have been several investigations into whether the mathematical technique of wavelet transforms provides any advantage in the processing of digitally modulated communications signals [1][2][3][4][5]. In these investigations two wavelet-based signal processing strategies have been identified as being especially promising.…”

“…The first is the strategy of wavelet-based de-noising of received digitally modulated signals that have been corrupted with AWGN [1]. It has been seen that pre-conditioning of such signals with a de-noising step prior to traditional matched filtering and demodulation results in the significant reduction of symbol errors.…”

“…One example is the case of Phase Shift Keyed (PSK) signals that were de-noised using wavelet-based techniques prior to matched filtering. It was found that Symbol Error Rates (SERs) were reduced by up to three orders of magnitude at Signal-to-Noise Ratios (SNRs) of 0 dB [1].…”