Low Complexity Phase-Unaware Detectors Based on Estimator-Correlator Concept

Our goal is to present an overview of a class of low complexity detectors working in linear fading multipath channels. In addition, we present briefly a unified theory based on the optimal maximum a posteriori probability (MAP) receiver concept (Woodward & Davies, 1952), which in additive Gaussian noise leads to the estimator-correlator receiver (Price, 1956; Middleton, 1957; Kailath, 1960; Kailath, 1969). The terms receiver and detector are interchangeable. Detectors are estimators where the parameter or symbol set to be estimated is discrete (Kay, 1993; Kay, 1998). We consider phase-unaware detectors (PUDs) such as differentially coherent detector (DD), noncoherent detector (ND), and energy detector (ED). The term PUD is used to emphasize that the receiver does not have any knowledge of the absolute phase of the received signal although it may have some knowledge of the internal phase structure. We use the term noncoherent to represent a special case of PUD system, and this will be clarified later. PUD detectors are more robust than coherent detectors in a fading multipath channel since the carrier phase of a signal with a wide bandwidth or high carrier frequency may be difficult to estimate with a low complexity. Earlier extensive reviews include (Schwarz et al., 1966; Van Trees, 1971) and more recently (Garth & Poor, 1994; McDonough & Whalen, 1995; Proakis, 2001; Mämmelä et al., 2002; Simon & Alouini, 2005; Witrisal et al., 2009). A summary of the estimator-correlator receiver is presented in (Kay, 1998). Unless stated otherwise, we exclude equalizers which increase the complexity of the receiver significantly (Lodge & Moher, 1990; Colavolpe & Raheli, 1999). Thus we avoid intersymbol interference (ISI) by signal design and concentrate on the reception of a single symbol, which may include several bits in 警-ary communications. It is, however, conceptually straightforward to generalize the single symbol or “one-shot”detectors to symbol sequence detection by replacing the symbols by symbol sequences. The noise is assumed to be additive white Gaussian noise (AWGN). The frequency offset caused by the channel is assumed to be known and compensated. We also assume that the receiver is synchronous in the sense that the start of each symbol interval is known. Estimation of frequency and timing is a highly nonlinear problem, which is studied in (Mengali & D’Andrea, 1997; Meyr et al., 1998), see also (Turin, 1980). Also because of complexity reasons in general we exclude coherent detectors which are such that they assume that the alternative received