A low-complexity graph-based LMMSE receiver designed for colored noise induced by FTN-signaling

Abstract

Abstract-We propose a low complexity graph-based linear minimum mean square error (LMMSE) equalizer which considers both the intersymbol interference (ISI) and the effect of non-white noise inherent in Faster-than-Nyquist (FTN) signaling. In order to incorporate the statistics of noise signal into the factor graph over which the LMMSE algorithm is implemented, we suggest a method that models it as an autoregressive (AR) process. Furthermore, we develop a new mechanism for exchange of information between the proposed equalizer and the channel decoder through turbo iterations. Based on these improvements, we show that the proposed low complexity receiver structure performs close to the optimal decoder operating in ISI-free ideal scenario without FTN signaling through simulations.

A Low-Complexity Graph-Based LMMSE Receiver for MIMO ISI Channels With $M$ -QAM Modulation

“…3. Since finding the optimal scalar value requires exhaustive search for each different configuration, the method in [23] is not a practical solution either. Another method is to compute the extrinsic information (in terms of mean and variance) in Gaussian domain and obtain the extrinsic LLRs using this information [18].…”

“…However, applying the WP or JG approaches directly is computationally intensive for factor graphs. Although a simplified expression for extrinsic LLR computation was proposed in [17] for BPSK signaling only, there is no such a work for higher order constellations in the literature within the knowledge of the authors except the heuristic methods in [22], [23]. To fill up this gap, we derive a transformation from the graph outputs to the bit LLRs based on the WP approach for higher order modulation alphabets.…”

Iterative Joint Channel Estimation, User Activity Tracking, and Data Detection for FTN-NOMA Systems Supporting Random Access

“…It is widely recognized that the optimal receiver's complexity grows exponentially both with the number of ISI taps and with the number of users. Hence, several authors have developed low complexity receivers for FTN signaling [21]- [24] and NOMA [25]- [30]. To elaborate, in [21], an Malgorithm based Bahl-Cocke-Jelinek-Raviv (BCJR) detector was proposed by Prlja and Anderson for eliminating the ISI imposed by FTN signaling.…”

“…However, the insertion of cyclic prefices reduces the effective throughput. As a further result, in [24], the state space model of the received signal was represented by a Forney-style factor graph, which conveniently lent it self to the employment of the classic Gaussian message passing algorithm to detect the FTN symbols. Upon invoking multi-user detection (MUD) for NOMA, the conventional minimum mean squared error (MMSE) detector suffers from an excessive complexity due to the inversion of high-dimensional matrices.…”

Iterative Receiver Design for FTN Signaling Aided Sparse Code Multiple Access

“…However, the effects of colored noise were not considered in [23] and the CP will also degrade the efficiency while almost eliminate the gain of FTN signaling. A Forney-style factor graph based detector was proposed in [25] to handle the colored noise imposed by FTN signaling for transmission over AWGN channels. An extension to doubly selective channels is considered in [26] and [27], where Gaussian message passing and variational inference techniques are employed to detect the symbols, respectively.…”