Reduced Receivers for Faster-than-Nyquist Signaling and General Linear Channels

Fast and reliable data transmission together with high bandwidth efficiency are important design aspects in a modern digital communication system. Many different approaches exist but in this thesis bandwidth efficiency is obtained by increasing the data transmission rate with the faster-than-Nyquist (FTN) framework while keeping a fixed power spectral density (PSD). In FTN consecutive information carrying symbols can overlap in time and in that way introduce a controlled amount of intentional intersymbol interference (ISI). This technique was introduced already in 1975 by Mazo and has since then been extended in many directions. Since the ISI stemming from practical FTN signaling can be of significant duration, optimum detection with traditional methods is often prohibitively complex, and alternative equalization methods with acceptable complexity-performance tradeoffs are needed. The key objective of this thesis is therefore to design reduced-complexity receivers for FTN and general linear channels that achieve optimal or near-optimal performance. Although the performance of a detector can be measured by several means, this thesis is restricted to bit error rate (BER) and mutual information results. FTN signaling is applied in two ways: As a separate uncoded narrowband communication system or in a coded scenario consisting of a convolutional encoder, interleaver and the inner ISI mechanism in serial concatenation. Turbo equalization where soft information in the form of log likelihood ratios (LLRs) is exchanged between the equalizer and the decoder is a commonly used decoding technique for coded FTN signals. The first part of the thesis considers receivers and arising stability problems when working within the white noise constraint. New M-BCJR algorithms for turbo equalization are proposed and compared to reduced-trellis VA and BCJR benchmarks based on an offset label idea. By adding a third low-complexity M-BCJR recursion, LLR quality is improved for practical values of M. M here measures the reduced number of BCJR computations for each data symbol. An improvement of the minimum phase conversion that sharpens the focus of the ISI model energy is proposed. When combined with a delayed and slightly mismatched receiver, the decoding allows a smaller M without significant loss in BER. The second part analyzes the effect of the internal metric calculations on the performance of Forney- and Ungerboeck-based reduced-complexity equalizers of the M-algorithm type for both ISI and multiple-input multiple-output (MIMO) channels. Even though the final output of a full-complexity equalizer is identical for both models, the internal metric calculations are in general different. Hence, suboptimum methods need not produce the same final output. Additionally, new models working in between the two extremes are proposed and evaluated. Note that the choice of observation model does not impact the detection complexity as the underlying algorithm is unaltered. The last part of the thesis is devoted to a different complexity reducing approach. Optimal channel shortening detectors for linear channels are optimized from an information theoretical perspective. The achievable information rates of the shortened models as well as closed form expressions for all components of the optimal detector of the class are derived. The framework used in this thesis is more general than what has been previously used within the area

Receivers for faster-than-Nyquist signaling with and without turbo equalization

Faster-than-Nyquist (FTN) signaling is a trellis coding method that maintains the error rate while reducing signal bandwidth. The combined effect is to move closer to capacity. We study some basic receiver issues: How to model the signaling efficiently in discrete time, how much the Viterbi receiver can be truncated, and how to combine the method with an outer code. The methods are modeling for minimum phase, minimum distance calculation and receiver tests. Concatenated FTN in a turbo equalization scenario proves to be a strong coding method

New reduced state space BCJR algorithms for the ISI channel

A critical component in detection under intersymbol interference (ISI) and in turbo equalization is the BCJR algorithm. We study two approaches to reducing its computation. First, the state space is reduced by optimizing the receiver's phase-maximizing all pass filter. Then the state space used by the BCJR calculation is reduced by breaking the state into an offset and a main state. These procedures are demonstrated by ISI detection and turbo equalization over strongly bandlimited channels

Faster-than-Nyquist modulation based on short finite pulses

We investigate faster-than-Nyquist modulation based on short finite pulses over the AWGN channel. We consider several pulse shapes and compare their information rates for several system setups. We compare the effect of increasing the alphabet size versus of increasing the signaling rate. The outcome is that for these pulses the FTN symbol rate is of greater importance than the alphabet size. Finally we test some concatenated coding schemes where faster-than-Nyquist modulation constitutes the innermost encoder; the outcome is very good

P O B o x 1 1 7 2 2 1 0 0 L u n d + 4 6 4 6 -2 2 2 0 0 0 0 Turbo equalization and an M-BCJR algorithm for strongly narrowband intersymbol interference Turbo Equalization and an M-BCJR Algorithm for Strongly Narrowband Intersymbol Interference

Abstract-An M-BCJR algorithm is proposed and tested over an AWGN channel with moderate to very intense intersymbol interference (ISI). Two M-BCJR applications are evaluated, simple detection over the ISI channel and turbo equalization. The signaling is binary faster than Nyquist linear modulation. The ISI models tested correspond to transmission of increasingly many bits/Hz-s with a fixed signal spectra; the paper studies the range 2-8 bits/Hz-s, which implies ISI models as long as 32 taps. As a simple detector, the M-BCJR achieves the ML error rate with small computation, even when the Viterbi algorithm is completely impractical. In turbo equalization, the M-BCJR needs somewhat more computation and a more careful design because it must produce accurate likelihoods

Optimal Channel Shortening for MIMO and ISI Channels

We deal with the construction of optimal channel shortening, also known as combined linear Viterbi detection, algorithms for ISI and MIMO channels. In the case of MIMO channel shortening, the tree structure to represent MIMO signals is replaced by a trellis. The optimization is performed from an information theoretical perspective and the achievable information rates of the shortened models are derived and optimized. Closed form expressions for all components of the optimal detector of the class are derived. Furthermore, we show that previously published channel shortening algorithms can be seen as special cases of the derived model

Reduced-Complexity Receivers for Strongly Narrowband Intersymbol Interference Introduced by Faster-than-Nyquist Signaling

We propose new M-algorithm BCJR (M-BCJR) algorithms for low-complexity turbo equalization and apply them to severe intersymbol interference (ISI) introduced by faster than Nyquist signaling. These reduced-search detectors are evaluated in simple detection over the ISI channel and in iterative decoding of coded FTN transmissions. In the second case, accurate log likelihood ratios are essential and we introduce a 3-recursion M-BCJR that provides this. Focusing signal energy by a minimum phase conversion before the M-BCJR is also essential; we propose an improvement to this older idea. The new M-BCJRs are compared to reduced-trellis VA and BCJR benchmarks. The FTN signals carry 4-8 bits/Hz-s in a fixed spectrum, with severe ISI models as long as 32 taps. The combination of coded FTN and the reduced-complexity BCJR is an attractive narrowband coding method

Turbo equalization and an M-BCJR algorithm for strongly narrowband intersymbol interference

An M-BCJR algorithm is proposed and tested over an AWGN channel with moderate to very intense intersymbol interference (ISI). Two M-BCJR applications are evaluated, simple detection over the ISI channel and turbo equalization. The signaling is binary faster than Nyquist linear modulation. The ISI models tested correspond to transmission of increasingly many bits/Hz-s with a fixed signal spectra; the paper studies the range 2–8 bits/Hz-s, which implies ISI models as long as 32 taps. As a simple detector, the M-BCJR achieves the ML error rate with small computation, even when the Viterbi algorithm is completely impractical. In turbo equalization, the M-BCJR needs somewhat more computation and a more careful design because it must produce accurate likelihoods

A Comparison of Ungerboeck and Forney Models for Reduced-Complexity ISI Equalization

This paper investigates the performance of reduced-state trellis-based intersymbol interference equalizers, which are based on the so-called Ungerboeck and Forney observation models. Although the two models are equivalent when an optimum equalizer is employed, their performances differ significantly when using reduced-complexity methods. It is demonstrated that practical equalizers operating on the Forney model outperform those operating on the Ungerboeck model for high signal-to-noise ratios (SNRs), while the situation is reversed for low SNR levels. A novel reduced-complexity equalization strategy that improves on previous Ungerboeck-based equalizers is proposed