Single carrier cyclic prefixed (SCCP) communications are a close relative of multicarrier communications. Both types of systems are robust to multipath, provided that the channel delay spread is shorter than the guard interval between transmitted blocks. If this condition is not met, a channel shortening equalizer can be used to shorten the channel to the desired length. Previous work on channel shortening has largely been in the context of digital subscriber lines, a wireline system that allows bit allocation, thus it has focused on maximizing the bit rate for a given bit error rate (BER). We propose and evaluate a channel shortener that attempts to directly minimize the BER for an SCCP system. The problem is shown to be analytically distinct from the analogous problem in multicarrier systems.

In a previous paper, we proposed a bitrate maximizing (BM) design criterion for the time-domain equalizer (TEQ) in a discrete multitone receiver. This BM-TEQ and the closely related BM per-group equalizers (PGEQ) get close to the performance of the so-called per-tone equalization (PTEQ). In this paper, we show that the BM-TEQ criterion, despite its nonlinear nature, is well suited for a recursive Levenberg-Marquardt (RLM) based design. This adaptive BM-TEQ also allows us to track slow variations of the transmission channel and the noise. This RLM-based design uses the same second-order statistics (SOS) as the earlier presented recursive least-squares (RLS) based adaptive PTEQ and opens up a complete range of adaptive BM equalizers: from the computationally efficient RLS-based PTEQ with largest memory cost, over the RLM-based BM-PGEQ with intermediate memory cost, towards an RLM-based BM-TEQ with considerably smaller memory cost, but larger equalizer updating complexity.

A time-domain equalizer (TEQ) is inserted in discrete multitone (DMT) receivers to impose channel shortening. Many algorithms have been developed to initialize this TEQ, but none of them really optimizes the bitrate. We present a truly bitrate-maximizing TEQ (BM-TEQ) cost function that is based on an exact formulation of the subchannel signal-to-noise ratio as a function of the TEQ taps. The performance of this BM-TEQ comes close to the performance of the per-tone equalizer.

Discrete multi tone (DMT) uses an inverse discrete Fourier transform (IDFT) to modulate data on the carriers. The rather high side lobes of the IDFT filter bank can lead to spurious emissions in unauthorised frequency bands. Applying a window function within the DMT symbol alleviates this, but introduces distortions that are generally not easy to compensate. In this paper a special class of window functions is derived for which this compensation only requires a modest amount of processing at the receiver.

Discrete multitone (DMT) offers an elegant way to achieve high capacity, dividing the spectrum into small bands and processing these individually. The per tone equalizer (PTEQ) optimizes the capacity for each band individually, thus optimizing the whole. However, it provides little protection against narrow band radio frequency interference (RFI), being spread over all tones because of the high side lobes of the DFT filter band used in the receiver. The use of windowing functions limits this noise spreading, but is difficult to combine with the PTEQ. This paper describes a method to combine the PTEQ with a raised cosine window, while keeping the complexity reasonable. Extensions to other windowing functions are also given.

A time-domain equalizer (TEQ) is inserted in discrete multitone (DMT) receivers to impose channel shortening and hence overcome the need for a too long cyclic prefix. Many algorithms have been developed to initialize this TEQ, but none of them really optimizes the bitrate. In this paper, we present a new bitrate maximizing TEQ (BM-TEQ), cost function that results in a TEQ design/initialization that outperforms any other TEQ design. In the derivation, we exploit the fact that the frequency-domain equalizers (FEQ) do not alter the SNR on the individual tones. The performance of this BM-TEQ comes close to the performance of the per-tone equalizer (PTEQ), an alternative DMT equalization structure that ensures consistently better performance than a TEQ. Finally, the presented BM-TEQ design is also used in a "per group" equalization scheme (PGEQ), which is intermediate (in terms of memory requirement and performance) between TEQ and PTEQ. The PGEQ design then encompasses BM-TEQ and PTEQ design procedures as extreme cases.

In the past, several papers have reported on echo canceller (EC) structures developed for discrete multitone transmission (DMT) based asymmetric digital subscriber lines (ADSL) transmission. The most commonly known scheme, developed by Ho, Cioffi and Bingham, is based on canceling the received echo noise efficiently in times as well as in the frequency domain. The time domain processing part, which is commonly called cyclic echo synthesis (CES), can be minimized by choosing the optimal temporal alignment between the echo transmitter and the EC in the modem. This paper improves previously published work by minimizing the CES complexity without choosing a specific temporal alignment. Moreover, the obtained structure is highly suitable for making the update process of the echo canceller coefficients independent of the far end signal, leading to improved convergence behavior.

Recently, an alternative receiver structure was presented for discrete multitone (DMT)-based systems. The traditional structure consisting of a (real) time domain equalizer (TEQ) with a (complex) 1-tap frequency domain equalizer (FEQ) per tone is modified into a structure with a (complex) multitap FEQ per tone. The signal-to-noise ratio (SNR) for each individual tone is maximized, hence the term "per tone equalization". Here, we derive an equalization scheme for DMT-based systems in an alternative way. We start from the assumption that the transmission channel to equalize has an infinite impulse response (IIR) or pole-zero model. We conclude that, under certain numerator and denominator conditions, the per tone equalizer is a close approximation of the optimal minimum mean square error (MMSE) equalizer. In case the numerator order condition is not fulfilled, we propose a low-complexity generalization of the per tone equalizer. This generalization is based on a suboptimal MMSE criterion and exploits transmit redundancy introduced by means of pilot and/or unused tones. We evaluate the performance of the new, generalized per tone equalizer in an ADSL context. The principles are applicable to OFDM as well.