Colin F. N. Cowan

The application of nonlinear structures to the reconstruction of binary signals

The problem of reconstructing digital signals which have been passed through a dispersive channel and corrupted with additive noise is discussed. The problems encountered by linear equalizers under adverse conditions on the signal-to-noise ratio and channel phase are described. By considering the equalization problem as a geometric classification problem the authors demonstrate how these difficulties can be overcome by utilizing nonlinear classifiers as channel equalizers. The manner in which neural networks can be utilized as adaptive channel equalizers is described, and simulation results which suggest that the neural network equalizers offer a performance which exceeds that of the linear structures, particularly in the high-noise environment, are presented. >

An LMS style variable tap-length algorithm for structure adaptation

Searching for the optimum tap-length that best balances the complexity and steady-state performance of an adaptive filter has attracted attention recently. Among existing algorithms that can be found in the literature, two of which, namely the segmented filter (SF) and gradient descent (GD) algorithms, are of particular interest as they can search for the optimum tap-length quickly. In this paper, at first, we carefully compare the SF and GD algorithms and show that the two algorithms are equivalent in performance under some constraints, but each has advantages/disadvantages relative to the other. Then, we propose an improved variable tap-length algorithm using the concept of the pseudo fractional tap-length (FT). Updating the tap-length with instantaneous errors in a style similar to that used in the stochastic gradient [or least mean squares (LMS)] algorithm, the proposed FT algorithm not only retains the advantages from both the SF and the GD algorithms but also has significantly less complexity than existing algorithms. Both performance analysis and numerical simulations are given to verify the new proposed algorithm.

A low-complexity soft-MIMO detector based on the fixed-complexity sphere decoder

This paper presents a soft-output version of the fixed-complexity sphere decoder (FSD) previously proposed for uncoded multiple input-multiple output (MIMO) detection. Thus, the soft-FSD (SFSD) can be used in turbo-MIMO systems to exchange extrinsic soft-information with the outer decoder. For that purpose, the SFSD generates a list of candidates that approximates that of the list sphere decoder (LSD) while containing information about all the possible bit values, removing the need for clipping. In addition, it overcomes the two problems of the LSD: its variable complexity and the sequential nature of its tree search. Simulation results show that the SFSD can be used to approximate the performance of the LSD while having a considerably lower and fixed complexity, making the algorithm suitable for hardware implementation.

High Speed FPGA-Based Implementations of Delayed-LMS Filters

A variation of the least means squares (LMS) algorithm, called the delayed LMS (DLMS) algorithm is ideally suited for highly pipelined, adaptive digital filter implementations. In this paper, we present an efficient method to determine the delays in the DLMS filter. Furthermore, in order to achieve fully pipelined circuit architectures for FPGA implementation, we transfer these delays using retiming. The method has been used to derive a series of retimed delayed LMS (RDLMS) architectures, which allow a 66.7% reduction in delays and 5 times faster convergence time thereby giving superior performance in terms of throughput rate when compared to previous work. Three circuit architectures and three hardware shared versions are presented which have been implemented using the Virtex-II FPGA technology resulting in a throughput rate of 182 Msample/s.

An adaptive Kalman equalizer: Structure and performance

The development of an adaptive infinite impulse response (IIR) linear equalizer is described. Using discrete time Wiener filtering theory, a closed form for the optimum mean-square error IIR filter is derived. A performance comparison using both minimum and non-minimum phase channels indicates the complexity/performance advantages inherent in the IIR system compared to an optimum finite impulse response (FIR) solution. The minimum phase spectral factorization, which is an integral part of the derivation of the IIR equalizer, may be circumvented through the use of a Kalman equalizer such as that originally proposed by Lawrence and Kaufman. The structure is made adaptive by using a system identification algorithm operating in parallel with a Kalman equalizer. In common with Luvison and Pirani, a least mean squares (LMS) algorithm was chosen for the system identification because the input to the channel is white and hence the LMS algorithm will produce consistent predictable results with little added complexity. A new technique is introduced which both estimates the variance of channel noise and compensates the Kalman filter for errors in the estimate of the channel impulse response. Computer simulation results show that the convergence performance of this new adaptive IIR filter is roughly equivalent to an FIR equalizer which is trained using a recursive least squares algorithm. However, the order of the new filter is always lower than the FIR filter.

Convergence and tracking analysis of a variable normalised LMF (XE-NLMF) algorithm

The least-mean-fourth (LMF) algorithm is known for its fast convergence and lower steady state error, especially in sub-Gaussian noise environments. Recent work on normalised versions of the LMF algorithm has further enhanced its stability and performance in both Gaussian and sub-Gaussian noise environments. For example, the recently developed normalised LMF (XE-NLMF) algorithm is normalised by the mixed signal and error powers, and weighted by a fixed mixed-power parameter. Unfortunately, this algorithm depends on the selection of this mixing parameter. In this work, a time-varying mixed-power parameter technique is introduced to overcome this dependency. A convergence analysis, transient analysis, and steady-state behaviour of the proposed algorithm are derived and verified through simulations. An enhancement in performance is obtained through the use of this technique in two different scenarios. Moreover, the tracking analysis of the proposed algorithm is carried out in the presence of two sources of nonstationarities: (1) carrier frequency offset between transmitter and receiver and (2) random variations in the environment. Close agreement between analysis and simulation results is obtained. The results show that, unlike in the stationary case, the steady-state excess mean-square error is not a monotonically increasing function of the step size.

A self-orthogonalizing efficient block adaptive filter

This paper deals with the development of a unique self-orthogonalizing block adaptive filter (SOBAF) algorithm that yields efficient finite impulse response (FIR) adaptive filter structures. Computationally, the SOBAF is shown to be superior to the least mean squares (LMS) algorithm. The consistent convergence performance which it provides lies between that of the LMS and the recursive least squares (RLS) algorithm, but, unlike the LMS, is virtually independent of input statistics. The block nature of the SOBAF exploits the use of efficient circular convolution algorithms such as the FFT, the rectangular transform (RT), the Fermat number transform (FNT), and the fast polynomial transform (FPT). In performance, the SOBAF achieves the mean squared error (MSE) convergence of a self-orthogonalizing structure, that is, the adaptive filter converges under any input conditions, at the same rate as an LMS algorithm would under white input conditions. Furthermore, the selection of the step size for the SOBAF is straightforward as the range and the optimum value of the step size are independent of the input statistics.

Rapid Prototyping of Clarkson's Lattice Reduction for MIMO Detection

This paper presents the field-programmable gate array (FPGA) implementation of a variant of the Lenstra-Lenstra-Lovasz (LLL) lattice reduction (LR) algorithm, known as the Clarksons Algorithm (CA), and its application to uncoded multiple input-multiple output (MIMO) detection. The CA provides practically the same performance as the LLL algorithm while having a considerably lower complexity, especially for MIMO systems with a large number of transmit and receive antennas. The algorithm has been implemented in real-time using a rapid prototyping methodology, greatly reducing its development time. Implementation results indicate that the variable complexity and the sequential nature of LR algorithms, like the CA, remain their main drawbacks from an implementation point of view.

HOS-Based Semi-Blind Spatial Equalization for MIMO Rayleigh Fading Channels

In this paper, we concentrate on the direct semi-blind spatial equalizer design for MIMO systems with Rayleigh fading channels. Our aim is to develop an algorithm which can outperform the classical training-based method with the same training information used and avoid the problems of low convergence speed and local minima due to pure blind methods. A general semi-blind cost function is first constructed which incorporates both the training information from the known data and some kind of higher order statistics (HOS) from the unknown sequence. Then, based on the developed cost function, we propose two semi-blind iterative and adaptive algorithms to find the desired spatial equalizer. To further improve the performance and convergence speed of the proposed adaptive method, we propose a technique to find the optimal choice of step size. Simulation results demonstrate the performance of the proposed algorithms and comparable schemes.

A comparison of complex lattice reduction algorithms for MIMO detection

The performance and complexity of two complex lattice reduction (LR) algorithms used in multiple input-multiple output (MIMO) detection are compared in this paper. The Seysens Algorithm (SA) has been previously proposed as a low-complexity alternative to the real version of the Lenstra-Lenstra-Lovasz (LLL) algorithm while providing a better performance in LR-aided linear detectors. However, this paper shows that the SA has a higher complexity than the complex version of the LLL algorithm, due to its more computationally intensive preprocessing stage and its higher complexity per iteration. In addition, both the SA and the complex LLL algorithm provide practically the same performance when used in LR-aided successive interference cancellation (SIC) detectors.