George P. White

Low-Complexity RLS Algorithms Using Dichotomous Coordinate Descent Iterations

In this paper, we derive low-complexity recursive least squares (RLS) adaptive filtering algorithms. We express the RLS problem in terms of auxiliary normal equations with respect to increments of the filter weights and apply this approach to the exponentially weighted and sliding window cases to derive new RLS techniques. For solving the auxiliary equations, line search methods are used. We first consider conjugate gradient iterations with a complexity of operations per sample; being the number of the filter weights. To reduce the complexity and make the algorithms more suitable for finite precision implementation, we propose a new dichotomous coordinate descent (DCD) algorithm and apply it to the auxiliary equations. This results in a transversal RLS adaptive filter with complexity as low as multiplications per sample, which is only slightly higher than the complexity of the least mean squares (LMS) algorithm ( multiplications). Simulations are used to compare the performance of the proposed algorithms against the classical RLS and known advanced adaptive algorithms. Fixed-point FPGA implementation of the proposed DCD-based RLS algorithm is also discussed and results of such implementation are presented.

Improving the system capacity of broadband services using multiple high-altitude platforms

A method of significantly improving the capacity of high-altitude platform (HAP) communications networks operating in the millimeter-wave bands is presented. It is shown how constellations of HAPs can share a common frequency allocation by exploiting the directionality of the user antenna. The system capacity of such constellations is critically affected by the minimum angular separation of the HAPs and the sidelobe level of the user antenna. For typical antenna beamwidths of approximately 5/spl deg/ an inter-HAP spacing of 4 km is sufficient to deliver optimum performance. The aggregate bandwidth efficiency is evaluated, both theoretically using the Shannon equation, and using practical modulation and coding schemes, for multiple HAP configurations delivering either single or multiple cells. For the user antenna beamwidths used, it is shown that capacity increases are commensurate with the increase in the number of platforms, up to 10 HAPs. For increases beyond this the choice of constellation strategy becomes increasingly important.

An FPGA-based MVDR Beamformer Using Dichotomous Coordinate Descent Iterations

The FPGA design of an adaptive antenna array beamformer is presented. The complex-valued array weights are calculated using the MVDR algorithm whose implementation is based on dichotomous coordinate descent (DCD) iterations. The DCD algorithm allows the multiplication-free solution of the normal equations, resulting in an area-efficient FPGA design that requires approximately 400 slices for the DCD core. Antenna beampatterns obtained from weights calculated in the fixed-point FPGA platform are compared with those of a floating-point simulation. The comparison shows good match of the results for linear arrays of as large as 64 elements. For a 64-element array, the proposed design could provide a weight update rate as high as 28 kHz.

Improving the system capacity of mm-wave broadband services using multiple high altitude platforms

An investigation is performed into the capacity enhancements achievable from deploying multiple high altitude platforms (HAPs) arranged in different constellations but sharing common frequency bands and serving the same coverage area. Single and multiple cell configurations per HAP are examined. It is shown how overall system capacity may be increased, largely commensurate with the number of extra platforms deployed. This enhanced spectrum utilisation relies upon the fixed users employing a sufficiently directive antenna, pointing to HAPs located in different parts of the sky. Such deployments allow services to be offered to a significantly increased user population density, and facilitate incremental service roll-out.

Fast RLS algorithm using dichotomous coordinate descent iterations

The recursive least squares (RLS) adaptive filtering problem is expressed in terms of auxiliary normal equations with respect to increments of the filter weights. By applying this approach to the exponentially weighted case, a new structure of the RLS algorithm is derived. For solving the auxiliary equations, dichotomous coordinate descent (DCD) iterations with no explicit division and multiplication are used. This results in a transversal RLS adaptive filter with as low complexity as 3N multiplications per sample (N being the filter length), which is only slightly higher than the complexity of the Least Mean Squares (LMS) algorithm (2 AT multiplications). Simulations are used to compare the performance of the proposed algorithm against the classical RLS and known advanced adaptive algorithms. Fixed-point FPGA implementation of the proposed DCD-based RLS algorithm is discussed and results of such implementation are presented.

Comparaison des performances de décodage itératif avec les bornes de l’union pour des turbo codes pour trames courtes

We consider short frame turbo codes, suitable for delay-sensitive services such as conversational speech, or for encoding single ATM cells. We compare the uniform interleaver bound of Benedetto and Montorsi, and a union bound obtained by estimating the weight distribution due to the actual pseudo-random interleaver, with the simulated BER using an iterative decoder. We show that the uniform interleaver bound is significantly pessimistic at high SNR, where the random interleaver union bound is quite close. However, at lower SNR the ber exceeds the union bound, showing that it does not achieve ml decoding. We also consider half rate turbo codes formed by puncturing various proportions of the data and parity sequences, and adapt the uniform interleaver bounds for these codes. We show that while the union bounds predict better performance for data-punctured codes, in practice they perform better only at high snr and for limited proportions of data puncturing.RésuméCet article traite des turbo codes pour frames courtes, bien adaptés pour le codage de la parole et des cellules atm. Le teb obtenu par simulation avec déco-dage ilératif est comparé avec la borne de la probabilité d’entreur, déterminée par Benedetto et Montorsi avec entrelacement uniforme et avec une borne de l’union déterminée à partir de l’estimation de la distribution des poids résultant de l’entrelacement pseudo-aléatoire. Les auteurs montrent que la borne avec entrelacement uniforme est particulièrement pessimiste aux forts rapports signal à bruit, alors que la borne de l’union avec entrelacement pseudo-aléatoire est trés fine. Cependant, à faibles rapports signal à bruit le teb simulé est supé-rieur à la borne de l’union, montrant ainsi que le déco-dage réalisé n’est pas au maximum de vraisemblance. lis traitent aussi des turbo codes de rendement 1/2 avec poinçonnage des bits de données et de parité et les auteurs déterminent, pour ce type de turbo code, une borne de la probabilité d’erreur. lls montrent que la borne de l’union prévoil une amélioration des performances pour les codes poinçonnés, mais qu ’en pratique ces performances sont atteintes uniquement à fort rapport signal à bruit, et pour certains masques de poingonnage.Cet article traite des turbo codes pour frames courtes, bien adaptes pour le codage de la parole et des cellules atm. Le teb obtenu par simulation avec deco-dage ileratif est compare avec la borne de la probabilite d’entreur, determinee par Benedetto et Montorsi avec entrelacement uniforme et avec une borne de l’union determinee a partir de l’estimation de la distribution des poids resultant de l’entrelacement pseudo-aleatoire. Les auteurs montrent que la borne avec entrelacement uniforme est particulierement pessimiste aux forts rapports signal a bruit, alors que la borne de l’union avec entrelacement pseudo-aleatoire est tres fine. Cependant, a faibles rapports signal a bruit le teb simule est supe-rieur a la borne de l’union, montrant ainsi que le deco-dage realise n’est pas au maximum de vraisemblance. lis traitent aussi des turbo codes de rendement 1/2 avec poinconnage des bits de donnees et de parite et les auteurs determinent, pour ce type de turbo code, une borne de la probabilite d’erreur. lls montrent que la borne de l’union prevoil une amelioration des performances pour les codes poinconnes, mais qu ’en pratique ces performances sont atteintes uniquement a fort rapport signal a bruit, et pour certains masques de poingonnage.