Subrahmanyam Mula

Linear Detection of a Weak Signal in Additive Cauchy Noise

The detection of a weak signal in additive Cauchy noise is of great importance in many applications. A locally optimum detector (LOD) exists for such a scenario; however, it is non-linear in nature. In general, implementation of non-linear detectors is difficult in practice, and linear detectors with good properties, such as high asymptotic relative efficiency (ARE) with respect to the LOD, are often desirable. In this paper, we propose a linear detector for a weak signal in additive Cauchy noise. The proposed test statistic is a linear combination of order statistics. For the special case of a constant signal in additive Cauchy noise, we prove the asymptotic normality of the trimmed linear detector, and show that the ARE of the trimmed linear detector with respect to the LOD is unity. Extensive simulation results are provided to demonstrate that the loss in the performance of the linear detector is very small compared with the non-linear LOD. We also discuss the hardware complexities of the LOD and the linear detector, and demonstrate the advantages of the linear detector over the LOD, in terms of hardware implementation.

Performance analysis of proportionate-type LMS algorithms

For real-time sparse systems identification applications, Proportionate-type Least Mean Square (Pt-LMS) algorithms are often preferred to their normalized counterparts (Pt-NLMS) due to lower computational complexity of the former algorithms. In this paper, we present the convergence analysis of Pt-LMS algorithms. Without any assumptions on input, both first and second order convergence analysis are carried out and new convergence bounds are obtained. In particular, it establishes the universality of the steady-state mean square deviation. Detailed simulation results are presented to validate the analytical results.

Improved proportionate-type sparse adaptive filtering under maximum correntropy criterion in impulsive noise environments

Abstract An improved proportionate adaptive filter based on maximum correntropy criterion (IP-MCC) is proposed for identifying systems with variable sparsity in an impulsive noise environment. Utilization of the MCC mitigates the effect of the impulsive noise while improved proportionate concept exploits the underlying system sparsity to improve the convergence rate. Performance analysis of the proposed IP-MCC reveals that the steady-state excess mean square error (EMSE) of the proposed IP-MCC filter is similar to that of MCC filter. Extensive simulations demonstrate that the proposed IP-MCC outperforms state-of-the-art algorithms in terms of convergence rate and detailed complexity analysis reveals that IP-MCC requires much less computational effort.

A novel framework for compressed sensing based scalable video coding

Abstract Considering high throughput values as specified by modern video processing standards, Scalable Video Coding (SVC) systems intended for such standards are generally implemented by means of dedicated hardware. However, the high computational complexity associated with the current Compressed Sensing (CS) based video coding schemes makes their hardware realization considerably challenging. In this paper, we present a novel CS based SVC framework that is amenable to real-time VLSI implementation. At the encoder, after applying the Three-Dimensional Discrete Wavelet Transform (3-D DWT) on the input video frames, a novel Adaptive Measurement Scheme (AMS) in CS is introduced, which is applied on the high frequency sub-bands of the 3-D DWT frames. The proposed AMS along with 3-D DWT not only achieves scalability and better compression ratio, but also reduces the overall computational complexity of the system. We have also proposed an Enhanced Approximate Message Passing (EAMP) algorithm to reconstruct the high frequency sub-bands from the CS measurements at the decoder. The proposed EAMP procedure combines the benefits of Approximate Message Passing (AMP) and Iterative Hard Thresholding (IHT) algorithms thereby simultaneously achieving sparsity measurement trade-off and good reconstruction quality. We have carried out the detailed complexity analysis and simulations to demonstrate the superiority of the proposed framework over the existing schemes.

Algorithm and Architecture Design of Adaptive Filters With Error Nonlinearities

This paper presents a framework based on the logarithmic number system to implement adaptive filters with error nonlinearities in hardware. The framework is demonstrated through pipelined implementations of two recently proposed adaptive filtering algorithms based on logarithmic cost, namely, least mean logarithmic square (LMLS) and least logarithmic absolute difference (LLAD). To the best of our knowledge, the proposed architectures are the first attempts to implement both LMLS and LLAD algorithms in hardware. We derive error computing algorithms to realize the nonlinear error functions for LMLS and LLAD and map them onto hardware. We also propose a novel variable-

Algorithm and VLSI Architecture Design of Proportionate-Type LMS Adaptive Filters for Sparse System Identification

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Logarithmic Cost Based Constrained Adaptive Filtering Algorithms for Sensor Array Beamforming

scheme to enhance the original LMLS algorithm and prove its robustness and suitability for VLSI implementations in practical applications. Detailed bit width and error analysis are carried out for the proposed VLSI fixed point implementations. Postlayout implementation results show that with an additional multiplier over conventional least mean square (LMS), 7-dB improvement in steady-state mean square deviation performance can be achieved and with the proposed variable-

Proportionate Adaptive Filtering under Correntropy Criterion in Impulsive Noise Environments.

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A Family of Constrained Adaptive filtering Algorithms Based on Logarithmic Cost

scheme, 12-dB improvement can be achieved without compromising the convergence. We will show that LMLS can potentially replace LMS in practical applications, by demonstrating a proof-of-concept by extending the framework to transform domain adaptive filters.