Mohammed Nafie

Deterministic and iterative solutions to subset selection problems

Signal decompositions with overcomplete dictionaries are not unique. We present two new approaches for identifying the sparsest representation of a given signal in terms of a given overcomplete dictionary. The first approach is an algebraic approach that attempts to solve the problem by generating other vectors that span the space of minimum dimension that includes the signal. Unlike other current techniques, including our proposed iterative technique, this algebraic approach is guaranteed to find the sparsest representation of the signal under certain conditions. For example, we can always find the exact solution if the size of the dictionary is close to the size of the space or when the dictionary can be represented by a Vandermonde matrix. Although our technique can work for high signal-to-noise cases, the exact solution is only guaranteed in noise-free cases. Our second approach is iterative and can be applied in cases where the algebraic approach cannot be used. This technique is guaranteed to achieve at least a local minimum of the error function representing the difference between the signal and its sparse representation.

Optimal subset selection for adaptive signal representation

A number of over-complete dictionaries such as wavelets, wave packets, cosine packets etc. have been proposed. Signal decomposition on such over-complete dictionaries is not unique. This non-uniqueness provides us with the opportunity to adapt the signal representation to the signal. The adaptation is based on sparsity, resolution and stability of the signal representation. The computational complexity of the adaptation algorithm is of primary concern. We propose a new approach for identifying the sparsest representation of a given signal in terms of a given over-complete dictionary. We assume that the data vector can be exactly represented in terms of a known number of vectors.

Reduced complexity M-ary hypotheses testing in wireless communications

We present a progressive refinement approach to M-ary detection problems. The approach leads on average to a logarithmic reduction in the complexity of the detector. It relies on designing binary decision trees that trade complexity with probability of error. We also discuss simplified solutions that can be used in several cases of interest in wireless communications such as CDMA multiuser detection and blind equalization.

Low power detection using stochastic resonance

Mobile communications dictates the use of low power detection and estimation algorithms to prolong the battery life. We present a very low power detection scheme and evaluate its performance. This scheme can be used instead of the optimal quantized detectors when the noise variance, or other problem parameters, are unknown or change online. This detector uses an adaptive discrete time stochastic resonator that consists of a simple Schmitt trigger. Theoretical results evaluating the detection capability of such a device are presented, and simulations show an improvement in the detection probability over other low power schemes.

Optimal FIR transmit filters for multiuser wireline communications

In the near future, very high data rates will be available over wirelines. The need to distribute these high rates among several users will arise. In this paper we explain a technique which allows several users to use the same communication medium while at the same time allowing their transmissions to be separated at the receiver. We show that an optimized FIR transmit filter, maximizing the channel throughput, outperforms both the flat FIR and the popular raised-cosine FIR transmit filters. We derive the throughput function for the fractionally sampled filter and show that more throughput maximization is achieved compared to the symbol-spaced sampled filter. We extend the optimization for multi-dimensional signaling to accommodate multiple users using two possible techniques. For the first option, we derive the multi-user throughput function, and optimize the multi-dimensional filter to maximize this throughput. This will outperform the time multiplexing technique. For the second option, we generate orthogonal signals incrementally. This offers flexibility in accommodating more users and relaxes the receiver equalization process.

Performance and complexity trade off in CDMA multiuser communications

In this paper, we describe a new tree-based CDMA receiver that can optimally trade complexity for detection performance. It yields the detector with the best detection performance for a given desired complexity level. Alternatively, it yields the lowest complexity receiver for any given desired detection performance. We describe a technique for designing receivers with linear complexity (including the optimal linear detector and decorrelator). We then explain how we can increase performance at the expense of a minimal increase in complexity. We show that as complexity increases to the level of that of the optimal receiver, our design approach automatically produces the optimal receiver. We also explain how our approach can be used with a minimum-mean-square-error design criterion and coded CDMA transmission. Finally, we illustrate with several examples the superiority of the receivers designed with our approach and discuss their advantages.

Low complexity M-hypotheses detection: M vectors case

Low complexity algorithms are essential in many applications which require low power implementation. We present a low complexity technique for solving M-hypotheses detection problems, that involve vector observations. This technique works in these cases where the number of vectors is equal to or smaller than the dimensionality of the vectors. It attempts to optimally trade off complexity with probability of error through solving the problem in a lower dimension.