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Systems currently being developed to operate across wide bandwidths with high sensitivity requirements are limited by the inherent dynamic range of a receiver's analog and mixed-signal components. To increase a receiver's overall linearity, we have developed a digital nonlinear equalization (NLEQ) processor which is capable of extending a receiver's dynamic range from one to three orders of magnitude. In this paper we describe the NLEQ architecture and present measurements of its performance., United States. Defense Advanced Research Projects Agency (Air Force contract FA8721-05-C- 0002)

In this paper we present a simple closed-form solution to the Wiener-Hammerstein (W-H) identification problem. The identification process occurs in the log-frequency domain where magnitudes and phases are separable. We show that the theoretically optimal W-H identification is unique up to an amplitude, phase and delay ambiguity, and that the nonlinearity enables the separate identification of the individual linear time invariant (LTI) components in a W-H architecture., United States Air Force (Contract FA8721-05-C-0002)

As the demand for higher data rates increases, commercial analog-to-digital converters (ADCs) are more commonly being implemented with multiple on-chip converters whose outputs are time-interleaved. The distortion generated by time-interleaved ADCs is now not only a function of the nonlinear behavior of the constituent circuitry, but also mismatches associated with interleaving multiple output streams. To mitigate distortion generated by time-interleaved ADCs, we have developed a polyphase NonLinear EQualizer (pNLEQ) which is capable of simultaneously mitigating distortion generated by both the on-chip circuitry and mismatches due to time interleaving. In this paper, we describe the pNLEQ architecture and present measurements of its performance., Defense Advanced Research Projects Agency (Air Force Contract FA8721-05-C-0002)

We analyze the Basis Pursuit recovery of signals with general perturbations. Previous studies have only considered partially perturbed observations Ax + e. Here, x is a signal which we wish to recover, A is a full-rank matrix with more columns than rows, and e is simple additive noise. Our model also incorporates perturbations E to the matrix A which result in multiplicative noise. This completely perturbed framework extends the prior work of Candes, Romberg and Tao on stable signal recovery from incomplete and inaccurate measurements. Our results show that, under suitable conditions, the stability of the recovered signal is limited by the noise level in the observation. Moreover, this accuracy is within a constant multiple of the best-case reconstruction using the technique of least squares. In the absence of additive noise numerical simulations essentially confirm that this error is a linear function of the relative perturbation., Comment: 11 pages, 1 figure, preprint

A stylized compressed sensing radar is proposed in which the time-frequency plane is discretized into an N by N grid. Assuming the number of targets K is small (i.e., K much less than N^2), then we can transmit a sufficiently "incoherent" pulse and employ the techniques of compressed sensing to reconstruct the target scene. A theoretical upper bound on the sparsity K is presented. Numerical simulations verify that even better performance can be achieved in practice. This novel compressed sensing approach offers great potential for better resolution over classical radar., Comment: New: Extended theory to include case of noisy signals; Re-ran numerical simulations with complex-valued data; Clarified definition of "random signal"; Minor language and typo fixes; 14 pages, 13 figures. Accepted to IEEE Transactions on Signal Processing, December 2008