Joel Goodman

The cube coefficient subspace architecture for nonlinear digital predistortion

In this paper, we present the cube coefficient subspace (CCS) architecture for linearizing power amplifiers (PAs), which divides the overparametrized Volterra kernel into small, computationally efficient subkernels spanning only the portions of the full multidimensional coefficient space with the greatest impact on linearization. Using measured results from a Q-band solid state PA, we demonstrate that the CCS predistorter architecture achieves better linearization performance than state-of-the-art memory polynomials and generalized memory polynomials.

A Log-Frequency Approach to the Identification of the Wiener–Hammerstein Model

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.

Identification and compensation of Wiener-Hammerstein systems with feedback

Efficient operation of RF power amplifiers requires compensation strategies to mitigate nonlinear behavior. As bandwidth increases, memory effects become more pronounced, and Volterra series based compensation becomes onerous due to the exponential growth in the number of necessary coefficients. Behavioral models such as Wiener-Hammerstein systems with a parallel feedforward or feedback filter are more tractable but more difficult to identify. In this paper, we extend a Wiener-Hammerstein identification method to such systems showing that identification is possible (up to inherent model ambiguities) from single- and two-tone measurements. We also calculate the Cramér-Rao bound for the system parameters and compare to our identification method in simulation. Finally, we demonstrate equalization performance using measured data from a wideband GaN power amplifier.

A New Approach to Achieving High-Performance Power Amplifier Linearization

Digital baseband predistortion (DBP) is not particularly well suited to linearizing wideband power amplifiers (PAs); this is due to the exorbitant price paid in computational complexity. One of the underlying reasons for the computational complexity of DBP is the inherent inefficiency of using a sufficiently deep memory and a high enough polynomial order to span the multidimensional signal space needed to mitigate PA-induced nonlinear distortion. Therefore we have developed a new mathematical method to efficiently search for and localize those regions in the multidimensional signal space that enable us to invert PA nonlinearities with a significant reduction in computational complexity. Using a wideband code division multiple access (CDMA) signal we demonstrate and compare the PA linearization performance and computational complexity of our algorithm to that of conventional DBP techniques using measured results.

A Polyphase nonlinear equalization architecture and semi-blind identification method

In this paper, we present an architecture and semi-blind identification method for a polyphase nonlinear equalizer (pNLEQ). Such an equalizer is useful for extending the dynamic range of time-interleaved analog-to-digital converters (ADCs). Our proposed architecture is a polyphase extension to other architectures that partition the Volterra kernel into small nonlinear filters with relatively low computational complexity. Our semi-blind identification technique addresses important practical concerns in the equalizer identification process. We describe our architecture and demonstrate its performance with measured results when applied to a National Semiconductor ADC081000.

Extending the dynamic range of RF receivers using nonlinear equalization

Systems currently being developed to operate across wide bandwidths with high sensitivity requirements are limited by the inherent dynamic range of a receivers analog and mixed-signal components. To increase a receivers overall linearity, we have developed a digital NonLinear EQualization (NLEQ) processor which is capable of extending a receivers dynamic range from one to three orders of magnitude. In this paper we describe the NLEQ architecture and present measurements of its performance.

Compressed Sensing Arrays for Frequency-Sparse Signal Detection and Geolocation

Compressed sensing (CS) can be used to monitor very wide bands when the received signals are sparse in some basis. We have developed a compressed sensing receiver architecture with the ability to detect, demodulate, and geolocate signals that are sparse in frequency. In this paper, we evaluate detection, reconstruction, and angle of arrival (AoA) estimation via Monte Carlo simulation and find that, using a linear 4- sensor array and undersampling by a factor of 8, we achieve near-perfect detection when the received signals occupy up to 5% of the bandwidth being monitored and have an SNR of 20 dB or higher. The signals in our band of interest include frequency-hopping signals detected due to consistent AoA. We compare CS array performance using sensor-frequency and space-frequency bases, and determine that using the sensor-frequency basis is more practical for monitoring wide bands. Though it requires that the received signals be sparse in frequency, the sensor–frequency basis still provides spatial information and is not affected by correlation between uncompressed basis vectors.

Variable Projection and Unfolding in Compressed Sensing

The performance of linear programming techniques that are applied in the signal identification and reconstruction process in compressed sensing (CS) is governed by both the number of measurements taken and the number of nonzero coefficients in the discrete basis used to represent the signal. To enhance the capabilities of CS, we have developed a technique called Variable Projection and Unfolding (VPU). VPU extends the identification and reconstruction capability of linear programming techniques to signals with a much greater number of nonzero coefficients in the basis in which the signals are compressible with significantly better reconstruction error.

Physical layer considerations for wideband cognitive radio

Next generation cognitive radios will benefit from the capability of transmitting and receiving communications waveforms across many disjoint frequency channels spanning hundreds of megahertz of bandwidth. The information theoretic advantages of multi-channel operation for cognitive radio (CR), however, come at the expense of stringent linearity requirements on the analog transmit and receive hardware. This paper presents the quantitative advantages of multi-channel operation for next generation CR, and the advanced digital compensation algorithms to mitigate transmit and receive nonlinearities that enable broadband multi-channel operation. Laboratory measurements of the improvement in the performance of a multi-channel CR communications system operating below 2 GHz in over 500 MHz of instantaneous bandwidth are presented.

Nonlinear Equalization for RF Receivers

This paper describes the need for high performance computing (HPC) to facilitate the development and implementation of a nonlinear equalizer that is capable of mitigating and/or eliminating nonlinear distortion to extend the dynamic range of radar front-end receivers decades beyond the analog state-of-the-art. The search space for the optimal nonlinear equalization (NLEQ) solution is computationally intractable using only a single desktop computer. However, we have been able to leverage a combination of an efficient greedy search with the high performance computing technologies of LLGrid and MatlabMPI to construct an NLEQ architecture that is capable of extending the dynamic range of radar front-end receivers by over 25dB