Modulus constraints in adaptive radar waveform design

Within the taxonomy of adaptive waveform generation methodologies is the family of arbitrary waveform design algorithms, which are capable of designing both the modulus and phase of a complex-valued waveform in response to changes in the operational environment of the sensor. Algorithms of this kind have been the subject of renewed research interest as a consequence of the relatively recent advances in linear RF power amplifiers, arbitrary waveform generators, and computational capability. In this paper, we use hardware considerations to argue that constraints on the maximum waveform modulus will generally supersede the total energy constraint commonly found in the literature. In order to illustrate the deleterious effects on system performance that can arise when these modulus constraints are not accounted for, we subjected recently published waveform design algorithms to maximum modulus limitations in simulation, and we present the results here. We also propose a novel arbitrary waveform design algorithm that accounts for both maximum modulus constraints and constraints on the waveformpsilas autocorrelation function. Simulation results that demonstrate the efficacy of this algorithm are presented.

I. Introduction

Traditionally, the transmit waveform of an active sensing system is specified as part of a holistic system design in which the waveform is expected to be utilized in specific operating modes, under specified environmental conditions. (e.g., [1]–[3]) In this context, the waveform design remains fixed regardless of changes in the operational environment. As such, system performance can significantly degrade when undesirable operating conditions such as clutter or additive interference are present, ¹

For ease of explication we will use radar-specific terminology. However, the results of this paper are equally applicable to sonar.