MMSE Adaptive Waveform Design for Active Sensing With Applications to MIMO Radar

Abstract

Minimising the expected mean squared error is one of the fundamental metrics applied to adaptive waveform design for active sensing. Previously, only cost functions corresponding to a lower bound on the expected mean squared error have been expressed for optimisation. In this paper we express an exact cost function to optimise for minimum mean squared error adaptive waveform design (MMSE-AWD). This is expressed in a general form which can be applied to non-linear systems. Additionally, we provide a general example for how this method of MMSE-AWD can be applied to a system that estimates the state using a particle filter (PF). We make the case that there is a compelling reason to choose to use the PF (as opposed to alternatives such as the Unscented Kalman filter and extended Kalman filter), as our MMSE-AWD implementation can re-use the particles and particle weightings from the PF, simplifying the overall computation. Finally, we provide a numerical example, based on a simplified multiple-input-multiple-output radar system, which demonstrates that our MMSE-AWD method outperforms a simple non-adaptive radar, whose beam-pattern has a uniform angular spread, and also an existing approximate MMSE-AWD method.

Adaptive transmission for radar arrays using Weiss–Weinstein bounds

“…The BMSE in (3) can be used as optimization metric for adaptive sensing [31], but is expensive to compute because it involves Monte Carlo integrals over the parameter space and over realizations of the observation. Instead, we follow the common practice of replacing the BMSE by one of its lower bounds, e.g.…”

“…The array's center of mass is at the origin, i.e.d = 1 N n d n = 0. We denote the optimal scaling choice according to the presented randomphase (RP) WWB in (31) and (34), as g…”

Computationally Simple MMSE (A-Optimal) Adaptive Beam-Pattern Design for MIMO Active Sensing Systems via a Linear-Gaussian Approximation

“…1]. In this paper, we are concerned with adaptive shaping the beampattern generated by a multiple-input-multiple-output (MIMO) array, which is also known as adaptive waveform design in some of the iterature [4], [5]. Specific MIMO active sensing system modalities to which this analysis applies include MIMO sonar [6] as well as the aforementioned MIMO radar.…”

“…The cost function for MMSE design in active sensing systems has been expressed [5,Eq. (11)], however evaluation thereof is shown to be computationally expensive and thus in this paper we provide an approximate method for MMSE ABD that is less computationally expensive than the exact solution.…”

“…Our approach is to use the current estimates of the target parameters to artificially construct a multivariate Gaussian distribution for the unique terms of the channel response (a non-linear function of the target parameters), and to optimally design the beam-pattern for the resultant linear Gaussian system accordingly. This approximate channel model is expressed in the standard form for linear Gaussian channels [9], and indeed yields an optimisation problem that is shown to be significantly less computationally complex than the exact MMSE ABD algorithm [5], and also the approximate MMSE ABD algorithm proposed by Huleihel et al [4], which has similar complexity to the exact MMSE ABD algorithm [5,Fig. 7].…”