MIMO Radar Waveform-Filter Design for Extended Target Detection from a View of Games

TL;DR

This paper models MIMO radar extended target detection as a Stackelberg game, deriving optimal waveform-filter strategies under various constraints and proving equilibrium existence through convex optimization and SDP relaxation.

Contribution

It introduces a game-theoretic framework for MIMO radar waveform-filter design against extended targets, with novel equilibrium analysis under energy and constant modulus constraints.

Findings

Stackelberg equilibrium aligns with Nash equilibrium under energy constraints.

Proposed algorithms effectively compute optimal waveform-filter pairs.

Theoretical proofs establish existence of equilibria for different constraints.

Abstract

This paper studies the Two-Person Zero Sum(TPZS) game between a Multiple-Input Multiple-Output(MIMO) radar and an extended target with payoff function being the output Signal-to-Interference-pulse-Noise Ratio(SINR) at the radar receiver. The radar player wants to maximize SINR by adjusting its transmit waveform and receive filter. Conversely, the target player wants to minimize SINR by changing its Target Impulse Response(TIR) from a scaled sphere centered around a certain TIR. The interaction between them forms a Stackelberg game where the radar player acts as a leader. The Stackelberg equilibrium strategy of radar, namely robust or minimax waveform-filter pair, for three different cases are taken into consideration. In the first case, Energy Constraint(EC) on transmit waveform is introduced, where we theoretically prove that the Stackelberg equilibrium is also the Nash equilibrium of the game, and propose Algorithm 1 to solve the optimal waveform-filter pair through convex optimization. Note that the EC can't meet the demands of radar transmitter due to high Peak Average to power Ratio(PAR) of the transmit waveform, thus Constant Modulus and Similarity Constraint(CM-SC) on waveform is considered in the second case, and Algorithm 2 is proposed to solve this problem, where we theoretically prove the existence of Nash equilibrium for its Semi-Definite Programming(SDP) relaxation form. And the optimal waveform-filter pair is solved by calculating the Nash equilibrium followed by the randomization schemes. In the third case,...