  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,...
