MIMO Radar Beampattern Design Via PSL/ISL Optimization

Abstract

We deal with the robust design of Multiple-Input Multiple-Output (MIMO) waveform covariance matrices that optimize the worst case (over steering mismatches) transmit beampattern assuming either the Peak Sidelobe Level (PSL) or the Integrated Sidelobe Level (ISL) as figure of merit. To this end, we model the uncertainty set associated with each steering vector through two double-sided, potentially non-convex, quadratic constraints. Additionally, we force two suitable constraints on the optimization variable. The former accounts for the width of the mainbeam, whereas the latter is either a uniform or a relaxed elemental power requirement allowing to control the amount of transmitted power. We prove that both the mentioned waveform covariance designs lead to non-convex optimization problems which remarkably share some hidden convexity properties. Hence, we devise polynomial time procedures aimed at synthesizing the desired optimal MIMO waveform covariance matrices. Finally, at the analysis stage, we assess the performance of the proposed techniques showing their capability to ensuring improved worst case performance than some counterparts available in open literature.

Robust constrained waveform design for MIMO radar with uncertain steering vectors

“…Interestingly, we observe that (9) can be solved by exploiting SDR technique [19]. Specifically, after the same line of reasoning as [19], this problem is tantamount to SDP problem given by…”

“…In particular, the detailed illumination of these constraints can be obtained in [19]. Furthermore, to control the amount of transmitted power, we force a uniform power constraint in each transmitting antenna, i.e.,…”

“…Specifically, after the same line of reasoning as [19], this problem is tantamount to SDP problem given by…”

“…Robust waveform design to resist uncertainty sets of target or clutter parameters (i.e., Doppler frequency, angle) has received considerable attention during the last decades [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. According to the structure of radar systems, these works can be classified into two categories.…”

“…In [18], based on the worst-case SNR over the uncertain on steering vector, an iterative algorithm is presented to optimize the waveform covariance matrix under a power constraint. In [19], assuming either the peak sidelobe level (PSL) or the integrated sidelobe level (ISL) as figure of merit, the robust waveform covariance matrixes design has been addressed for the purpose of optimizing the worst-case transmit beampattern over steering mismatches accounting for power constraint and 3 dB main-beam width constraint.…”