ℓp-Norm Minimization of Auto and Cross Correlation Sidelobes in MIMO Radars

In this paper, we consider designing a set of constant modulus sequences with good auto- and cross-correlation properties in multiple-input multiple-output (MIMO) radar systems. In order to minimize the sidelobes level, we chose ℓ
p
-norm (p ≥ 2) minimization of auto- and cross-correlation under constant modulus constraint as the design metric. This metric gives a good degree of freedom to the radar designers and cognitive radar systems to adopt the waveform in different situations. For instance, choosing the p helps to achieve different properties of waveforms, such as good integrated sidelobe level (ISL), peak sidelobe level (PSL) and sparsity. The problem formulation of ℓ
p
-norm minimization leads to a non-convex and NP-hard optimization problem. To tackle the problem we deploy an iterative framework based on block successive upper bound minimization (BSUM) method. In this framework we convert the weighted ℓ
p
-norm problem to a simpler quadratic form then we optimize the problem with respect to a vector iteratively. For each iteration, the approach to obtain a local optimum solution is gradient descent (GD) based method. Numerical results show that the proposed method meets the ISL lower bound and outperforms the state of the art methods based on PSL criterion.