Fast Computation of the Optimal Integrated Sidelobe Level Filter for Large-Scaled Problems

Abstract

The growth of spectral demand due to congestion in the electromagnetic spectrum is skyrocketing through the past years. Joint radar-communications systems are thus attracting more attention as they can share their bandwidth to alleviate the frequency spectrum. In such a system, communication codes are used to both transmit information and perform radar missions. The latter notably requires mitigating the sidelobe level energy, which is generally achieved via the use of a mismatched filter. However, such a filter may be costly to optimize, especially for largescale problems. Hence, this paper proposes a fast algorithm for computing the optimal integrated sidelobe level mismatched filter, based on the Lagrangian dual function of the primal problem. Once the Lagrangian function is calculated, the optimum values of its variables are computed, after formulating it as a monodimensional problem, in order to provide the desired filter. The resulting computational time shows a dramatic improvement on the execution time of the proposed method compared to the classical Matlab convex solver CVX, especially for large-scale problems.

A Cooperative SAR-Communication System Using Continuous Phase Modulation Codes and Mismatched Filters

“…In the considered joint SAR-communications framework, we must solve many large-scale convex optimization problems, one per transmitted pulse, so the use of CVX tool becomes infeasible. This led us to find a faster algorithm to solve the optimization problem (5) [19].…”

“…We show that the optimization of the ISL problem can be calculated analytically in the dual space so that the solution can be obtained via a simple monodimensional gradient descent algorithm. The main steps are summarized below, but more details can be found in [19]:…”

“…The computation time gain is enormous, as the filters are computed 250 times faster than using the classical CVX Matlab Toolbox. More precisely, it took roughly 16 days to compute 6522 filters, instead of 11 years of computational time needed when using the CVX algorithm [19].…”

“…It is thus required to solve a large number of large-scaled problems, which unfortunately cannot be computed with classical tools such as Matlab Software CVX [18], in acceptable time limits. Therefore we use our proposed solution [19], which enables to obtain the same optimal ISL solution as CVX at a highly reduced computational cost, by directly solving the dual problem.…”