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

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 large-scale 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 mono-dimensional 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.