Robust joint code-filter design under uncertain target interpulse fluctuation

The robust joint transmit code and receive filter design under uncertain target interpulse fluctuation is considered in this paper. Two effective robust design schemes under diverse criteria are devised. In the first scheme, the fluctuation vector is modeled as a stochastic vector and the statistical expectation of the Signal-to-Interference-plus-Noise Ratio (SINR) is used as the figure of merit. We formulate the design as a non-convex maximization problem and devise the Iterative Convex Approximation based Average Maximization (ICA-AM) algorithm to solve it. In the second scheme, we aim to enhance the worst-case SINR over the modeled uncertainty set. The corresponding design is cast as a non-convex minimax problem and a novel Relaxed Duality based Worst-Case Optimization (RD-WCO) algorithm is developed. By adding a series of bow-shaped piece to the fan-ring-shaped sector, we slightly relax the uncertainty set with its convex hull. The relaxed inner minimization problem is proved to meet the strong duality condition and can be equivalently replaced by its dual form, which makes the resultant formulation solvable. Simulation results show significant performance enhancement of the proposed algorithms under uncertain interpulse fluctuation over the nominal design.