Compressive sensing based sparse antenna array design for directional modulation

Abstract

Abstract. Directional modulation (DM) can be achieved based on uniform linear arrays (ULAs)where the maximum spacing between adjacent antennas is half wavelength of the frequency of interest in order to avoid spatial aliasing. To exploit the additional degrees of freedom (DOFs) provided in the spatial domain, sparse antenna arrays can be employed for more effective DM. In this work, the spare array design problem in the context of DM is formulated from the viewpoint of compressive sensing (CS), so that it can be solved using standard convex optimisation toolboxes in the CS area. In detail, we need to find a common set of active antennas for all modulation symbols generating a response close to the desired one. The key to the solution is to realise that we have to employ the group sparsity concept, as a common antenna set cannot be guaranteed if we optimise antenna locations for each modulation symbol individually. Moreover, we have also considered two practical scenarios for our proposed design: robust design with model errors, and design with practical non-zero-sized antennas, and corresponding solutions are found by modifying the proposed standard solution.

Sparse array extension for non-circular signals with subspace and compressive sensing based DOA estimation methods

“…Note that the l 1 norm is used here as an approximation to the l 0 norm for sparsity maximization. Since the l 1 norm penalizes lager weight coefficients more heavily than smaller ones, the reweighted l 1 norm minimisation method can be employed for a closer approximation to the l 0 norm [31,32,33,34]. Using the reweighted l 1 norm minimisation method, a lager weighting term is introduced to those coefficients with smaller non-zero values and a smaller weighting term to those coefficients with larger non-zero values.…”

Antenna Array Based Positional Modulation with a Two-Ray Multi-Path Model

“…, N − 1, are selected to give a uniform grid. Through selecting the minimum number of non-zero valued weight coefficients, where the corresponding antennas are kept, and the rest of the antennas with zero-valued coefficients are removed, to generate a response close to the desired one, sparseness of the design is acquired [5,6]. Then for the m-th constellation point, the cost function is min wm ||w m || 1 and the…”

“…where || · || 1 is the l 1 norm, used as an approximation to the l 0 norm and α is the allowed difference between the desired and designed responses. As each antenna element corresponds to M weight coefficients and these M coefficients correspond to M symbols, to remove the n-th antenna, we need all coefficients in the following vectorw n to be zero-valued or ||w n || 2 = 0 [5,6],w n = [w n,0 , . .…”

“…Here the superscript u indicates the u-th iteration, and δ n is the reweighting term for the n-th row of coefficients, given by δ u n = (||w u−1 n || 2 + γ) −1 . (γ > 0 is required to provide numerical stability and the iteration process is described as in [5].) The problem in (18) and (19) can be solved by cvx [29,30].…”

Synthesis of Sparse Concentric Ring Arrays Based on Fitness-Associated Differential Evolution Algorithm

“…In recent years, population-based stochastic methods are proven to be effective for these problems, such as genetic algorithm (GA) [6][7][8][9][10][11], particle swarm optimization (PSO) [12][13][14], differential evolution algorithm (DE) [15][16][17][18][19][20], invasive weed optimization (IWO) [21], and cuckoo search (CS) algorithm [22][23][24]. Besides, Bayesian compressive sensing (BCS) [25][26][27][28][29][30][31] and matrix pencil method (MPM) [32][33][34] have also aroused great interest.…”