Robust Block Sparse Beamforming for Strictly Non-Circular Signals and Unknown Array Mutual Coupling

Block Diagonalization Precoding and Power Allocation for Multiple-Antenna Systems With Coarsely Quantized Signals

“…The vectors e t ∈ R (2 M −1)×1 and e c ∈ R (2 M−1)×1 consist of all zeros, except for a 1 in the central position. In comparison with x in (5), both v t and v c in (10) work as if the signals received by a longer difference coarray whose sensors positions are computed by the diverse values in the set { x i − x j | i ≥ 1, j ≤ M }, where x i stands for the position vector of the ith sensor. The source signal vector p composed by the powers σ 2 k , k = 1, 2, .…”

“…, K of the truly existing sources acts like coherent sources. This associated with the fact that the difference coarrays are ULAs allow the application of spatial smoothing to equations (10) to estimate full-rank covariance matrices, which are also NND. The resulting smoothed matrices obtained for TLNA [19], [20] and for CPA [21], [22] can be expressed respectively as follows:…”

“…where the vector v ti is formed by the entries between the M + 1 − i and the 2 M − i rows of v t in (10) and B t1 denotes an array manifold composed with the final M rows of B t in (10). Similarly, v ci is composed with the entries included between the 2 M + 1 − i and the 2 M − i rows of v t in (10) and B c1 stands for an array manifold composed by the latest M rows of B c in (10). More specifically, covariance matrices Ω t in (13) and Ω c in ( 14) respectively are expressed as Ω t = Ω c = diag (p).…”

“…Among some innovative solutions proposed to overcome these drawbacks are coarse quantization [17], which provides energy savings. Another is the use of sparse or super-resolution arrays (SRAs) [4], [5], [6], [7], [8], [9], [10] in the BS whose large degrees of freedom can be obtained by the virtual expansion of the number of physical sensors.…”

Acoustic Imaging Method for Gas Leak Detection and Localization Using Virtual Ultrasonic Sensor Array

“…That same year, a detecting and locating gas leakage method based on data fusion of energy decay and time difference of arrival, using a rectangular array of four ultrasonic sensors was proposed [ 30 ]. Compared with the contact measurement methods, the non-contact measurement methods further improve the accuracy of leakage localization and are more widely used; combined with the recent robust beamformer algorithms [ 31 , 32 , 33 ], the localization accuracy can be further improved. However, the localization accuracy is susceptible to the spacing between adjacent array elements and the number of array elements.…”