An extrapolation procedure for band-limited signals

Enhancing resolution properties of array antennas via field extrapolation: application to MIMO systems

“…Accordingly, we can apply to it all results known for band-limited functions, in particular, the noteworthy property that these functions are analytical, i.e., such that their exact knowledge in a finitelength interval allows, in principle, their extrapolation over the entire domain of definition, having infinite extension [4][5][6][7][8][9], thus potentially prospecting the achievement of unlimited angular resolution. As extensively discussed in these references, however, the implementation aspects, such as the need to sample the field by means of a sensor array, with consequent loss of information due to the finiteness of the spatial sampling frequency, and the errors inherent in the analog-to-digital conversion and in the array implementation, along with other limiting factors, make the above extrapolation process reliable only within a limited range in the vicinity of the array.…”

“…In the literature, the mentioned techniques have been addressed with reference to different categories of problems. On the one hand, super-resolution algorithms have been studied extensively in the past in conjunction with ingenious extrapolation schemes to improve the discrimination capability of specific instrumentation, such as optical sensors or spectrum analyzers, in response to one-or two-dimensional band-limited signals observed in truncated intervals [4][5][6][7][8][9]. In these references the interest of researchers is mainly focused on the extrapolation schemes and the relevant performance limits, with no reference to their possible applications to beamforming issues.…”

An Effective Technique for Reducing the Truncation Error in the Near-Field-Far-Field Transformation With Plane-Polar Scanning

“…As well-known, this is an ill-posed problem widely studied in literature with reference to the case of bandlimited signals which are known only in a finite time interval [12][13][14][15][16][17][18][19][20][21].…”

“…Moreover, in the same paper, a noniterative method has been proposed for solving the extrapolation problem from noise-free observations by means of an extrapolation matrix. In [15], Cadzow proposed a different extrapolation matrix, which does not have the existence problem of that suggested in [14]. In both papers, the solutions for the discrete case have been obtained by sampling the continuous solutions.…”

Convergence of iterative nonexpansive signal reconstruction algorithms

“…Although our discussion centers on two specific examples, timelimited extrapolation (and consequently, bandlimited extrapolation) and phase-only reconstruction, our approach is 1U general and may be applied to other iterative algorithms that satisfy the same assumptions. Since the convergence of the iteration for bandlimited extrapolation has been demonstrated by others [2,3,4], the present paper offers an alternative approach into which nonlinear constraints, such as positivity [8,9] can be incorporated. The generality of our approach also yields the first proof of convergence for the phase-only reconstruction problem.…”