High-resolution phase sampled interferometry using symmetrical number systems

Abstract

High-resolution phase sampled interferometry using symmetrical number systems Pace, Phillip E. Abstract-This paper identifies a new phase sampling interferometer approach that can be easily incorporated into the established techniques to provide a high resolution, small-baseline array with fewer number of phase sampling comparators. The approach is based on preprocessing the received signal using symmetrical number systems (SNS). Antennas based on both an optimum symmetrical number system (OSNS) and a robust symmetrical number system (RSNS) are investigated. The SNS preprocessing is used to decompose the spatial filtering operation into a number of parallel suboperations (moduli) that are of smaller computational complexity. A much higher direction finding (DF) spatial resolution is achieved after the different moduli are used and the results of these low precision suboperations are recombined. By incorporating the OSNS or RSNS preprocessing concept, the field of view of a specific configuration of interferometers and phase sampling comparator arrangements can be analyzed exactly. The OSNS gives the maximum dynamic range or number of spatial resolution bins while the RSNS reduces considerably the number of possible encoding errors. Experimental results for both a 5-bit OSNS and a 6-bit RSNS array are compared. The errors in the encoding of the direction of arrival are quantified for both architectures.Index Terms-Directional finding, electronic warfare, symmetrical number system.

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“…In order to acquire the high precision of direction finding, the traditional phase interferometers usually use the antenna array with long baseline. But when the baseline length exceeds the half wavelength of the incident signal, there will be the phase difference ambiguity problems for each array element [5], [6]. Although different authors proposed many methods to solve ambiguity [5][6][7][8][9][10][11], the success rate of solving ambiguity for a direction-finding system cannot be guaranteed because of the influence of array element structure, radome, element mutual coupling, etc.…”

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“…15 Each RSNS sequence is periodic with a period equal to 2Nm i , such that x hþ2Nm i ¼ x h . The N-sequence RSNS is also periodic with a fundamental period of 15,16 …”

“…15,16 Several additional closed-form expressions for M for other specific families of moduli sets have also been developed. 22 …”

“…This integer Gray code property makes the RSNS particularly well suited for DF antenna arrays and error control applications. 7,[15][16][17][18][19][20][21] The dynamic rangeM of the RSNS is the longest run of distinct N-tuples. However, unlike other residue-based number systems, the values comprising the dynamic range do not begin at zero and end atM − 1.…”

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“…These ambiguities occur when the spacing between antenna elements is greater than half of the signal wavelength. As a result of this, multiple baselines are commonly used to resolve ambiguities in DF systems [Pace, 2001;Kwai et al, 2008]. However, there is a need to take into account that the presence of unknown mutual coupling between array elements degrades significantly the performance of most highresolution DF algorithms.…”