Ambiguity Resolution in Direction of Arrival Estimation with Linear Antenna Arrays Using Differential Geometry

Abstract

Linear antenna arrays (LAs) can be used to accurately predict the direction of arrival (DOAs) of various targets of interest in a given area. However, under certain conditions, LA suffers from the problem of ambiguities among the angles of targets, which may result in misinterpretation of such targets. In order to cope up with such ambiguities, various techniques have been proposed. Unfortunately, none of them fully resolved such a problem because of rank deficiency and high computational cost. We aimed to resolve such a problem by proposing an algorithm using differential geometry. The proposed algorithm uses a specially designed doublet antenna array, which is made up of two individual linear arrays. Two angle observation models, ambiguous observation model (AOM) and estimated observation model (EOM), are derived for each individual array. The ambiguous set of angles is contained in the AOM, which is obtained from the corresponding array elements using differential geometry. The EOM for each array, on the other hand, contains estimated angles of all sources impinging signals on each array, as calculated by a direction-finding algorithm such as the genetic algorithm. The algorithm then contrasts the EOM of each array with its AOM, selecting the output of that array whose EOM has the minimum correlation with its corresponding AOM. In comparison to existing techniques, the proposed algorithm improves estimation accuracy and has greater precision in antenna aperture selection, resulting in improved resolution capabilities and the potential to be used more widely in practical scenarios. The simulation results using MATLAB authenticates the effectiveness of the proposed algorithm.

Application of Differential Geometry to the Array Manifolds of Linear Arrays in Antenna Array Processing

“…However, due to the complex and complicated iterative procedures, it does not provide the global convergence. In [23], the authors proposed a DLA consisting of two different LAs, whose antenna locations are decided in accordance with some specific rules in order to avoid ambiguity. An efficient algorithm is proposed, which effectively chooses the unambiguous direction of sources estimated via genetic algorithm (GA) as a direction-finding technique.…”

“…An efficient algorithm is proposed, which effectively chooses the unambiguous direction of sources estimated via genetic algorithm (GA) as a direction-finding technique. The proposed work in [23] resolved the problem of ambiguity but had lower estimation accuracy, due to the fact that it uses only GA as a direction-finding technique. Table 1 shows the summary of weaknesses regarding the related work.…”

“…Moreover, these techniques are constrained, dependent, and do not provide a guaranteed resolution of direction ambiguities for any generalized array structure. Moreover, the recent work presented for ambiguity resolution in [23] uses a DLA along with GA as a DF technique, which works well, but unfortunately its estimation accuracy is lower, due to the fact that GA has a heuristic nature that does not necessarily guarantee estimation accuracy. We need to extend the existing work for effective and accurate estimation of DOA of sources at the output of the array without having any directional ambiguities among multiple sources.…”

“…The location of the elements of both the individual NULAs are selected such that none of the ambiguous DOAs become common between both the arrays. Every element of the DLA is placed according to the rule discussed in [23]. Observation vector received at the output of each individual antenna array can be written as…”

“…Firstly, all the possible ambiguous set of DOAs for the DLA are calculated using the technique discussed in [23]. After all the ambiguous sets of DOAs for the DLA are achieved, the data are stored as they will always remain unchanged for the same DLA unless the position of any of the element becomes changed.…”