Abstract
Frequency diverse array (FDA) has received much attention due to its both range- and angle-dependent beampatterns. However, the range–angle coupling and time-variant beampattern in FDA may affect its applicability. In order to address the beampattern range–angle coupling problem and time variance, many existing algorithms, by using the time-modulated optimized frequency offset (TMOFO) scheme, are presented to obtain the spatial-focusing time-invariant transmit beampattern synthesis for the FDA. To discuss their irrationality, we first give a time-modulated optimized weight vector (TMOWV) scheme with frequency offset optimization, which is a more general time-modulated scheme for the FDA beampattern synthesis and more convenient for the statistical analysis of the designed FDA transmit beampattern characteristics. Then, the statistical analysis of the designed FDA transmit beampattern is investigated through both theoretical derivations and numerical examples. The extensive simulation results demonstrate that the time-modulated approach for the time-invariant FDA transmit beampattern is invalid.
Highlights
Linear frequency diverse array (FDA) radar was first proposed by Antonik et al [1], [2] and Wicks and Antonik [3], [4] for range-angle-dependent beamforming
To decouple the range-angle beampattern and unambiguously localize targets, we need synthesize a thin dotshaped transmit beampattern to focus the transmit energy into desired positions, which can be obtained by optimizing a function of frequency offsets according to the following constraints: a main beam radiated in a predefined location with sidelobes below a given upper bound over a spatial region
STATISTICAL ANALYSIS OF FDA WITH time-modulated optimized weight vector (TMOWV) For spatial-focusing beampattern, we usually consider the spatial-focusing property for mainlobe spatial region, while the transmit beampattern energy P(θ, r, t) changes with the target angle θ, range r and t, to derive the statistical properties of focusing energy near the target location, we refer to statistical properties analysis methods [50], [51] and give the formulas of expected value, and variance about FDA beampattern based on different probability distribution of range/angle errors
Summary
Linear frequency diverse array (FDA) radar was first proposed by Antonik et al [1], [2] and Wicks and Antonik [3], [4] for range-angle-dependent beamforming. The FDA using progressive incremental frequency offsets will generate a time-variant 4-dimensional (4-D) beampattern with periodic multiple maxima in space [5] This results in an increased difficulty in controlling the main beam direction and degraded performance of the received signal-tointerference-plus-noise ratio (SINR) and target detectability. To address this problem, several time-invariant beampattern design schemes have been proposed [30]–[37]. Existing time-invariant FDA beampattern synthesis methods produce quasi-static beampatterns, or are generally implemented by using time-modulated frequency offset, and the question of whether FDA can achieve time-invariant spatial-focusing beampattern is discussed by other authors [42]–[45].
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