Doppler Resilient Golay Complementary Waveforms

Abstract

We present a systematic way of constructing a Doppler resilient sequence of Golay complementary waveforms for radar, for which the composite ambiguity function maintains ideal shape at small Doppler shifts. The idea is to determine a sequence of Golay pairs that annihilates the low-order terms of the Taylor expansion of the composite ambiguity function. The Prouhet-Thue-Morse sequence plays a key role in the construction of Doppler resilient sequences of Golay pairs. We extend this construction to multiple dimensions. In particular, we consider radar polarimetry, where the dimensions are realized by two orthogonal polarizations. We determine a sequence of two-by-two Alamouti matrices, where the entries involve Golay pairs and for which the matrix-valued composite ambiguity function vanishes at small Doppler shifts.

Range sidelobe suppression in a desired Doppler interval

“…In this paper, we extend the result of [13]- [15] to construct pulse trains of Golay complementary waveforms, for which the range sidelobes of the ambiguity function vanish inside a desired Doppler interval away from zero. This is accomplished by coordinating the transmission of a Golay pair of phase coded waveforms in time according to the 1's and −1's in a …”

“…One way to accomplish this is to design the sequence P so that its spectrum S P (θ) has a high-order null at a Doppler frequency inside the desired interval. This idea has been explored in [13]- [15], where it is shown that the spectrum of a PTM sequence of length 2 M+1 has an M th-order null at θ = 0. Definition 3: [16], [17] The Prouhet-Thue-Morse (PTM) sequence P = (p k ) k≥0 over {−1, 1} is defined by the following recursions:…”

“…This question was recently considered in [13], [14], where it is shown that by carefully choosing the order in which a Golay pair of phase coded waveforms is transmitted over time we can clear out the range sidelobes of the pulse train ambiguity function along modest (close to zero) Doppler shifts. The developments in [13], [14] led to the discovery that if the transmission of a Golay pair of phase coded waveforms is coordinated in time according to the entries in a biphase sequence then the magnitude of the range sidelobes can be controlled by shaping the spectrum of the biphase sequence [15].…”

Novel design of Doppler resilient complete complementary sequence for MIMO radar

“…Definition: An ðM; K; NÞ sequence set S can be defined as an ðM; K; NÞ CCS if it satisfies [4,7,8,9]. In such a system, the received signal at the kth pulse can be expressed as…”

Sidelobe suppression in a desired range/doppler interval

“…Recently, we showed [7]- [9] that by proper sequencing of only two complementary waveforms across time it is possible to achieve an ambiguity response that is free of range sidelobes inside a desired Doppler interval. The complementary codes used are Golay complementary codes [10]- [12] invented Marcel Golay, which have the property that the sum of their autocorrelation functions is an impulse in delay.…”