Mutually dispersive pulse coding to enhance non-linear ambiguity suppression

Abstract

Abstract-Results from design, synthesis, and analysis of optimal mutually dispersive symbols are presented as an improvement over existing symbol sets employed in Non-linear Ambiguity Suppression (NLAS). A recently proposed theorem formulates the existence of symbol families having optimal mutual dispersion, a highly desirable property for NLAS applications. Results from theorem analysis are presented and compared to other suitable NLAS symbol sets, showing significant improvement in mutual dispersion characteristics. NLAS ambiguity suppression effectiveness is demonstrated using a set of optimal mutually dispersive symbols. I. INTRODUCTIONRadars employing pulsed waveforms are inherently ambiguous in range and Doppler. In 1962 Palermo [1] used two conjugate linear frequency modulated (LFM) pulses to demonstrate a Non-linear Ambiguity Suppression (NLAS) signal processing technique for reducing ambiguous energy in processed radar returns. The use of conjugate LFM pulses for diverse pulse coding does not extend to larger symbol families and thus has severe limitations for Mchannel (M > 2) NLAS applications. Desirable NLAS symbol sets posses 1) large partial period autocorrelation peaks with low integrated sidelobe levels and 2) maximum signal dispersion when cross-correlating pulse codes within the family [2]. Symbol sets comprised of pseudo-random discrete codes, such as Gold codes, exhibit mutual dispersion properties [3] but are not optimum for NLAS. A root mean square (rms) time duration metric of correlation functions is introduced to formulate a process for obtaining optimal mutually dispersive NLAS symbols for arbitrary code family sizes [4]. II. SYMBOL DESIGNThe discovery of symbol families having desirable characteristics for NLAS applications is by no means a recent achievement. Code Division Multiple Access (CDMA) communication schemes use discrete codes exhibiting desirable properties for NLAS [3]. The search for optimal symbol sets has historically focused on discrete codes; an avenue of research not yet providing an optimal solution. Using rms time duration of correlation functions as the metric for optimality, the search for mutually dispersive codes begins by considering a pulse coded radar signal given by:where T is the Pulse Repetition Interval (PRI) and f k (t) has a Fourier transform of the form:The processed pulse return is represented as follows:When k = l, the processed output represents a matched filter response whose inverse Fourier transform is the signal autocorrelation function (ACF), ρ kk (t) given by:The NLAS process requires the ACF to be as compressed (impulse-like) as possible and the crosscorrelation function (CCF) (mismatched filter response) to be as dispersed (flat) as possible. The rms time duration of correlation functions, σ lk as defined in (5a), is used to quantify correlative dispersion [5]. This definition of σ lk assumes ρ lk (t) is normalized to unity energy with zero mean; the dot operator (⋅) in (5a) and (5b) represents differentiation. Mutually Dispersive Pulse Codin...