Ambiguity Removal When Using Burst Waveforms. Part II: Nonlinear Processing

An effective technique for removing range ambiguities (detections at ranges other than the true range of the object) arising when using a burst waveform is to transmit two bursts with different pulse repetition frequencies nearly simultaneously and then to process their outputs nonlinearly. This correspondence introduces two nonlinear processors which combine coincidence detection with either noncoherent multiplication or integration. It is shown that the combined false alarm and ambiguity removal performance of these nonlinear processors is superior to the performance of coincidence detection, noncoherent multiplication, or noncoherent integration when used separately.     

Generalized Response of a Linear FM Pulse Compression Matched Filter

A pulse compression matched filter is analyzed so that the response may be computed when the pulse width, FM rate, and center frequency simultaneously differ from design conditions. Unilateral and bilateral time domain amplitude weighting for sidelobe reduction is included. A general cross-ambiguity function is defined to include these effects and some basic computed results are presented for the peak envelope response with various degrees of Hamming weighting. Computer evaluation of this cross-ambiguity function allows one to choose a combination of mismatches for signal design trade-off between resolution and detection performance. Since no restrictions are placed upon the mismatch parameters, this analysis may also be used to evaluate the filter discrimination against various interfering signals.     

Some High-Velocity Clutter Effects in Matched and Mismatched Receivers

A generalized ambiguity function including the effects of Doppler dispersion is defined as the time cross correlation of the complex envelopes of two signals, both derived from the same basic waveform but with different delays and Doppler effects. The Doppler effects include the frequency shift and expansion or contraction of the modulation time scale. This expansion or contraction is the Doppler dispersion. While the general ambiguity function cannot be expressed directly in terms of the Woodward or undispersed ambiguity function, its squared magnitude can be expressed in terms of the Woodward ambiguity function. The relation is not simple, being an integral form. Nevertheless, since the Woodward ambiguity function is known for many signals, the relation may simplify the determination of the squared magnitude of the general ambiguity function. We consider the clutter output of a matched filter or correlation receiver where the receiver is matched to a waveform having a specific delay and specific time compression. The variance of the clutter output is the two-dimensional convolution of the clutter ``scattering function' with the squared magnitude of the general ambiguity function. This is a generalization of an earlier result which is formally the same but using the Woodward ambiguity function. This last result is generalized for a mismatched receiver. In such a case, the variance of the clutter output is the double convolution of the clutter scattering function with the cross ambiguity function of the transmitted waveform, modified by the average velocity of the clutter, and the receiver reference waveform.     

Ambiguity properties of quadratic congruential coding

The ambiguity characteristics of multiple access frequency hop codes based on standard quadratic congruences are investigated in the light of results obtained for codes based on Costas arrays and extended quadratic congruences. While the autoambiguity properties are found to be very similar to those of Costa codes, i.e. nearly ideal, the cross-ambiguity properties of quadratic congruential codes are much better. These results are valid across the whole class of code sets considered, but they are obtained at some expense in the pulse compression characteristics of the codes. A uniform upper bound is placed on the entire cross-ambiguity function surface, and bounds are placed on the amplitude of spurious peaks in the autoambiguity function. These bounds depend on the time-bandwidth product and code length exclusively and lead naturally to a discussion of the design tradeoffs for these two parameters. Examples of typical autoambiguity and cross-ambiguity functions are given to illustrate the performance of quadratic congruential coding with respect to Costas coding     

Self-Clutter Cancellation and Ambiguity Properties of Subcomplementary Sequences

In radar signal design it is well known that a fixed volume under the ambiguity surface representing signal energy can only be shifted but not eliminated in the delay-Doppler plane because of the constraint imposed by Woodward's total volume invariance. Rihaczek has shown that periodic signal repetition, though appealing to increased energy, increases the time-bandwidth product at the expense of introducing pronounced ambiguities in the delay-Doppler plane, and thus self-clutter is generated when signals are repeated in the time domain to increase energy. The undesirable self-clutter has a masking effect on targets in different resolution cells thereby limiting performance. An analysis is presented to show that a class of waveforms described in an earlier paper as the subcomplementary set of sequences which are basically repetitive and Hadamard coded, exhibit the property of cancelling self-clutter completely in the delay-Doppler plane if their ambiguity functions are combined. By this technique it is possible to repeat contiguously a basic waveform N times in a prescribed manner to increase signal energy and to cancel totally the resulting self-clutter by combining the ambiguity functions of N different repetitive waveforms which are Hadamard coded. A convenient matrix method to combine the ambiguity functions of subcomplementary sequences, which is an extension of known methods to derive the ambiguity function of repetitive waveforms, is presented. Radar implementation considerations and comparison of performance with various forms of linear frequency modulation (FM) are also discussed.     

Ambiguities in Spacebornene Synthetic Aperture Radar Systems

Several aspects of range and azimuth (time delay and Doppler) ambiguities in spaceborne synthetic aperture radars (SARs) are examined. An accurate method to evaluate the ratio of the intensities of the ambiguities to that of the signal is described. This method has been applied to the nominal SAR system on SEASAT and the variations of this ratio as a function of orbital latitude and attitude control error are discussed. It is also shown that the detailed range migration-azimuth phase history of an ambiguity is different from that of a signal. The images of ambiguities are, therefore, dispersed. Several examples of such dispersed images observed by the SEASAT SAR are presented. These dispersions are eliminated when the processing parameters are adjusted appropriately. Finally, a method is described which uses a set of multiple pulse repetition frequencies to determine the absolute values of the Doppler centroid frequencies for SARs with high carrier frequencies and relatively poor attitude measurements.     

Variable Format Radar Receiver Using a SAW Convolver

A technique for receiving radar pulse trains is presented [which can be of a variable format in the sense that they vary from pulse to pulse]. The heart of the receiver is a sufrace ascoustic wave (SAW) convolver. In addition to prsenting experimental results for variable format waveform reception, it is shown that the convolver can easily generate ambiguity functions for virtually any waveform, and specific results for signals such as Barker codes and linear FM (chirp) waveforms are presented.     

Synthesis of Ambiguity Functions for Prescribed Responses

The synthesis of radar ambiguity functions is approached using burst-pulse time-frequency waveform coding. Noting that the parameters that define the central response of the ambiguity function for these code classes also define the waveform code, a statistical decision procedure based upon the central response is employed to obtain Bayes-type codes. The selection of the code parameters is subject to restrictions imposed by the noncentral response of the ambiguity function. Three classes of random time-frequency codes are treated: 1) uniform amplitude, uniform pulsewidth matched codes; 2) uniform amplitude, nonuniform pulsewidth matched codes; and 3) uniform amplitude, uniform pulsewidth with receiver amplitude mismatch.     

Range, radial velocity, and acceleration MLE using radar LFM pulsetrain

An efficient implementation of the maximum likelihood estimator (MLE) is presented for the estimation of target range, radial velocity, and acceleration when the radar waveform consists of a wideband linear frequency modulated (LFM) pulse train. Analytic properties of the associated wideband ambiguity function are derived; in particular the ambiguity function, with acceleration set to zero, is derived in closed form. Convexity and symmetry properties of the ambiguity function over range, velocity, and acceleration are presented; these are useful for determining region and speed of convergence for recursive algorithms used to compute the MLE. In addition, the Cramer-Rao bound (CRB) is computed in closed form which shows that the velocity bound is decoupled from the corresponding bounds in range and acceleration. A fast MLE is then proposed which uses the Hough transform (HT) to initialize the MLE algorithm. Monte Carlo simulations show that the MLE attains the CRB for low to moderate signal-to-noise depending on the a priori estimates of range, velocity, and acceleration     

On cross-ambiguity properties of Welch-Costas arrays

We discuss cross-ambiguity properties of a specific family of Costas arrays called Welch-Costas (W-C) arrays. These properties are of interest in multiuser radar and sonar system, especially since Costas arrays are known to possess ideal auto-ambiguity functions. The theory of W-C arrays is reviewed. It is then proved that only pairs of W-C arrays can have at most two hits in their cross-ambiguity function (best possible case). The maximum number of hits in the cross-ambiguity functions of a family of W-C arrays is shown to be a function of the number of W-C arrays in the family. The upper bound on the number of hits in the cross ambiguity functions for a family of W-C arrays is also derived. Specific examples of how reducing the number of W-C arrays improves the cross-ambiguity properties are given for various types of prime numbers     

附加双差模糊度网解约束的GNSS相位延迟估计

针对现有相位延迟估计方法未利用双差模糊度网解约束的特点,提出了一种附加双差模糊度网解约束的相位延迟估计方法。首先以整周双差模糊度网解为真值更新精密单点定位(PPP)估计的非差浮点模糊度,再通过网平差法估计未校正相位延迟(UPD)。实验结果表明,PPP双差模糊度与双差模糊度网解一致性好,其宽、窄巷中误差分别为0.07周和0.11周,误差大于1周的PPP双差模糊度主要出现在卫星初升阶段。约束改变了非差浮点模糊度,从而改变了参与UPD网平差的测站,使14%新升起卫星的窄巷UPD在短时间内较无约束有大于0.2周的差异。附加约束/无约束的全天星间单差UPD差异在大于99.9%的置信水平下满足零均值假设,表明整周双差模糊度网解约束方法与无约束方法估计UPD相关产品具有等效性。研究结果可为参考网非差模糊度解算和PPP与网络实时动态定位(RTK)的融合工作提供参考。     

Resolution Performance of Pulse Trains with Large Time-Bandwidth Products

The coherent pulse train has good clutter suppression performance because the energy in its matched-filter response is essentially concentrated within sharp ambiguous spikes. However, this is so only when the Doppler distortions are neglected, so that the Doppler effect is taken as a simple translation of the carrier frequency. This paper analyzes the consequences of Doppler distortions on the resolution performance of pulse trains. It is found that Doppler distortions widen the Doppler ambiguities of the pulse train response, with the widening factor proportional to the order of the Doppler ambiguity. This reduces the interval between Doppler ambiguities, and hence the Doppler width of a clutter space that can be accommodated without severe clutter interference. For an operation in a Doppler-ambiguous mode, it also degrades nominal Doppler resolution performance. A detailed analysis of the effects is presented, and numerical results on the widening of the Doppler ambiguities are obtained.     

Slope Coding of Coherent Pulse-Burst Waveforms

Useful new properties are obtained with a coherent pulse-burst waveform if the FM slopes are allowed to change from pulse to pulse. A design feature using such a "slope-coded" waveform is the ability to transfer, in a controllable manner, ambiguity volume from the range ambiguity peaks to regions located between the peaks (in the frequency direction). Slope coding thus provides a useful mechanism for matching the waveform to the environment; i. e., it permits the signal designer to make some compromise between range ambiguity-peak heights and low-velocity clutter rejection.     

Time-frequency hop codes based upon extended quadratic congruences

Time-frequency hop codes are developed that can be used for coherent multiuser echolocation and asynchronous spread spectrum communication systems. They represent a compromise between Costas codes, which have nearly ideal autoambiguity but not so good cross-ambiguity properties, and linear congruential codes, which have nearly ideal cross-ambiguity but unattractive autoambiguity properties. Extended quadratic congruential code words are shown to have reasonably good autoambiguity and cross-ambiguity properties across the whole class of code sets considered. A uniform upper bound is placed on the entire cross-ambiguity function surface, and bounds are placed on the position and amplitude of spurious peaks in the autoambiguity function. These bounds depend on the time/bandwidth product and code length exclusively and lead naturally to a discussion of the design tradeoffs for these two parameters. Examples of typical autoambiguity and cross-ambiguity functions are given to illustrate the performance of the new codes     

Radar Waveform Synthesis by Mean Square Optimization Techniques

The synthesis of the phase-modulated waveform whose ambiguity function is the optimum estimate of some desired ambiguity function is accomplished by expanding the phase modulation in an orthogonal series. The ambiguity function x (?, ?d)|2 and the value of an arbitrary cost function defined on the (?, ?d) plane are then expressed in terms of the coefficients of the orthogonal series. The optimum waveform can then be determined by solving the variational equations for the coefficients. Numerical examples are presented for the case where it is desired to synthesize a desired ambiguity function x(?, ?d) for some rectangular region of the (?, ?d) plane.     

Doppler ambiguity resolution using multiple PRF

An algorithm for velocity ambiguity resolution in coherent pulsed Doppler radar using multiple pulse repetition frequencies (PRF) is presented. It relies on the choice of particular values for the PRFs. The folded frequency of the target signal is obtained by averaging the folded frequency estimates for each PRF, and a quasi maximum likelihood criterion is maximized for ambiguity order estimation. The fast implementation of this nonambiguous estimation procedure is based on the fast Fourier transform (FFT), The proposed waveform allows full exploitation of any (even) number of PRFs, which appears to be important for estimation improvement. The effects of the waveform parameters and the folded frequency estimation variance on the performance of the ambiguity order estimation procedure are evaluated theoretically and through computer simulations. Mean square error (MSE) curves are given to assess the Doppler frequency estimation accuracy. Finally, the new method is compared with a classical technique and the implementation of the algorithm in a clutter environment is addressed.     

Periodic ambiguity functions of EQC-based TFHC

The time-frequency hop codes based upon extended quadratic congruences (TFHC-EQC) were developed previously (1988, 1991). The known results about the ambiguity functions of the TFHC-EQC are extended from aperiodic cases to periodic cases. Precisely, the following new results are proved: (1) The tight upper bound for the periodic auto-ambiguity function of the TFHC-EQC is 6; (2) the periodic cross-ambiguity upper bound of the TFHC-EQC is at least (N-1)/2; (3) there exists a subset TFHC-EQC of volume (N-1)/2 such that its periodic cross-ambiguity is tightly upper bounded by 8     

Cochannel Interference Analysis between Spaceborne and Terrestrial Radars

An analysis of cochannel interference between spaceborne and terrestrial radars is presented. A generic modeling methodology is applied, which, it is felt, will represent the worst-case situation. In order to account for Doppler shifts, auto-and cross-ambiguity functions ions have been developed for determining matched filter outputs. The results support the ability of such radar systems to coexist relatively harmoniously utilizing currently accepted assignment procedures.     

Multiple Access Frequency Hopping Patterns with Low Ambiguity

A technique is discussed for the design of multiple access frequency hopping patterns which will allow a number of users to communicate reliably over a limited bandwidth in the presence of Doppler and timing asynchronies. The patterns are based on a subset of the Reed-Solomon codewords. They possess nearly flat ambiguity and cross-ambiguity functions and thus could be useful as discrete radar signals. In addition the structure of the patterns permits a straightforward Implementation.     

Efficient wideband signal parameter estimation using a radon-ambiguity transform slice

A novel efficient technique based on a single slice Radon-ambiguity transform (RAT) for time-delay and time-scale estimation is proposed. The proposed approach combines the narrowband cross-ambiguity function (NBCAF), the wideband cross-ambiguity function (WBCAF), and a single slice RAT to estimate multiple target parameters in noisy environments. The square modulus of Gaussian-enveloped linear frequency modulated (GLFM) signals has high-energy centrality in the ambiguity plane. Its peaks in the NBCAF fall along nearly straight lines whose slopes depend on the Doppler rates of the moving targets. These lines could be effectively detected by computing the entire Radon transform of the NBCAF for all possible angles; however, it is a computationally intensive procedure. It is shown that without calculating the entire RAT, it is possible to estimate target parameters using only a single slice of the RAT, i.e., using an appropriate projection of the NBCAF. It is demonstrated that the proposed method can successfully separate overlapping targets efficiently. The efficiency is achieved due to fast Fourier transform (FFT)-bascd processing, use of a single slice of RAT, and the use of only one-dimensional (1-D) searches.