A Time Sidelobe Reduction Technique for Small Time-Bandwidth Chirp

A filtering technique is described which permits time sidelobe suppression of small time-bandwidth product shirp. Signal-to-noise loss and time sidelobe level sensitivity to Doppler shift are presented for a filtered chirp waveform whose time-bandwidth product is 10.     

Some Properties and Effects of Reverberation in Acoustic Surveillance

Following the work of Van Trees,[1] the effect of wide-sense stationary clutter on signal detectability with a matched filter is determined. The improvement to be gained by a high time-bandwidth product in the transmitted waveform for the detection of low-velocity targets is clearly shown. The additional noise contributed by the clutter is reduced by a factor equal to the time-bandwidth product. This reducing effect occurs provided that the transmitted waveform is adjusted properly. The optimum transmitted waveform for detection of low-velocity targets turns out to be one whose energy density spectrum is flat over the bandwidth of interest. This derivation is made by a simple application of Schwarz's inequality rather than the application of the calculus of variations that was done by Manasse.[14] Computations were made of the loss encountered by a narrow-band single-frequency waveform and by a wide-band linear FM waveform, each used in a matched-filter detector. The contrast is especially marked for very low target speeds where the narrow-band waveform is very bad. Its loss drops off sharply with target speed while the loss of the wide-band waveform drops off very slowly in comparison. Beyond a certain small target speed, the narrow-band loss is negligible. However, with enough bandwidth, the wide-band waveform can be made to have acceptable loss at all target speeds.     

Likelihood-ratio detection of frequency-hopped signals

The optimum system for intercepting frequency-hopped signals uses a channelized receiver and a likelihood-ratio test (LRT). Previous results on the performance of the optimum system have been based on Gaussian assumptions, which are generally valid for transmissions having large time-bandwidth areas. Results, obtained by Monte Carlo simulation, for relatively small time-bandwidth transmissions are given here. The signal model is a simple one known as “pure frequency hopping.” Comparisons with the LRT show that energy detection loss increases when the time-bandwidth product of the transmission is increased by increasing the number of frequencies, even when the number of pulses is also increased. The loss decreases when only the number of pulses is increased. Over the parameter range observed, binary detection loss tends to increase with the number of pulses and decrease with the number of frequencies. Results are included for a moving-window version of the LRT. A parameter of the LRT is the signal-to-noise ratio (SNR). The effect of using a design value not equal to the true SNR is shown     

Maximum Likelihood Energy Detection of Mary Orthogonal Signals

The literature on energy detection is extended by applying it to the processing of M'ary orthogonal communication signals of arbitrary time-bandwidth product. Guassian noise channel transition probabilities are derived for maximum likelihood energy detection, modified to the extent of including an erasure threshold. Relations and computational techniques are described for determining the symbol erasure and error probabilities for general signal alphabet sizes (M) and time-bandwidth products. When time of arrival is known exactly and Doppler is negligible, gible, it is determined that energy detection is inferior to noncoherent matched filter detection. For time-bandwidth products of the order of 100 and error probabilities around 10 3, a loss of about 5 dB occurs which is attributable to a lack of knowledge of the detail signal structure. However, for problems where time of arrival and/ or Doppler are unknown, energy detection will perform nearly as well as matched filter detection of, for example, spread spectrum signals, and is also simpler to implement. General energy detection performance curves are given in terms of required signal energy for specific error and erasure probabilities, as a function of M'ary and time-bandwidth product.     

Linear FM Signal Formats for Beacon and Communication Systems

This paper examines the capabilities of the class of linear FM spread-spectrum signals within the context of potential communications systems usage in order to establish some performance criteria and bounds that permit comparison with other spread-spectrum formats. A systematic basis is provided for parameter selection for this class of signals by examining the interaction a mong the frequency-modulation indices, time-bandwidth product, and cross-talk criteria that determine the number of effective linear FM signals (or channels) that can be used within the constraints of a bounded time-frequency region. A general expression is derived relating N, the number of useful signals, R2, a cross-talk parameter, ToWo, the mean time-bandwidth product, and ?max and ?min, the maximum and minimum FM rates of the signal set. Canonic signal processor structures are described for ensembles of linear FM signals that have either constant duration or constant bandwidth. It is then shown that the signal modulation format can be modified in accordance with classical paired-echo theory to expand the utility of this class of signals in both synchronous and nonsynchronous operations to yield the equivalent of time-division and code multiplexing. Possible applications for this signal format are discussed.     

Recent advances in analog signal processing

Analog signal processors which perform convolution, correlation, matched filtering, and Fourier transformation are considered. Specifically, the authors focus on one- and two-dimensional signal processors using charge-coupled-device, surface-acoustic-wave, acoustooptic, and superconductive components. The device performances are compared in terms of parameters such as signal bandwidth, time-bandwidth product, and dynamic range. These analog components are compared with existing and planned digital processor designs. Potential applications are highlighted in wideband spread-spectrum packet-radio communication, radar range-Doppler imaging, wideband compressive receivers, and low-bit-rate image-coding systems     

Sonar Array Detection of Gaussian Signals in Gaussian Noise of Unknown Power

A statistical test is postulated for detecting, with an M-element hydrophone array, a Gaussian signal in spatially independent Gaussian noise of unknown power. The test is an extension of the uniformly-most-powerful (UMP) unbiased test for a two-element array. The output signal-to-noise ratio of the test is calculated and, for a large number of independent space-time samples, is shown to be no better than a mean-level detector (MLD). Receiver operating characteristic curves (ROC) for the MLD are computed and compared to the ROC curves for the optimum (Bayes) parametric detector. The input signal-to-noise power ratios required to provide a detection probability of 0.5 differ by less than 0.2 dB for a fifty-element array with wide variation in false-alarm probability and time-bandwidth product. This result suggests that both the extended bivariate UMP unbiased test and the MLD perform close to the unknown UMP unbiased test for independence of a multivariate Gaussian distribution.     

A Matched-Filter Pulse-Compression System Using a Nonlinear FM Waveform

The realization of a rectangular pulse-compression waveform having low time sidelobes and zero mismatch loss due to spectral weighting is discussed. The theoretical aspects of the design of such a waveform are presented with particular reference to frequency modulated, rectangular pulses. The design and performance of a matched-filter pulse-compression system having essentially zero mismatch loss are presented. The system discussed has a time-bandwidth product of 22 and time sidelobes suppressed at least 27 dB; the measured mismatch loss is 0.1 dB. The difficulty of achieving the required nonlinear time delay dispersion is overcome by synthesizing the dispersive network as a cascade of all-pass networks.     

Performance Evaluation of Energy Detectors

The prediction of energy detector performance requires a complicated calculation or a tedious manipulation of nomograms. For a large time-bandwidth product WT, however, it is commonplace to use the formula (E/No) = d?WT to anticipate the required average input energy-to-noise spectral density ratio for a wanted signal detectability parameter d and thus avoid the computational difficulty. This paper proposes a modified formula (E/No) = ?d?WT that is applicable for all range of WT, where ? is the modification factor derived on an empirical basis. The Van Trees measure of the signal detectability parameter of the energy detector also is derived analytically and compared to the modified equation.     

Detection of Narrowband Signals Using Time-Domain Adaptive Filters

The detection performance of a conventional narrowband analyzer is compared with two adaptive processor mechanizations based on the Widrow least mean squares algorithm. Comparisons are based on both analysis and extensive digital simulation. With a narrowband signal in stationary, white background noise, the performance of the three systems is shown to be essentially the same. With nonstationary background noise, the performance of the conventional system degrades by an amount proportional to the processing time-bandwidth product. The adaptive systems appear to be less sensitive to the nonstationary background, resulting in a potential performance advantage relative to the conventional system.     

The CLFM: A Method of Generating Linear Frequency-Coded Radar Pulses

A simple method of generating a coherent linear frequency-modulated pulse, suitable for use in a radar pulse-compression system, is described. The method, termed CLFM, employs a swept-frequency oscillator with closed-loop control of its phase. The phase-error voltages for the loop are obtained by sampling the waveform at regular intervals. The sampling technique itself is unconventional and avoids the need for large bandwidth circuitry. Results obtained with a demonstration model of the CLFM, generating a signal with a time-bandwidth product of 1000, are described.     

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.     

Phase-Coded Interrupted CW Signals and Processors

High resolution radars require signals with large time-bandwidth product such as CW signal and coherent pulse train (CPT). We discuss a phase-coded interrupted CW (ICW) signal which is the combination of CW signal and CPT. Phase codes used here are with perfect periodic autocorrelation. The periodic ambiguity function of ICW signals is studied including single-carrier signal and multi-carrier signal. It is interesting that the gate function has different effects on two signals and contributes to a multi-carrier ICW signal which yields nearly perfect autocorrelation. Meanwhile we also suggest an efficient receiver approach to ICW signals, which can reduce the computational burden of the processor and utilize the good properties of P3 and P4 codes.     

Time-Frequency HOP Signals Part II: Coding Based upon Quadratic Congruences

High-efficiency multicomponent signals for maximization of signalto-noise ratio are investigated. Maximization of signal-to-noise ratio in colored noise requires control of volume distribution of the signal ambiguity function and transmission of unity efficiency signals. Signal efficiency is defined as the ratio of average power to the peak power. It is concluded that the signals must be frequency hop pulse trains. Quadratic congruences are chosen to place the components in time-frequency space. The number-theoretic properties of these signals provide bounds on the position and amplitude of the various peaks of the signal ambiguity function. The tradeoffs are shown between volume removal, number of component signals, and the time-bandwidth product.     

Bandpass Signal Sampling and Coherent Detection

Coherent detectors in radar and communications receivers are generally implemented in the form of two parallel baseband channels which form in-phase (I) and quadrature (Q) components of a received RF/IF signal. Phase errors of several degrees due to imperfect matching of these separate channels limit the performance achievable from signal processors such as moving target indicators (MTI), coherent integrators, Doppler filters, antenna array processors, and coherent sidelobe cancellers. Thus methods in which a single analog to digital (A/D) converter samples and digitizes the IF signal directly, eliminating the need for IF to baseband conversion, have been of recent interest and are the subject of this paper. To obtain accurate coherent detection from IF samples taken near the Nyquist rate requires interpolation based upon a number of stored samples. An algorithm derived from sampling theory is defined and used to demonstrate accurate reconstruction of the original IF signal from digitized samples. In-phase and quadrature components of the signal are shown to be available from processed samples with demonstrated phase errors less than 0.2°.     

The hit array: an analysis formalism for multiple access frequencyhop coding

A formalism is presented for the analysis of general frequency hop waveforms, such as those suitable for use in coherent active radar and sonar echolocation systems as well as multiple-access spread-spectrum communications. This formalism is based on the concept of coincidence, or `hit', between two frequency hopping patterns. The collection of all possible hits, together with their locations, is recorded in time-frequency space, which produces the high array associated with the two patterns considered. If the code length is sufficiently small with respect to the time-bandwidth product chosen, the hit array can be viewed as a digital representation of the corresponding ambiguity function. Salient properties of the hit array formalism are derived, including simple relationships between hit arrays resulting from basic symmetry-preserving transformations. These properties make it possible to predict the performance of a given set of frequency hop waveforms directly from the associated set of frequency hopping patterns     

Stability of Parameter Estimates for a Gaussian Process

Maximum-likelihood estimates for the levels of the mean value function and the covariance function of a Gaussian random process are investigated. The stability of these estimates is examined as the actual covariance function of the process deviates from the form assumed in the estimators. It is found that the time-bandwidth product for stationary processes represents an upper bound on the number of estimator terms that can be safely used when estimating with uncertainty about the process covariance function. This result is consistent with other interpretations of the time-bandwidth product and tempers the conclusion that, in principle, an infinite number of estimator terms can be used to obtain a perfect estimate of the covariance level. In practice, the estimate of the level can never be perfect, and the accuracy of the estimate depends on the observation interval. Finally, conditions are established to ensure asymptotic stability of the estimates and physical interpretations are presented.     

Radiometric detection of spread-spectrum signals in noise ofuncertain power

The standard analysis of the radiometric detectability of a spread-spectrum signal assumes a background of stationary, white Gaussian noise whose power spectral density can be measured very accurately. This assumption yields a fairly high probability of interception, even for signals of short duration. By explicitly considering the effect of uncertain knowledge of the noise power density, it is demonstrated that detection of these signals by a wideband radiometer can be considerably more difficult in practice than is indicated by the standard result. Worst-case performance bounds are provided as a function of input signal-to-noise ratio (SNR), time-bandwidth (TW) product and peak-to-peak noise uncertainty. The results are illustrated graphically for a number of situations of interest. It is also shown that asymptotically, as the TW product becomes large, the SNR required for detection becomes a function of noise uncertainty only and is independent of the detection parameters and the observation interval     

Experiments in Adaptive Estimation of Unknown Binary Waveforms

A special-purpose adaptive machine is described which carries out estimation in real time of an unknown binary waveform which is perturbed with additive Gaussian noise. Unknown waveforms of over 103 samples in duration can be recovered. The unknown waveforms are of unknown epoch and can reappear at either random or periodic time intervals. The observed signal is received at moderate or low signal-to-noise ratios so that a single observation of the received data (even if one knew the precise signal arrival time) is not sufficient to provide a good estimate of the signal waveshape. Experimental results are described which show transient behavior waveform estimate. The transient behavior is expressed as the number of errors in the current estimate of the signal plotted vs. time. In a noisy environment, each ``learning' transient is a random time function. These learning transients are shown for several different signal-to-noise ratios and indicate the threshold noise levels for various types of initial states of the machine memory.     

Stretch: A Time-Transformation Technique

Stretch is a passive, linear, time-variant technique for performing temporal operations on many classes of signals. The technique employs three dispersive networks and a mixer. Signal slowdown, speedup, or time reversal can be attained by choice of network slopes. These temporal operations are performed within a signal "window," and the duration of the window is determined by the network time-bandwidth products. Both heuristic argumentation and rigorous analysis are presented, as are the results of a simple laboratory experiment.