Mismatched filtering of odd-periodic binary sequences

Binary sequences with perfect periodic autocorrelation functions, as required in communications, radar, and measuring, are not known for any lengths >4. As a possible remedy, mismatched filtering can be used to entirely suppress any sidelobes of the periodic autocorrelation function at the expense of a reduced signal-to-noise ratio (SNR). In this work, the mismatched filtering method is extended to the odd-periodic autocorrelation function whose technical implementation is no more complex than that of periodic sequences. A new class of odd-periodic binary sequences is constructed that exist for many more lengths and exhibit significantly lower mismatched filtering losses than any known periodic sequences     

Low sidelobe radar waveforms derived from orthogonal matrices

Novel waveforms are described that have low sidelobes when individual or multiple waveforms are approximately processed. They are related to orthogonal matrices that may be associated with complementary sequences and also with periodic waveforms having autocorrelation functions with constant zero-amplitude sidelobes. Also described are sets of sequences whose cross-correlation functions sum to zero everywhere. A potential application is the elimination of ambiguous range stationary clutter     

Weight effects on the periodic ambiguity function

CW radar signals and processors are discussed. The use of the periodic ambiguity function (PAF) to analyze the delay-Doppler performance of CW signals and their corresponding correlation receivers, is extended to include weight function effects. This work provides tools which can predict the delay-Doppler response of almost any phase-coded CW radar. Examples demonstrate that a combination of CW signals having perfect periodic autocorrelation, a matched reference signal with a large number of modulation periods and a smooth weight function, can create a delay-Doppler response with extremely low sidelobes, strongly resembling the response of a coherent pulse train     

Two-valued frequency-coded waveforms with favorable periodic autocorrelation

There are known phase-coded (two-valued or polyphase) CW radar signals that exhibit perfect periodic autocorrelation function (PACF). A PACF is perfect when all its out-of-phase autocorrelation values are identically equal to zero. This paper investigates periodic, two-valued, frequency-coded signals. While none could be found with perfect PACF, we present examples with nearly perfect PACF. Their relationship to binary phase-coded signals is also considered. These signals should be attractive for CW radars because of their simple implementation, clean spectrum, and the favorable range response of their matched receiver.     

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.     

Sparse frequency transmit-and-receive waveform design

A computationally efficient algorithm derives complex digital transmit and receive ultra-wideband radar and communication waveforms with excellent arbitrary frequency band suppression and range sidelobe minimization. The transmit waveform minimizes a scalar function penalizing weighted spectral energy in arbitrary frequency bands. Near constant power results from another penalty function for deviations from constant power, or constant power is enforced by a phase-only formulation. Next, a least squares solution for the receive waveform minimizes a weighted sum of suppressed band spectral energy and range sidelobes (for pulse and continuous wave operation), with a mainlobe response constraint. Both waveforms are calculated by iterative algorithms whose updates require only linear order in memory and computation, permitting quick calculation of long pulses with thousands of samples.     

Range-time-sidelobe reduction technique for FM-derived polyphase PCcodes

A simple, easy to implement technique is presented that can significantly reduce the range-time-sidelobes of a class of polyphase pulse compression codes. This technique reduces the highest sidelobes to only one code element magnitude independent of effective pulse compression ratio. The codes considered are polyphase codes that are derived from the step-approximation-to-linear-frequency-modulation and linear-frequency-modulation waveforms such as the P1, P3, P4, and the Frank codes. The characteristics of these codes that make this possible are explained     

Removing autocorrelation sidelobes by overlaying orthogonal coding on any train of identical pulses

A coherent train of identical linear FM (LFM) pulses is used extensively in radar because of its good range and Doppler resolution. Its relatively high autocorrelation function (ACF) sidelobes are sometimes reduced through spectrum shaping (e.g., nonlinear FM, or intrapulse weighting on receive). We show how to completely remove most of the ACF sidelobes about the mainlobe peak, without any increase to the mainlobe width, by diversifying the pulses through overlaying them with orthonormal coding. A helpful byproduct of this design is reduced ACF recurrent lobes. The overlaid signal also results in reduced Doppler tolerance, which can be considered as a drawback for some applications. The method is applied to several trains of identical pulses (LFM and others) using several orthonormal codes. The effect on the three important properties of the radar signal: ACF, ambiguity function (AY), and frequency spectrum is presented. The effect on Doppler tolerance is studied, and implementation issues are discussed. The new design is also compared with complementary and sub-complementary pulse trains and is shown to be superior in many aspects.     

Time-Frequency HOP Signals Part I: Coding Based upon the Theory of Linear Congruences

Time-frequency hop codes are developed based upon the theory of linear congruences. These codes can be used for multiuser radar and asynchronous spread spectrum communications systems. A uniform upper bound is placed on the cross-correlation function between any two elements of the code set. The upper bound is minimized by choice of time-bandwidth product and is shown to diminish as 2/N, where N is the number of elements in the code set. The size and position of spurious peaks in the autocorrelation functions are discussed. The results are extended to narrowband ambiguity functions.     

Range Sidelobe Suppression for Barker Codes

The utility of Barker-type phase-reversal codes is extended by the use of sidelobe suppression techniques that can be easily implemented in digital form. It is shown that sidelobe suppression techniques can be found where the tapped delay line used to reduce the sidelobes has only a few distinct tap weights, in which case the complexity of the digital processor is greatly reduced. An example is given where the technique is applied to Barker codes with positive sidelobes, specifically, the 13-element Barker code. If higher pulse compression factors are desired than are obtainable with Barker codes, multistage Barker codes may be used. The sidelobes then may be suppressed for any one or all of the different coding stages.     

Digital and Analog Subcomplementary Sequences for Pulse Compression

Golay's complementary pairing has been a method to increase the utility of binary sequences, because of the temporal sidelobe suppression in the autocorrelation vector summation. Complementary sets of Tseng and Liu and of Hollis exhibit the same effect when several autocorrelations are combined. These complementary pairs and sets of sequences can be extended into long complementary chains by a simple transformation. This transformation is extended here to all pulse compression waveforms. By this method, even though analog complementary sequences cannot be formed, a new class of waveforms, called subcomplementary waveforms, can be formed. Following these rules, repetition of waveforms such as linear frequency modulation (LFM) or linear stepped frequency modulation (LSFM) in a prescribed manner is possible without creating autocorrelation grating lobes or repetitive sidelobes. This method is equally applicable to all analog or digital pulse compression waveforms.     

A new algorithm to optimize Barker code sidelobe suppressionfilters

The authors suggest a new algorithm for binary coding waveform sidelobe reduction after matched filtering and present a general method by which optimized sidelobe suppression filters for Barker codes can be obtained with a peak output sidelobe 2.62 dB lower than the results found in the literature (for 13-b Barker code). This optimization algorithm is also promising for other binary coding waveforms, such as truncated pseudonoise (PN) sequences and concatenated codes. This new approach can readily be applied to sidelobe-reduction filter design for other binary coding waveforms, such as truncated PN sequences, concatenated codes, etc., which often find their applications in radar systems and spread spectrum communication systems     

Group-Complementary Array Coding for Radar Clutter Rejection

A radar waveform design technique which utilizes Lagrange's method of multipliers to control temporal sidelobes and to reduce Doppler sidelobes is described. This classical method of constrained optimization is applied to the problem of synthesizing a radar wave-form where mismatch loss is the objective function to be minimized. The associated constraints are taken from expressions for the composite temporal sidelobes of the cross-correlation response and the peak correlation response where sets of code words are used to modulate a series of radar pulses. The resulting code sets and receiver reference sets are called group-complementary and produce a trench parallel to or on the range axis of the cross-ambiguity surface.     

Radar/Sonar Signal Design for Bounded Doppler Shifts

In many detection and estimation problems, Doppler frequency shifts are bounded. For clutter or multipath that is uniformly distributed in range and symmetrically distributed in Doppler shift relative to the signal, detectability of a point target or a communication signal is improved by minimizing the weighted volume of the magnitude-squared autoambiguity function. When clutter Doppler shifts are bounded, this volume is in a strip containing the range axis on the range-Doppler plane. For scattering function estimation, e.g., for weather radar, Doppler flow meters, and distributed target classifiers, it is again relevant to minimize ambiguity volume in a strip. Strip volume is minimized by using a pulse train, but such a signal has unacceptably large range sidelobes for most applications. Other waveforms that have relatively small sidelobe level within a strip on the range-Doppler plane, as well as small ambiguity volume in the strip, are obtained. The waveforms are composed of pulse pairs that are phase modulated with Golay complementary codes.     

Poly-phase codes and optimal filters for multiple user ranging

A technique is introduced to select poly-phase codes and optimal filters of a pulse compression system that have specific temporal and frequency characteristics. In the particular problem under study, multiple vehicles are assigned unique codes and receiver filters that have nearly orthogonal signatures. Narrowband users, that act as interference, are also present within the system. A code selection algorithm is used to select codes which have low autocorrelation sidelobes and low cross correlation peaks. Optimal mismatched filters are designed for these codes which minimize the peak values in the autocorrelation and the cross correlation functions. An adjustment to the filter design technique produces filters with nulls in their frequency response, in addition to having low correlation peaks. The method produces good codes and filters for a four-user system with length 34 four-phase codes. There is considerable improvement in cross and autocorrelation sidelobe levels over the matched filter case with only a slight decrease in the signal-to-noise ratio (SNR) of the system. The mismatched filter design also allows the design of frequency nulls at any frequency with arbitrary null attenuation, null width, and sidelobe level, at the cost of a slight decrease in processing gain     

Sets of One and Higher Dimensional Welti Codes and Complementary Codes

A Welti code is a binary sequence with an impulse-like autocorrelation function. A set of such codes may possess vanishing cross-correlation functions. The elements of Welti codes must be members of a set of at least two orthogonal vectors or subcodes. First, methods for synthesizing sets of one-dimensional Welti codes with vanishing cross-correlation functions, and conditions upon their existence are discussed. Then, construction methods of sets of two and higher dimensional Welti codes are presented. Based on these constructions, further sets of mutually orthogonal complementary codes in one or more dimensions can be derived. The use of such signals relates to various topics such as communication, radar and navigation systems, measuring and identification in one or higher dimensional systems, synchronization and spatial alignment, or coded aperture imaging.     

Thinned stepped frequency waveforms to furnish existing radars withimaging capability

Introducing imaging capability to an existing radar, even if it is a high RF bandwidth radar, may be difficult, due to limitations on the IF bandwidth, limitations on the pulse repetition frequency and electromagnetic compatibility problems. This paper discusses the use of thinned stepped frequency waveforms, which enable the radar to switch between RF frequencies to provide a synthesized wide RF bandwidth, while the thinning may alleviate some of the constraints imposed on the radar. Random and periodic thinning are discussed in the first part of this paper. However, thinning may cause degradation in image quality, thus an additional technique-Sequence CLEAN deconvolution-is suggested. Sequence CLEAN is an iterative deconvolution algorithm, adopted from the field of radioastronomy, which is capable of resolving close targets in a dense environment, where the system response is heavily affected by high sidelobes     

General forms and properties of zero cross-correlation radarwaveforms

General forms for both the complementary and noncomplementary zero cross-correlation waveform sets are developed. Various properties of these codes and their relationship to zero sidelobe periodic codes are stated and proved. Some radar applications and practical considerations of using these codes are briefly discussed     

Reduction of sidelobe self-interference in an agile beam radar

In an agile beam phased array radar, the beam is often multiplexed over several angular positions, and “listens” in each position only over an instrumented range that may be a fraction of the unambiguous range as determined by the pulse repetition period in each position. After transmitting a pulse in a given direction, the beam is switched, essentially instantaneously, to another position, after the instrumented range delay. In this second position, echoes from the first position, from multiple trips of the instrumented range, enter the one-way angular sidelobes of the first position. This interference is compounded if there are several beam positions in a pulse repetition period. The author proposes a method of phase coding the pulses in such a way that the pulse-to-pulse phase variation in each direction is orthogonal to every other phase code in the other directions. The codes are Walsh functions. These are sets of binary valued (+1 or -1) functions such that all of the functions in the set are mutually orthogonal. Not every possible number N of pulses in each direction and number K of beam positions can be accommodated, but a large variety of such combinations can be accommodated. Several examples are given. The combination of low one-way sidelobes and orthogonality (or near orthogonality) of the phase codes should provide for very stringent sidelobe self interference rejection