Perfect Periodic Autocorrelation Research Articles

Mismatched filtering of periodic and odd-periodic binary arrays

Arrays with good correlation properties are required for coded-aperture imaging, as well as for other applications of two-dimensional signal processing. Since binary arrays with perfect periodic autocorrelation functions exist for only a few sizes, mismatched filtering is discussed. Mismatched filtering entirely suppresses any sidelobes of the periodic autocorrelation function at the expense of a slightly reduced signal-to-noise ratio. New construction methods for binary arrays are presented for which this loss, with respect to periodic or odd-periodic correlation, converges to zero with an increasing array size.

Perfect pseudoperiodic binary arrays

Arrays with good correlation properties are required for coded-aperture imaging, as well as for other applications of two-dimensional signal processing. Since binary arrays with perfect periodic autocorrelation are rather sparse, ‘pseudoperiodic’ binary arrays are discussed. The transmitted binary array is correlated in the receiver with the same array which is surrounded periodically by similar ternary arrays. A construction method is presented that permits the construction of such ‘pseudoperiodic’ binary arrays with perfect correlation properties for all sizes p1a1 × p2a2 (p1, p2 odd prime, a1, a2 = 1, 2, 3...).

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.

Accurate system identification using inputs with imperfect autocorrelation properties

The application of periodic pseudorandom sequences to system identification via input-output crosscorrelation is well established. Accurate estimates of system impulse response can be obtained if the pseudorandom test signal has a perfect (impulsive) periodic autocorrelation function. The authors present theoretical results which show that it is also possible to use sequences with imperfect autocorrelation functions as test inputs while maintaining identification accuracy. Simulation results are provided which verify the theoretical basis of this method.

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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Autocorrelation of Golomb sequences

Golomb sequences form a class of polyphase sequences which have perfect periodic autocorrelation. Given certain constraints, they also have favourable aperiodic autocorrelation. The paper presents a comprehensive study of the asymptotic behaviour of the aperiodic autocorrelation function of Golomb sequences. Some bounds for this function are obtained.

Perfect periodic correlation sequences

Sequences with the property of perfect periodic autocorrelation are used in various fields such as communication and radar systems. Various methods were introduced to construct such sequences. Most of these methods concentrated on binary or N-phase sequences. In this paper two methods to construct general phase sequences are introduced. The methods are based upon the properties of the Fourier transform of perfect periodic autocorrelation sequences. The sensitivity of these codes to errors is also elaborated.

Comparison between linear FM and phase-coded CW radars

The classical linear FM CW radar signal is compared with P3 and P4 phase-coded CW signals. The comparison covers the theoretical delay-Doppler response, the spectrum and the performances in digital receiver processors. The receivers produce a matrix of delay and Doppler cells. Three receiver approaches are considered: (a) Doppler compensation followed by a multicorrelation processor. This is a general and efficient implementation of many matched filters, which applies to any phase-coded signal. (b) A modification of (a), applicable to P3, P4 signals, in which the multicorrelators are efficiently replaced by FFTs, without altering the performances. (c) A single correlator followed by two levels of spectral analysis, for range and for Doppler. In the two matched filter implementations, (a) and (b), the P signals exhibit lower range sidelobes, due to their inherent property of perfect periodic autocorrelation. The LFM signal requires additional weighting (hence additional SNR loss) and even then does not approach the low range sidelobes of P signals. In the single correlator receiver, the two signals exhibit almost identical performances, which are similar to the performances of LFM in the matched receiver.

Polyphase sequence with low autocorrelations

It is proved that Golomb sequences have perfect periodic autocorrelation. It is also proved that the magnitudes of the out-of-phase aperiodic autocorrelation values of Golomb sequences of length L for all L>or=14 are bounded by square root (L/3). It is shown that B/sub g/(L) is asymptotic to square root (L/c) (where c approximately=4.348. . .), as L goes to infinity. >

Two-valued sequences with perfect periodic autocorrelation

Periodic two-valued signals which exhibit two-level autocorrelation can, in many cases, be made to yield an out-of-phase autocorrelation value identically equal to zero. This can be achieved by replacing the two values of the sequence (normally +1 and -1) with the two values +1 and e/sup i phi /, or with +1 and beta ( beta real). Simple expression for phi and beta are given, based on the parameters of the difference set to which such signals correspond. Another strategy is to transmit a sequence of +1s and -1s, but of +1s and bs (b real and negative). An expression for b is also obtained. >

Periodic ambiguity function of CW signals with perfect periodic autocorrelation

A periodic ambiguity function (PAF) is discussed which describes the response of a correlation receiver to a CW signal modulated by a periodic waveform, when the reference signal in the receiver is constructed from an integral number N, of periods T, of the transmitted signal. The PAF is a generalization of the periodic autocorrelation function, to the case of non-zero Doppler shift. It is shown that the PAF of N periods is obtained by multiplying the PAF of a single period by the universal function sin(N pi nu T)/N sin( pi nu T), where nu is the Doppler shift, to phase-modulated signals which exhibit perfect periodic autocorrelation when there is no Doppler shift. The PAF of these signals exhibits universal cuts along the delay and Doppler axes. These cuts are functions only of t, N and the number M, the modulation bits in one period.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Sequences and arrays with perfect periodic correlation

Properties and methods for synthesizing sequences with perfect periodic autocorrelation functions and good energy efficiency are discussed. The construction is extended to two-dimensional perfect arrays. The construction methods used are based mainly on a search in the frequency domain and on a multiplication theorem for periodic sequences and arrays.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Perfect binary arrays with 36 elements

The letter presents a new two-dimensional binary array with a perfect periodic autocorrelation function (PACF). Four decompositions of the new array in two-, three- and four-dimensional arrays with the same property are shown. These can be applied, for example, in time-frequency coding, two-dimensional synchronisation and image coding.

Ternary sequences with perfect periodic autocorrelation (Corresp.)

We construct <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0, \pm 1</tex> sequences of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(q^{2l+1}-l)/(q-1)</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q=2^{s}</tex> , with out-of-phase periodic autocorrelation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</tex> , and in-phase correlation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q^{2l};</tex> SUch that the peak factor of radiation is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(q^{2l+1}-1) /(q^{2+l}-q^{2l})</tex> , which is close to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</tex> as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</tex> becomes large.