Short-time Fourier transform: two fundamental properties and an optimal implementation

Shift and rotation invariance properties of linear time-frequency representations are investigated. It is shown that among all linear time-frequency representations, only the short-time Fourier transform (STFT) family with the Hermite-Gaussian kernels satisfies both the shift invariance and rotation invariance properties that are satisfied by the Wigner distribution (WD). By extending the time-bandwidth product (TBP) concept to fractional Fourier domains, a generalized time-bandwidth product (GTBP) is defined. For mono-component signals, it is shown that GTBP provides a rotation independent measure of compactness. Similar to the TBP optimal STFT, the GTBP optimal STFT that causes the least amount of increase in the GTBP of the signal is obtained. Finally, a linear canonical decomposition of the obtained GTBP optimal STFT analysis is presented to identify its relation to the rotationally invariant STFT.     

Complementary sets of sequences

A set of equally long finite sequences, the elements of which are either + 1 or - 1, is said to be a complementary set of sequences if the sum of autocorrelation functions of the sequences in that set is zero except for a zero-shift term. A complementary set of sequences is said to be a mate of another set if the sum of the cross-correlation functions of the corresponding sequences in these two sets is zero everywhere. Complementary sets of sequences are said to be mutually orthogonal complementary sets if any two of them are mates to each other. In this paper we discuss the properties of such complementary sets of sequences. Algorithms for synthesizing new sets from a given set are given. Recursive formulas for constructing mutually orthogonal complementary sets are presented. It is shown that matrices consisting of mutually orthogonal complementary sets of sequences can be used as operators so as to per form transformations and inverse transformations on a one- or two-dimensional array of real time or spatial functions. The similarity between such new transformations and the Hadamard transformation suggests applications of such new transformations to signal processing and image coding.     

优化参数对CPM-PSWF信号性能的影响

基于椭圆球面波信号的连续相位调制(Continuous Phase Modulation Based on Prolate Spheroi-dal Wave Function,CPM-PSWF)方法是一种新颖的数字调制方式,调制参数的优化与其调制信号性能有着直接联系.分析不同调制参数对CPM-PSWF信号性能的影响,优...     

基于FPGA的雷达信号处理板设计与实现

基于CPCI总线,使用FPGA实现了雷达信号处理板的设计与实现。实现数字下变频,大时宽带宽积数字脉冲压缩以及FFT等通用雷达信号处理功能。最后给出了数字下变频和大时宽带宽积数字脉冲压缩在某雷达系统中的测试结果,测试结果满足系统要求。     

Output effect of a quadrature receiver with an input band-pass filter at reception of a phase-keyed wideband signal

An output effect of a quadrature correlation receiver with an input band-pass filter at reception of a phase-keyed wideband signal is considered. Analytical expressions for output effect of a receiver proportional to the absolute value of a complex envelope of a cross-correlation function for received and reference signals are obtained. Dependences of cross-correlation function absolute value on a time delay, frequency mismatch of a received and reference signals, and passband width of input filter are analyzed. It is shown, that cross-correlation function’s maximum is reached in case of non-zero time delay of a received signal when there is no frequency mismatch between input and reference signals. The time delay value corresponding to cross-correlation function’s maximum depends on passband width of input filter.     

Surface-wave matched delay lines for pulse compression

A system using dispersive ultrasonic lines for radar signal generation and compression has been tested. Surface waves on quartz are employed. Dispersion does not result from propagation but from nonuniform spacing of taps. Some oscilloscope traces of the correlation output are shown for linear f.m. signals having a time-bandwidth product of 80.     

Intersymbol Interference with Orthogonal Signaling

The occurrence of both inter- and intrasymbol interference in a communications system utilizing orthogonal signals and memoryless correlation detection is described, and a system model is presented. A relationship between a bound on peak interference and time-bandwidth product for several well known orthogonal signal sets is reported.     

Upper bounds and construction techniques for signal sets with constrained synchronous correlation and specified time - bandwidth product (Corresp.)

Upper bounds are presented on the size of equal energy continuous time signal sets occupying a given time-bandwidth (TB) product under specified synchronous correlation constraints. Both time-limited (aperiodic) and periodic signal sets are addressed, with appropriate measures of bandwidth for each. Signal set construction techniques are derived which illustrate that the bounds for periodic signal sets are relatively tight, while those obtained for aperiodic signal sets are tight under certain conditions.     

基于稀疏矩阵和相关函数联合优化的MIMO-OFDM线性调频波形复用设计与实现方法

多输入多输出合成孔径雷达(Multiple-Input Multiple-Output Synthetic Aperture Radar, MIMO SAR)发射信号应该具有大时间带宽积和良好的模糊函数特性。该文联合优化稀疏矩阵和相关函数来设计多路正交的MIMO SAR 正交频分复用线性调频(OFDM chirp)信号,首先将MIMO SAR波形设计转化为跳频频率与跳频幅度的联合设计,并提出以最小化稀疏矩阵块相关系数及信号互相关峰值和为约束条件,采用迭代搜索法求解最佳编码矩阵;并以最小化信号自相关旁瓣峰值与互相关峰值之和为约束条件,采用遗传算法确定最佳幅度矩阵;最后采用组合优化搜索法设计出最佳信号。文中还分析了发射阵元数目、跳频总间隔数及总频率选择数与信号性能之间的关系。仿真结果表明此方法可以设计多路正交大时间带宽积OFDM chirp信号,同时降低信号的互相关峰值与自相关旁瓣峰值、提高互模糊性能。      

Multidimensional maximum-entropy covariance extension

A universal characterization of maximum-entropy covariances for multidimensional signals is presented. It is shown that the maximum-entropy extension of an arbitrary partial covariance of a nonstationary multidimensional signal always has a banded inverse, i.e the inverse is sparse and has the same support as the given partial covariance. A dual formulation of the problem that makes it possible to approximate maximum-entropy extensions with models selected from suitably constrained model sets is introduced. It is proved that the best approximation in terms of multidimensional recursible autoregressive models can be determined by solving a set of linear equations. A simple graph-theoretic criterion is introduced to characterize those partial covariances whose maximum-entropy extension coincides with its autoregressive approximation, as in the conventional (one-dimensional stationary) maximum-entropy problem     

Sidelobe Suppression in Low and High Time-Bandwidth Products of Linear FM Pulse Compression Filters

The peak sidelobe suppression of unweighed linear FM surface acoustic wave filters limits the dynamic range of pulse compression systems. Using a discrete inverse Fourier transform "sampling technique" and complex Fresnel integral algorithms, this paper extends previous results of other authors from a time-bandwidth product of 50 up to the high value of 720. In the present work, the weighting is applied in the frequency domain, employing an external Hamming weighting function. The output waveforms are determined for different sampling rates. The results show that a peak sidelobe suppression of -38 dB from the main Iobe is achieved for high time-bandwidth product (TB = 720) at a sampling rate of 512 with broadening in the main lobe, while it is -41 dB for a low time-bandwidth product of TB = 50. Also, the paper contains charts showing the sidelobe suppression of unweighed and Hamming externally weighted linear FM pulse compression filters at different values of time-bandwidth products TB (50,100,250,370,510,720) with different central frequencies, dispersion times, and bandwidths B. The skirt steepness, sidelobe ripple rejection, Gibbs ripples of the wave spectrum, reduction of the insertion loss, and suppression of Fresnel ripples are also compared.     

On the capacity of a noiseless photon channel

An expression is derived for the capacity of a noiseless photon channel as a function of bandwidth, carrier frequency, and average signal power. This expression is an extension of a formula derived by Gordon which is applicable in the limit of narrow bandwidth. By comparison of the two results, it is shown that Gordon's formula is highly accurate over a large range of bandwidth, and that significant deviations occur only when the average signal power is extremely small. The derivation is based on a model of transmitting photons at different frequencies, distinguishable to the limit of the Heisenberg principle, which allows distinguishable states to have the same energy. This degeneracy, which in the narrow-band limit is simply related to the time-bandwidth product, plays a role in the (maximum entropy) energy distributions. These distributions are shown to vary from noise-like (where the rms fluctuations exceed the mean value) to Poisson as the time-bandwidth product varies from unity (or nondegenerate) to infinity. For any degeneracy, the distribution is the discrete analog of its continuous (classical) counterpart. For infinite degeneracy, when photon frequencies may take a continuum of values, the channel capacity is achieved for a signal power spectral density which has the same form as the average energy of a quantized oscillator in thermal equilibrium. As a concluding result, it is shown that for a noiseless channel with fixed average power but without any frequency restrictions, there exists an upper bound to channel capacity which is proportional to the square root of the average signal power.     

Performance of the variable-length stochastic gradient lattice filter in adaptive noise cancellation of nonstationary signals—A simulation case study

The variable-length filter for adaptive noise cancellation of nonstationary signals is introduced. The optimum length of number of filter stages is shown to be chosen in terms of the algorithm noise. It is shown that such an optimal filter can always act positively even when the cross-correlation between the input channels is close to zero. The performance of the variable-length stochastic gradient (SG) lattice filter is theoretically studied for a given nonstationary (time variable) system simulated on a computer. The results of the simulation are then compared with theory. It is shown that, for nonstationary signals, the variable-length filter yields a better noise reduction than the conventional LMS (Widrow et al., 1976) and lattice filters.     

On the identification of exponentially decaying signals

Studies a new approach to estimating the component amplitudes and decay rates of transient signals that consist of real decaying exponentials. A set of predetermined “basis” exponentials is fitted to discrete samples of a signal. The basis is required to be selective, each basis exponential “selecting” signal exponents that are close to its own and “rejecting” others. The first part of the paper is concerned with determining such basis sets. The authors take a single-exponential test signal, analyze it in terms of the basis exponentials, and consider each fitted amplitude as a function of test exponent. Each such function is then required to peak in a manner familiar to the discrete Fourier transform (DFT) theory, when the test and basis exponents coincide, diminishing in magnitude as their difference increases. It is shown that for equispaced data, such selective bases exist and are uniquely determined by model order and sampling interval. Formulas for basis decay rates and fitting amplitudes are obtained in closed form. It is shown that a time-bandwidth relationship also holds. However, the selective basis set turns out to be unacceptably sensitive to noise. The second part of the paper explores a method to overcome this drawback. The authors study the effect of overdetermination and a small simultaneous relaxation of the peaked-shape requirement for a test exponential. Of these, the latter implies usage of nonexponential basis functions, and this is the more fundamental strategy     

一种低信噪比下线性调频信号回波时延高分辨估计新方法

本文以雷达距离域超分辨应用为例，研究了基于高分辨阵列处理算法的线性调频信号重叠回波时延高分辨估计技术。首先，针对线性调频信号提出了一种信号增强算法用于回波信号的预处理，以有效地降低超分辨处理适用的信噪比门限。     

The strong simplex conjecture is false

The design of M average-energy-constrained signals in additive white Gaussian noise is addressed. The long-standing strong simplex conjecture, which postulates that the regular simplex signal set maximizes the probability of correct detection under an average-energy constraint, is disproven. A signal set is presented that performs better than the regular simplex signal set at low signal-to-noise ratios for all M⩾7. This leads to the result that, for all M⩾7, there is no signal set of M signals which is optimal at all signal-to-noise ratios. Furthermore, the optimal signal set at low signal-to-noise ratios is not an equal energy set for any M⩾7. The regular simplex is shown to be the unique signal set which maximizes the minimum distance between signals. It follows that a signal set which maximizes the minimum distance is not necessarily optimum. However, the regular simplex is shown to be globally optimum in the sense of uniquely maximizing the union bound on error probability at all signal-to-noise ratios     

基于OFDM调制雷达信号仿真分析

基于OFDM(Orthorgonal Frequency Division Multiplexing,正交频分复用)调制雷达信号是近年来新体制雷达信号研究热点。由于其具有大时宽带宽积,良好的抗干扰性能,较高的频谱利用率和易于数字化处理等诸多优点近年来备受关注。首先分析了OFDM雷达信号基本原理,给出了该雷达信号时域结构表示、频域结构表示,并通过仿真分析验证了OFDM雷达信号具有良好的距离分辨率。     

Polarization Ellipse Analysis of Nonstationary Random Signals

We present a novel way of extending rotary-component and polarization analysis to nonstationary random signals. If a complex signal is resolved into counterclockwise and clockwise rotating phasors at one particular frequency only, it traces out an ellipse in the complex plane. Rotary-component analysis characterizes this ellipse in terms of its shape and orientation. Polarization analysis looks at the coherence between counterclockwise and clockwise rotating phasors and whether there is a preferred rotation direction of the ellipse (counterclockwise or clockwise). In the nonstationary case, we replace this ellipse with a time-dependent local ellipse that, at a given time instant, gives the best local approximation of the signal from a given frequency component. This local ellipse is then analyzed in terms of its shape, orientation, and degree of polarization. A time-frequency coherence measures how well the local ellipse approximates the signal. The ellipse parameters and the time-frequency coherence can be expressed in terms of the Rihaczek time-frequency distribution. Under coordinate rotation, the ellipse shape, the degree of polarization, and the time-frequency coherence are invariant, and the ellipse orientation is covariant. The methods presented in this paper provide an alternative to ellipse decompositions based on wavelet ridge analysis.      

Channel coding with quadrature-quadrature phase shift-keying(Q2PSK) signals

Channel coding due to trellis modulation has been proved to be useful for bandlimited channels. However, these modulations, mostly designed with n-use of 2D signals, are primarily aimed at coding gain only. It is pointed out that utilization of all available signal dimensions, which is limited by the time-bandwidth product, may improve the bandwidth efficiency and simultaneously bring an additional coding gain. Trellis coding with a spectrally efficient 4D signal set based on Q²PSK is addressed. Without any expansion of the Q ²PSK signal set, a simple hand-designed 16-state trellis code provides a coding gain of 6.02 dB. With the same number of states in G. Ungergoeck's (1982) 8-PSK trellis, the gain is 4.1 dB. In low intersymbol interference situations, the bandwidth efficiency of this coded Q²PSK is twice that of coded 8-PSK; if both operate at 2 b/s Hz and P_b(E)=10^-5, the coded Q²PSK provides a saving of about 4 dB over the coded 8-PSK. Some fully connected trellises with an expanded signal due to 2-use of Q²PSK signals are also presented. Two such codes ar rate-7/8 achieve a gain of 5.45 dB with only eight states     

Block-Based Methods for the Reconstruction of Finite-Length Signals From Nonuniform Samples

Two novel block-based algorithms are presented for the reconstruction of uniform samples given the nonuniform samples. The first algorithm uses a sinc interpolator whereas the second one uses a DFT-based interpolator. It is shown that the proposed algorithms are stable and the error due to noise and sampling jitter is bounded by the corresponding error norms of noise and jitter, respectively. We show that both of the block-based algorithms provide nearly perfect reconstruction for a class of practically time and bandlimited signals. Boundary effects are considered and single and multiblock processing is discussed. A modified block-based algorithm is developed by using the windowing technique in order to improve the mean-squared error (MSE) performance for nonbandlimited signals. It is shown that this algorithm performs better than a group of alternative algorithms, including Yen's third algorithm, for a variety of signal, noise, and sampling grids