Mismatched Filtering of Sonar Signals

A replica correlator (matched filter) is an optimum processor for a receiver employing a pulse of continuous wave (CW) signal in a white Gaussian noise background. In an active sonar, however, when the target of interest has low Doppler shift and is embedded in a high reverberation background, this is not so. High sidelobes of the correlator frequency response pass a significant portion of the signal contained in the mainlobe of the reverberation spectrum. In order to reduce the sidelobes of the correlator output spectrum and at the same time keep the increase in its 3 dB bandwidth to a small amount, we propose lengthening of the replica of the transmitted signal and weighting it by a Kaiser window. It is demonstrated that by extending the weighted replica by 50 percent compared with the transmitted signal, it is possible to reduce the sidelobe levels to at least 40 dB below the mainlobe peak, with the concomitant increase of the 3 dB band-width by less than 5 percent. The degradation in signal-to-noise ratio (SNR) performance for such a ?mismatched? filter receiver with respect to the matched filter is less than 1.5 dB.     

Effect of Particular Gain Changes upon LFM Sidelobes

The envelope variation of an LFM waveform due to transmitter droop or receiver STC tends to cause range sidelobes. A parametric analysis of the magnitude of the sidelobes has been performed. It is shown that the sidelobes can be quite high at the matched filter output, but are low at the output of the sidelobe reduction filter. 40-dB sidelobes can be achieved even with a 4-dB envelope droop. It is shown that these results are consistent with conventional paired-echo theory. Similar results are shown to hold for droop variations of the filter transfer function.     

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     

Remarks on ?Comments on 'Signal Resolution via Digital Inverse Filtering'?

Published comments on a recent paper criticized the use of inverse filtering as applied to resolution of overlapping radar signal returns. It is shown that an inadequate model of the inverse filter was assumed by the critic, which lead him to predict excessive time sidelobes at the filter output. It is demonstrated, by computer simulation, that the time sidelobes at the output of the true inverse filter are down 30 dB or more.     

Multistatic adaptive pulse compression

A new technique denoted as multistatic adaptive pulse compression (MAPC) is introduced which exploits recent work on adaptive pulse compression (APC) in order to jointly separate and pulse compress the concurrently received return signals from K proximate multistatic radars operating (i.e., transmitting) within the same spectrum. For the return signal from a single pulse of a monostatic radar, APC estimates the particular receive filter for a given range cell in a Bayesian sense reiteratively by employing the matched filter estimates of the surrounding range cell values as a priori knowledge in order to place temporal (i.e., range) nulls at the relative ranges occupied by large targets and thereby suppress range sidelobes to the level of the noise. The MAPC approach generalizes the APC concept by jointly estimating the particular receive filter for each range cell associated with each of several concurrently-received radar return signals occupying the same spectrum. As such, MAPC is found to enable shared-spectrum multistatic operation and is shown to yield substantial performance improvement in the presence of multiple spectrum-sharing radars as compared with both standard matched filters and standard least-squares mismatched filters     

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     

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.     

Range sidelobe reduction for the quadriphase codes

Filters that reduce the sidelobes of the quadriphase-coded waveform are realized by applying the biphase-to-quadriphase transformation to the filter designs that reduce the sidelobes of the prototype biphase code. The mismatch loss is invariant under this transformation, but the resulting peak-to-sidelobe ratio (PSR) can decrease 1.5 dB maximum. An example illustrates the procedure for a compressor composed of a sidelobe reducing filter cascaded with the matched filter and a compressor realized as one mismatched filter     

Resolution in Doppler and Acceleration with Coherent Pulse Trains

The resolution properties and clutter performance of a simultaneous Doppler and acceleration measurement are investigated in detail with particular emphasis given to coherent pulse trains. The analysis is based on the concept of a matched-filter receiver, although receiver weighting of the type that reduces Doppler sidelobes is also analyzed in detail. Near the main lobe of the acceleration response is a pedestal-ike sidelobe region, the height of which is about 1/N of the main response lobe power where N is the number of pulses in the train. The extent of this pedestal along the acceleration axis is proportional to N. The acceleration measurement in a clutter environment is best performed when both targets and clutter are confined to this pedestal region, since some response sidelobes outside of this region are extremely large.     

Minimum Peak Range Sidelobe Filters for Binary Phase-Coded Waveforms

Linear programming techniques are utilized to determine the optimal filter weights for minimizing the peak range sidelobes of a binary phase-coded waveform. The resulting filter is compared with the filter obtained by use of the least square approximation to the ideal inverse filter. For a test case using the 13-element Barker code the linear programming filter is found to have peak sidelobes as much as 5 dB lower than the least squares filter of the same length.     

Concatenated Sequences for Spread Spectrum Systems

Concatenated sequences are suggested and developed for use in spread spectrum (SS) systems. Special receiver realization is discussed and it is shown that the concatenated sequences offer great advantage in reducing the size of the matched filter correlators (MFC) in the SS receiver. Experimental systems have been built using concatenated sequences and their performance is reported here. It has been shown that a processing gain of 60 is obtainable with a 15 × 4 concatenated sequence which requires three tapped delay lines (TDL), two of length 15 and one of 4. Thus a total of only 34 delay units (with a nonlinear interface network, only 19 delay units) are required. Teleprinter signals can be transmitted over telephone channels using a bandwidth (BW) expansion of 60 with an input signal-to-noise ratio (SNR) of only -5.1 dB, resulting in a character- error-rate of 1 in 103. Techniques have been developed to reduce the sidelobe levels in the aperiodic autocorrelation functions (ACF) of the pseudonoise (PN) codes. For 15 length and 7 length PN sequences, sidelobes are reduced by 9 dB and 9.4 dB, respectively, using transversal filters. Application of the SS systems to the problem of multiaccessing and antijamming are discussed.     

Clutter Suppression by Complex Weighting of Coherent Pulse Trains

Uniform coherent pulse trains offer a practical solution to the problem of designing a radar signal possessing both high range and range-rate resolution. The Doppler sensitivity provides some rejection of off-Doppler (clutter) returns in the matched filter receiver. This paper considers the use of a processor in which members of the received pulse train are selectively weighted in amplitude and phase to improve clutter suppression. The techniques described are particularly suitable for rejecting interference entering the processor through ambiguous responses (range sidelobes) of the signal. The complex weights which are derived are optimum in the sense that they produce the maximum clutter suppression for a given detection efficiency. In determining these weights, it is assumed that the distribution of clutter in range and range rate relative to targets of interest is known. Thus, clutter suppression is achieved by reducing the sidelobe levels in specified regions of the receiver response. These techniques are directly applicable to array antennas; the analogous antenna problem would be to reduce sidelobe levels in a particular sector while preserving gain. Complex weighting is most successful when the clutter is limited in both range and velocity.     

Thinned spectrum ultrawideband waveforms using stepped-frequencypolyphase codes

An ultrawideband (UWB) radar can interfere with external RF sources because of the mutual occupancy of the same frequency band. A stepped-frequency polyphase code (SFPC) waveform is proposed as a generic UWB waveform whose interference with the external RF sources is significantly reduced. The subpulses of the individual stepped-frequency (SF) pulses are phase coded using small phase perturbations. This results in a waveform which places nulls at the frequency locations of the external RF sources. Because the phase perturbations are small, a mismatched filter which uses the unperturbed pulses (no phase modulation) as a reference signal results in a simple receiver design and a small mismatch loss on receive. Furthermore, the proposed methodology also has application to narrowband or wideband radars     

An experiment with an S-band radar using pulse compression andrange sidelobe suppression for meteorological measurements

A major technology barrier to the application of pulse compression for the meteorological functions required by a next generation ATC radar is range/time sidelobes which mask and corrupt observations of weak phenomena occurring near areas of strong extended meteorological scatterers. Techniques for suppressing range sidelobes are well known but without prior knowledge of the scattering medium's velocity distribution their performance degrades rapidly in the presence of Doppler. Recent investigations have presented a “doppler tolerant” range sidelobe suppression technique. The thrust of the work described herein is the extension of previous simulations to actual transmitted dispersed/coded waveforms using the S-band surveillance radar located at Rome Laboratory Surveillance Facility. The objectives of the experiment are: 1) to extend the verification of the simulation of the Doppler tolerant technique; and 2) to demonstrate that the radar transmitter, waveform generator, and receiver imperfections do not significantly degrade resolution, performance or reliability of meteorological spectral moment estimates     

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     

Multipath-adaptive GPS/INS receiver

Multipath interference is one of the contributing sources of errors in precise global positioning system (GPS) position determination. This paper identifies key parameters of a multipath signal, focusing on estimating them accurately in order to mitigate multipath effects. Multiple model adaptive estimation (MMAE) techniques are applied to an inertial navigation system (INS)-coupled GPS receiver, based on a federated (distributed) Kalman filter design, to estimate the desired multipath parameters. The system configuration is one in which a GPS receiver and an INS are integrated together at the level of the in-phase and quadrature phase (I and Q) signals, rather than at the level of pseudo-range signals or navigation solutions. The system model of the MMAE is presented and the elemental Kalman filter design is examined. Different parameter search spaces are examined for accurate multipath parameter identification. The resulting GPS/INS receiver designs are validated through computer simulation of a user receiving signals from GPS satellites with multipath signal interference present The designed adaptive receiver provides pseudo-range estimates that are corrected for the effects of multipath interference, resulting in an integrated system that performs well with or without multipath interference present.     

Doppler Properties of Polyphase Coded Pulse Compression Waveforms

Doppler properties of the Frank polyphase code and the recently derived P1, P2, P3, and P4 polyphase codes are investigated and compared. An approximate 4 dB cyclic variation of the peak compressed signal is shown to occur as the Doppler frequency increases. The troughs in the peak-signal response occur whenever the total phase shift across the uncompressed pulse, due to Doppler, is an odd multiple of ? radians. It is shown that while the P3 and P4 codes have larger zero-Doppler peak sidelobes than the other codes, the P3 and P4 codes degrade less as the Doppler frequency increases. Also, the effects of amplitude weighting and receiver bandlimiting for both zero and nonzero Doppler are investigated.     

Optimum Mismatched Filters for Sidelobe Suppression

This paper discusses the application of least-mean-squares approximate inverse filtering techniques to radar range sidelobe reduction. The method is illustrated by application to the 13-element Barker code. The performance of the least-mean-square inverse filter is compared with the matched filter and with the simplified sidelobereducing filters of Rihaczek and Golden. A filter which completely suppresses the range sidelobes of a 13-element Barker sequence is only 0.2 dB worse than a matched filter in noise.     

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.     

适用于矢量接收机的模糊自适应CKF方法研究

卫星导航接收机矢量跟踪环路的核心就是用一个Kalman滤波器将标量接收机的信号跟踪和导航解算一起完成,优点是能够形成通道之间的相互辅助,缺点是也会相互影响。尤其在部分卫星信号被遮挡或者部分通道信号质量较差的环境下,问题通道会影响其他通道,甚至导致矢量跟踪环路滤波器发散,常规的方法是检测故障通道然后将故障通道剔除,这样需要对导航滤波器进行变维操作。针对此问题,提出了一种新的消除问题通道对其他通道影响的方法,同时不需要对导航滤波器进行变维。首先给出了一种标度因子,用来判断通道是否存在故障通道,然后给出一种利用模糊控制的导航滤波器自适应调整方法。仿真表明,在通道卫星信号被频繁遮挡的极端情况,矢量接收机依旧能保持正常的导航精度,并没有明显受到误差通道的影响,同时避免了对导航滤波器进行变维操作。