This letter presents model expressions describing the steady-state behavior of proportionate normalized least-mean-square (PNLMS)-type algorithms, taking into account both complex- and real-valued correlated Gaussian input data. Specifically, based on energy-conservation arguments, general expressions for the excess mean-square error (EMSE) in steady state and misadjustment are obtained. Such general expressions are then applied to two well-known PNLMS-type algorithms, namely the improved PNLMS (IPNLMS) and the individual-activation-factor PNLMS (IAF-PNLMS). Simulation results are shown confirming the accuracy of the proposed model expressions under different operating conditions.

We have implemented a same-frequency cellular repeater that uses adaptive signal processing to cancel the feedback path, thereby allowing high gain while maintaining stability. Preliminary results are presented for a real-time laboratory demonstration using an FPGA development board, realizing cancellation of about 20 dB over a 10-MHz bandwidth.

Recently, a sensor delay-line (SDL) based array structure was proposed for broadband beamforming. It is similar in form to the traditional narrowband beamformer, the only difference being a re-arrangement of the sensor positions according to the SDL concept. However, it is well-known that the narrowband beamformer can perform broadband beamforming to some degree, which gives rise to the question of whether this new arrangement is superior to the narrowband approach or not. The aim of this work is to answer this question by providing a detailed study of sensor positions for broadband beamforming. We show that when the bandwidth exceeds some threshold value, the SDL beamformer significantly outperforms the narrowband beamformer, which well justifies the new structure and gives a clear endorsement to the SDL concept.

A same-frequency cellular repeater is proposed that uses adaptive signal processing to cancel the feedback path, thereby allowing high gain while maintaining stability. This technique has application wherever it is desired to boost signal strength in outlying areas of cell coverage, particularly inside homes and buildings. It is intended to provide useful gain without needing special donor/transmit antennas requiring directional gain, separation beyond a meter or so, or roof installation. A simulation of a 900-MHz repeater with 10-MHz bandwidth is presented that demonstrates the feasibility and determines the effect of parameter values on convergence and cancellation performance.

We describe the design, implementation, and experimental evaluation of a clock recovery algorithm suitable for synchronization over a packet-based metro-area network (MAN) using the Precision Time Protocol (PTP). The algorithm consists of a packet-based phase error estimator and a phase-locked loop (PLL). The loop is augmented with a step detector that detects discontinuities in the packet arrival process due to route or network load changes, and a congestion detector that filters out unusable samples. The PLL requires a number of interesting tradeoffs that are specific for a high noise environment, while the congestion and step detector are non-traditional mechanisms specifically designed to deal with the peculiarities of a packet network.

We analyze the statistical properties of slope estimates obtained from linear regression with sample-minimum Erlang variates. The sample-minimum of sequential blocks has the effect of introducing non-uniform time samples. It is shown that this non-uniformity has negligible effect on the slope estimate variance, but introduces a spurious low-frequency component in the power spectrum, which may be detrimental for ultra-low-bandwidth tracking applications. The analysis shows that this effect can be moderated by choosing a sufficiently large number of sample-minimum output samples in the linear regression. These results are useful, for example, in clock synchronization over packet networks, where the random variates model packet arrival times.

We explore the concept of combining multiple antenna signals with complex weights so as to realize an overall transfer function that is as flat as possible over a given bandwidth. This differs from conventional equalization in that no time delay taps are used in the process, and has the advantage of diversity-like noise immunity to deep fades. A frequency- selective fading model is postulated for the propagation paths and the equalization performance is calculated using the optimal complex weights. It is shown that the bandwidth over which a given deviation from flatness can be achieved is proportional to the number of antennas, provided that they are spaced far enough apart so that the fading is independent. Performance of a conventional beamformer is also assessed, but is found to be far less effective than optimal weighting. Applications are envisaged as an alternative to orthogonal frequency-division multiplexing (OFDM) for wideband communication over channels with large delay spread, as well as channel shortening in OFDM, and other possible applications such as ultra wideband (UWB) communication.

In this letter, we develop a means for sensing changes within building structures using wideband RF probe signals with an array of sensors. A unique signature is formed for a given building by plotting the angles of specular return versus distance along a drive-by path in a ldquogramrdquo format, with coloring to indicate the path delay. This signature can be stored as a reference file and differentially compared to subsequent grams to detect significant internal changes. A simulation is presented using a ray-trace program to analyze a specific building structure. When an artificial occlusion is added inside the building, it is clearly detected by observing the differential gram. To establish feasibility in a realistic scenario, this is compared to differential grams corresponding to small changes in the drive path. As a first indication, it appears that changes of 0.1 m in any dimension produce comparable changes to a perfectly reflecting 2-m cube placed in one of the rooms.

We analyze a simple frequency-selective fading model that is formulated as a sequence of independent discrete-time impulse responses, each with independent Gaussian variates scaled by an exponential power-delay profile. This model is useful for simulating propagation path responses in a scattering environment. Various expressions and relationships are derived for the frequency correlation function, correlation bandwidth, rms delay spread, and decay time. Realization techniques are also discussed, and it is concluded that the most straightforward and efficient approach is to generate a block of samples by multiplying i.i.d. complex Gaussian variates by the square root of the exponential power-delay profile and then taking the FFT.

Power amplifiers (PAs) are essential in communication systems, but are inherently nonlinear. To achieve linearity with good efficiency, PA linearization is necessary. Digital baseband predistortion is a highly cost-effective way to linearize PAs, but most existing architectures assume that the PA has a memoryless nonlinearity. For wider bandwidth applications, such as wideband code-division multiple access, PA memory effects can no longer be ignored. Therefore, in order to achieve good linearization performance, the predistorter needs to also have memory structure. In this paper, we propose a new model for the wideband predistorter and a least-squares(LS)/Newton algorithm to estimate the model parameters. Performance of the LS/Newton algorithm is studied through computer simulations. Good linearization performance is achieved by using the new model in an experimental testbed.

We address the problem of downlink throughput improvement for IEEE 802.11a/g systems by using a modified access point (AP) equipped with multiple antennas. The main restriction is that the standard terminals should not be modified in any way. An alternating time-offset space division multiple access (SDMA) solution is considered for a conference room scenario. A simulation is based on channel models approved by the IEEE 802.11 Standard Group and takes into account the main features of the IEEE 802.11a/g standard. It is demonstrated that a near doubling of downlink capacity can be achieved in a conference room environment.

This paper explores the enhancement of WLAN downlink throughput in a conference room environment using a multi-access point. The downlink transmission uses antenna patterns to spatially separate multiple users so that they can be served simultaneously, rather than sequentially, thereby speeding up the downlink throughput. This can be useful when several users are attempting to download long documents at the same time and sequential transmission causes a throughput bottleneck. A theoretical analysis with a room response model is used to obtain the statistics of separability in terms of minimum signal-to-interference-plus-noise ratio (SINR). It is shown that for this modeled conference room environment, a two-antenna access point can theoretically deliver a two-user minimum SINR of 18 dB for about 80% of the realizations, which would, neglecting overhead, likewise increase the throughput by 80%.

Acoustic reverberation severely limits the performance of multiple microphone blind speech separation (BSS) methods. We show that the limited performance is due to random permutations of the unmixing filters over frequency. This problem, which we refer to as permutation inconsistency, becomes worse as the length of the room impulse response increases. We explore interesting connections between BSS and ideal beamforming, which leads us to propose a permutation alignment scheme based on microphone array directivity patterns. Given that the permutations are properly aligned, we show that the blind speech separation method outperforms the nonblind beamformer in a highly reverberant environment. Furthermore, we discover the tradeoff where permutations can be aligned by affording a loss in spectral resolution of the unmixing filters. We then propose a multistage algorithm, which aligns the unmixing filter permutations without sacrificing the spectral resolution. For our study, we perform experiments in both real and simulated environments and compare the results to the ideal performance benchmarks that we derive using prior knowledge of the mixing filters.

Power amplifiers (PAs) are inherently nonlinear devices and are used in virtually all communications systems. Digital baseband predistortion is a highly cost-effective way to linearize PAs, but most existing architectures assume that the PA has a memoryless nonlinearity. For wider bandwidth applications such as wideband code-division multiple access (WCDMA) or wideband orthogonal frequency-division multiplexing (W-OFDM), PA memory effects can no longer be ignored, and memoryless predistortion has limited effectiveness. In this paper, instead of focusing on a particular PA model and building a corresponding predistorter, we focus directly on the predistorter structure. In particular, we propose a memory polynomial model for the predistorter and implement it using an indirect learning architecture. Linearization performance is demonstrated on a three-carrier WCDMA signal.

A technique known as digital predistortion (DPD) is the subject of much current research and is being contemplated for the next generation RF power amplifiers. DPD has the capability of linearizing the overall amplifier response and is a cost effective technique for applications requiring wideband operation with low out-of-band spurious emissions, also known as spectral regrowth. Estimation of the DPD parameters is hampered by the presence of measurement noise at the output of the amplifier, even though this noise is not actually transmitted on air. The end effect of the noise is to degrade the DPD performance, leading to higher spectral growth. This paper shows that a major cause of this degradation can be attributed to coefficient bias induced by measurement noise in a nonlinear model. Two techniques are proposed for mitigating these effects. One uses a specially designed periodic training signal with frame averaging, and the other uses forward estimation followed by offline noiseless inverse estimation. Simulations show that spectral regrowth reductions in excess of 10 dB are possible using these techniques.

The capacity of wireless downlink communication to mobile receivers in a dense urban environment is limited primarily by co-channel interference. Downlink adaptive arrays can be used to mitigate this limitation by maximizing the power transmitted to desired in-cell mobiles in the reference cell while minimizing power to co-channel mobiles in neighboring cells. This is accomplished by using uplink measurements to estimate downlink covariance matrices and then solving a generalized eigenvalue problem. Several algorithms are proposed to adaptively estimate the optimal solution and are evaluated using a simplified signal model that allows efficient deterministic performance calculations.

Power amplifiers (PAs) are inherently nonlinear devices and are used in virtually all communications systems. Digital baseband predistortion is a highly cost effective way to linearize PAs, but most existing architectures assume that the PA has a memoryless nonlinearity. For wider bandwidth applications such as WCDMA, PA memory effects can no longer be ignored, and memoryless predistortion has limited effectiveness. In this paper, instead of focusing on a particular PA model and building a corresponding predistorter, we focus directly on the predistorter structure. In particular, we propose a memory polynomial model for the predistorter and implement it using an indirect learning architecture. Linearization performance is demonstrated on a 3-carrier UMTS signal.

In this work, we explore important connections between blind source separation (BSS) and ideal beamforming. We first compare the performance of a null-steering beamformer against that of a frequency-domain BSS method in a reverberant environment, drawing some interesting conclusions. We then examine the feasibility of using beamformer concepts to resolve permutation inconsistency across frequency, which degrades the performance of BSS methods in a reverberant environment. We also propose a permutation alignment scheme based on information gathered from the microphone array directivity patterns. This technique is novel in the sense that it works satisfactorily even when the directivity patterns exhibit grating lobes, where, in fact, better separation can be achieved in principle. We perform experiments that support the viability of the proposed method under different operating conditions and microphone spacings.

The performance of existing blind speech separation methods is limited in a realistic reverberant environment, where a need for long un-mixing filters is imperative. We first show how these methods suffer while trying to balance the competing objectives of frequency-domain permutation alignment and spectral resolution. We then propose a multistage multiresolution algorithm, which aligns the un-mixing filter permutations over the whole frequency band without sacrificing spectral resolution. We perform experiments in both real and simulated reverberant environments, and obtain improved separation results that are comparable to the ideal benchmark obtained by aligning the permutations using prior knowledge of the mixing filters.

In this paper, we investigate several types of nonlinearities used for the unique identification of receiving room impulse responses in stereo acoustic echo cancellation. The effectiveness is quantified by the mutual coherence of the transformed signals. The perceptual degradation is studied by psycho-acoustic experiments in terms of subjective quality and localization accuracy in the medial plane. The results indicate that, of the several nonlinearities considered, ideal half-wave rectification appears to be the best choice for speech. For music, the nonlinearity parameter of the ideal rectifier must be readjusted. The smoothed rectifier does not require this readjustment, but is a little more difficult to implement.

We derive a new frequency-domain adaptive algorithm by using a frequency-domain recursive least squares criterion, minimizing an error signal in the frequency-domain. We then derive an exact adaptive algorithm from the so-called normal equation. It is shown that the obtained algorithm is complex to implement, and to reduce the complexity we need to remove a constraint resulting in the unconstrained frequency-domain LMS (UFLMS) algorithm. Most importantly, we generalize all this to the multi-channel case, thereby exploiting the cross-power spectra among all the channels which is very important (for a fast convergence rate) in multichannel acoustic echo cancellation (AEC), where the input signals are highly correlated.

We study and explore the limitations of methods for blind separation of a mixture of multiple speakers in a real reverberant environment. To support our results, we analyze a frequency-domain method, which achieves blind source separation (BSS) by transforming the time-domain convolutive problem to multiple short-term problems in the frequency domain. We show that treating the problem independently at different frequency bins introduces a "permutation inconsistency" problem, which becomes worse as the length of room impulse response increases. Our studies prove that the ideas proposed in the existing literature are not capable of effectively handling this problem and a need exists for its satisfactory solution. We speculate that time-domain BSS techniques may also suffer from an equivalent permutation inconsistency problem when long un-mixing filters are used.

A doubletalk detector (DTD) is used with an echo canceler to sense when far-end speech is corrupted by near-end speech. Its role is to freeze the adaptation of the model filter when near-end speech is present in order to avoid divergence of the adaptive algorithm. Several authors have proposed to use the cross-correlation coefficient vector between the input signal vector x and the scalar output y for a DTD. We show in this paper that this measure is not appropriate and propose a modified form that meets, in an optimal way, the needs for an efficient DTD. By extension, we also propose a definition of the normalized cross-correlation matrix between two vectors and show a link with the coherence function.

We describe a new method for blind system identification that uses the cross relation properties between two or more sensor signals to estimate the impulse responses of the channels. The method performs as well or better than other similar blind identification techniques under noisy and ill-conditioned channel conditions, and is computationally simpler to implement.

One promising application in communications is desktop conferencing, which can involve several participants over a widely distributed area. Synthesized stereophonic sound will enable a listener to spatially separate one remote talker from another and thereby improve understanding. In such a scenario, we assume we are located in a hands-free environment where the composite acoustic signal is presented over loudspeakers, thus requiring acoustic echo cancellation. In this paper, we explain some of the methods that can be used to synthesize stereo sound and how such methods can be combined efficiently with stereo acoustic echo cancellation in the face of several difficult problems.

Active noise control (ANC) is achieved by introducing a cancelling "antinoise" wave through an appropriate array of secondary sources. These secondary sources are interconnected through an electronic system using a specific signal processing algorithm for the particular cancellation scheme. ANC has application to a wide variety of problems in manufacturing, industrial operations, and consumer products. The emphasis of this paper is on the practical aspects of ANC systems in terms of adaptive signal processing and digital signal processing (DSP) implementation for real-world applications. In this paper, the basic adaptive algorithm for ANC is developed and analyzed based on single-channel broad-band feedforward control. This algorithm is then modified for narrow-band feedforward and adaptive feedback control. In turn, these single-channel ANC algorithms are expanded to multiple-channel cases. Various online secondary-path modeling techniques and special adaptive algorithms, such as lattice, frequency-domain, subband, and recursive-least-squares, are also introduced. Applications of these techniques to actual problems are highlighted by several examples.

Echo cancelers commonly employ a doubletalk detector (DTD), which is essential to keep the adaptive filter from diverging in the presence of near-end speech and other disruptive noise. There have been numerous algorithms to detect doubletalk in an acoustic echo canceler (AEC). In those applications, typically, the threshold is chosen only by some heuristic method and the performance evaluation is very subjective. In this study, we develop a way to objectively evaluate DTD algorithms based on the standard statistical methods of detection theory. A receiver operating characteristic (ROC) is derived to characterize DTD performance. Several DTD algorithms are examined and simulated under typical real-world operating conditions using measured room responses and signals taken from a digital speech database. The DTD methods are then evaluated and compared using the ROC metric.

A paradox arises in a paper by Kuo and Vijayan (see ibid., vol.5, p.374-7, 1997) because notching out narrowband primary noise would seem to also prevent secondary path identification at the primary center frequency. This conundrum is resolved by examining the notch bandwidth in comparison to the resolution of the model filter.

Stereophonic sound becomes more and more important in a growing number of applications (such as teleconferencing, multimedia workstations, televideo gaming, etc.) where spatial realism is demanded. Such hands-free systems need stereophonic acoustic echo cancelers (AECs) to reduce echos that result from coupling between loudspeakers and microphones in full-duplex communication. We propose a new stereo AEC based on two experimental observations: (a) the stereo effect is due mostly to sound energy below about 1 kHz and (b) comb filtering above 1 kHz does not degrade auditory localization. The principle of the proposed structure is to use one stereo AEC at low frequencies (e.g. below 1 kHz) with nonlinear transformations on the input signals and another stereo AEC at higher frequencies (e.g. above 1 kHz) with complementary comb filters on the input signals.

We discuss the philosophy of evaluating estimated impulse responses for applications in which the overall scaling or gain is irrelevant, as, for example, in blind channel identification. We argue that no matter how the estimate is obtained, the performance should be independently evaluated using an error measure that is appropriate for a problem of this class. Of several possible error measures, the normalized projection error, which is obtained by minimizing the l/sub 2/ norm over all possible gain values, seems to be the most natural and consistent. An example demonstrates that using an inappropriate error measure can produce misleading results.

Teleconferencing systems employ acoustic echo cancelers to reduce echoes that result from coupling between the loudspeaker and microphone. To enhance the sound realism, two-channel audio is necessary. However, in this case (stereophonic sound) the acoustic echo cancellation problem is more difficult to solve because of the necessity to uniquely identify two acoustic paths. We explain these problems in detail and give an interesting solution which is much better than previously known solutions. The basic idea is to introduce a small nonlinearity into each channel that has the effect of reducing the interchannel coherence while not being noticeable for speech due to self masking.

In many applications, such as teleconferencing, multimedia workstations, televideo gaming, etc., stereo sound is already, or will soon be, implemented to give spatial realism that mono systems cannot offer. In such hands-free systems, stereophonic acoustic echo cancelers are absolutely necessary for full-duplex communication. We propose a new acoustic echo canceler (AEC) based on a fundamental experimental observation that the stereo effect is due mostly to sound energy below about 1000 Hz. The principle of the hybrid mono/stereo AEC is to use stereophonic sound with a stereo AEC at low frequencies (e.g., below 1000 Hz) and monophonic sound with a conventional mono AEC at higher frequencies (e.g., above 1000 Hz). This solution is a good compromise between the complexity of a full-band stereo AEC and spatial realism. For the stereo case, we borrow from a previous innovation and add a small nonlinearity into each channel in order to accurately identify the two receiving room impulse responses.

Teleconferencing systems employ acoustic echo cancelers (AECs) to reduce echos that result from coupling between the loudspeaker and microphone. To enhance the sound realism, two-channel audio is necessary. However, in this case (stereophonic sound) the acoustic echo cancellation problem is more difficult to solve because of the necessity to uniquely identify two acoustic paths. We explain these problems in detail and give an interesting solution which is much better than previously known solutions. The basic idea is to introduce a small nonlinearity into each channel that has the effect of reducing the interchannel coherence while not being noticeable for speech due to self masking.

Over the last decade, a certain computationally efficient, rapidly converging adaptive filtering algorithm has been independently discovered many times. The algorithm can be viewed as a generalization of the normalized LMS (NLMS) algorithm that updates on the basis of multiple input signal vectors. This article compares and discusses the different approaches to and embellishments of the basic algorithm, and contrasts the various interpretations from different perspectives.

As teleconferencing systems evolve to an ever more lifelike and transparent audio/video medium, it will be necessary to incorporate multichannel audio, which at a minimum involves two channels, i.e., stereophonic sound. However, before full-duplex stereophonic teleconferencing can be deployed, the acoustic echo cancellation (AEC) problem must be solved in this regime. This paper draws attention to a fundamental problem of multichannel AEC that concerns the nonunique nature of the estimated receiving room impulse responses. Various potential solutions are discussed but are shown to be not entirely satisfactory.>

In most acoustic echo canceler (AEC) applications, an adaptive finite impulse response (FIR) filter is employed with coefficients that are computed using the LMS algorithm. The paper establishes a theoretical basis for the slow asymptotic convergence that is often noted in practice for such applications. The analytical approach expresses the mean-square error trajectory in terms of eigenmodes and then applies the asymptotic theory of Toeplitz matrices to obtain a solution that is based on a general characterization of the actual room impulse response. The method leads to good approximations even for a moderate number of taps (N>16) and applies to both full-band and subband designs. Explicit mathematical expressions of the mean-square error convergence are derived for bandlimited white noise, a first-order Markov process, and, more generally, pth-order rational spectra and a direct power-law model, which relates to lowpass FIR filters. These expressions show that the asymptotic convergence is generally slow, being at best of order 1/t for bandlimited white noise. It is argued that input filter design cannot do much to improve slow convergence. However, the theory suggests postfiltering as a remedy that would be useful for the full-band LMS AEC and may also be applicable to subband designs.>

Because conventional feedback control systems have a gain-bandwidth limitation, a given level of noise reduction can only be achieved over a limited bandwidth. For a conventional control system, this limitation can be alleviated by using multiple stages in cascade, each stage dedicated to a portion of the desired operating band. However, for active noise cancellation there is a problem because only one entry point to the system is available and a direct cascade is not physically possible. The pseudocascade configuration is introduced for alleviating this problem. An analysis of a single-stage broadband active control system characterizes the response by the cancellation bandwidth and the out-of-band overshoot. These results are then used to synthesize a multistage cascade with offset reference frequencies. A numerical example of a sixth-order three-stage design shows that for a 4 dB overshoot constraint, the 15 dB cancellation bandwidth is increased by a factor of 2 compared with the single-stage design. A further increase of cancellation bandwidth can be achieved with additional stages.>

Cancellation path delay limits the bandwidth performance of the FXLMS (filtered-x least-mean-square) notch filter. A cascade of FXLMS notch filters using multiple reference tones is examined in order to alleviate this problem. An analysis of a single-stage notch filter characterizes the response by the cancellation bandwidth and out-of-band overshoot, which are analytically expressed in terms of the loop gain and cancellation path delay. These results are then used to synthesize a multistage cascade with offset reference tones. A pseudocascade configuration is also formulated that only requires one entry point to the primary disturbance plant, which is a prerequisite for many applications. A numerical example of a three-stage FXLMS notch filter shows that for a 3 dB overshoot constraint, the 20 dB cancellation bandwidth is increased by a factor of 2.56.>

The effect of coherence is examined using an exponential-power-law model for the signal wavefront correlation. Detection performance is quantified by the small-signal deflection criterion, which is first reviewed in the general setting of quadratic detectors and then applied to matched-field and optimal quadratic beamformers. It is shown that the detection performance of matched-field beamforming is substantially degraded for large arrays and typical coherence lengths. The optimal quadratic processor reduces this coherence loss, but at a cost of greatly increased processor complexity. Several suboptimal beamformers with reduced computational load are also developed, and their detection performance is compared to that of the matched-field and optimal beamformers. One suboptimal processor, the subarray beamformer, has proved outstanding for this application in three respects: it can realize within 1 dB of optimal performance; it is robust over a class of correlation functions; and it entails a computational burden no greater than that of full-array matched-field beamforming.>

Noting that a fine analysis is presented for the convergence and misadjustment of the normalized least-mean-square (NLMS) algorithm in the paper by Tarrab and Feuer (see ibid., vol.3, no.4, p.468091, July 1988), the commenter claims that the results and comparisons with the LMS algorithm are not in a form that readily enables the reader to draw practical conclusions. He points out that plotting mean-square error on a linear, instead of logarithmic (dB), scale hides the important detail of the error as it converges to its minimum value, which is exactly the region where the practical engineer requires detailed knowledge to assess performance. Moreover, in the comparison of the NLMS and LMS algorithm convergence rate and misadjustment, the practitioner wants to know how fast the algorithm will converge when the misadjustment is constrained to a specified value.>

The theory of finite limiting effects for a band-limited Gaussian random process is reviewed and a mathematical expression for the asymptotic distortion spectrum is derived which is accurate for frequencies outside of the original bandwidth. An expression is also derived for the total distortion power which is shown to be useful for estimating the aliased distortion spectrum when sampling is employed to form a discrete-time signal. An important application of these results is in A/D conversion, where the input signal is implicitly limited by the largest quantization level. Curves are given for the overall signal-to-distortion-plus-quantization-noise ratio (SDQR) as a function of normalized input level and number of bits carried, and show that the maximum SDQR is realized over a narrow range of input levels which is centered at about -12 dB relative to full-scale for an 8-bit A/D.

The steady-state performance of a narrowband adaptive array processor using a single auxiliary tapped delay line is analyzed for a simple two-path interference scenario, and computer solutions are presented for various combinations of signal and multipath parameters. It is shown that auxiliary delay taps are required for effective cancellation of multipath interference, even for fractional bandwidth-delay products. Good cancellation is generally achieved provided that (a) the delay line taps are spaced somewhat closer than the Nyquist sampling rate, and (b) the total length of the delay line considerably exceeds the longest multipath delay, depending on multipath component strengths. A simple impulse response model is also developed to provide an understanding of the behavior of cancellation performance and how it relates to the various parameters involved.

An analysis is presented for the response of a delay-constrained adaptive linear predictor filter to a sinusoid in white noise. Expressions are derived for the steady-state adaptive weights, frequency response, and line suppression. A useful bound is also derived for the worst-case output signal-to-noise ratio as a function of normalized frequency and the order of the filter.

An analysis of digital random numbers generated from serial samples of Gaussian noise is presented. A methodology is developed for calculating the word probability distribution in terms of the autocorrelation function of the noise. Examples are presented for three and four bit words. A related problem is also considered which concerns the noise autocorrelalion function. Bounds are derived which take into account nonideal effects of the filter used to shape the noise spectrum. An example is given for a modified double-pole bandpass model.

A technique known as a "multiple correlation cancellation loop" and also as the "LMS algorithm" is widely used in adaptive arrays for radar, sonar, and communications, as well as in many other signal processing applications. In this paper, an analysis of this technique is extended to the case when a linear filter appears in the auxiliary signal path. A general solution to this problem is obtained and several examples for narrowband and broad-band signals are presented.

A closed-form expression is obtained for the autocorrelation function of sequential M-bit, base α digital words formed by serial bits of a single binary PN sequence of length L = 2N − 1. Plots are presented for several values of M and N, showing detailed behavior and limiting curves for the binary case (α= 2).

In this paper, an adaptive spectral equalization technique is developed for multipath cancellation, and more generally for any minimum-phase distortion, which is implemented by a constrained form of adaptive linear prediction. The technique does not use decisiondirected feedback, has guaranteed convergence and stability, and is simple to realize using conventional circuit technology. Binary amplitude-shift-keying (ASK) is considered as an example of the technique, and the theoretical performance characteristics are derived for a bandlimited pulse shape. Experimental results are also presented for an operational real-time processing system which has been developed for this application and are shown to conform favorably to theory. The analytic and experimental results presented in this paper clearly indicate the usefulness of this concept for a single multipath channel, yielding a performance advantage of between 5 and 20 dB. Particularly significant is the potential of this adaptive technique to acquire and track the multipath without any a priori knowledge of the specific parameters.

A digital signal processing technique is described which utilizes a built-in automatic gain control (AGC) function. A particularly attractive algorithm called "geometric feedback" is developed which has certain desirable properties. A simple analytic solution of the response is derived for the special case of linear geometric feedback.

Several expressions are derived for the probability of error of a binary coherent phase-shift keyed communication system in the presence of interference due to discrete multipath propagation.