Visible light communications (VLC) rely on white light emitting diodes (LEDs) to provide communication and illumination simultaneously. Orthogonal frequency division multiplexing (OFDM) enables bit loading in VLC to make the best use of available modulation bandwidth of white LEDs. However, OFDM signals in VLC exhibit high peak-to-average power ratio (PAPR) as in radio frequency (RF) communications. VLC-OFDM differs from RF-OFDM in that the baseband signals are real-valued and there are two PAPRs to be reduced, namely upper PAPR and lower PAPR. Moreover, upper PAPR and lower PAPR are not independently distributed, and are often subject to asymmetric constraints. In this paper, we propose a distortion-based PAPR reduction scheme to minimize the weighted upper PAPR and lower PAPR in VLC-OFDM. The proposed method takes bit loading into consideration that ensures allocating less distortions to subcarriers with more bits loaded (higher order constellations).

Orthogonal frequency-division multiplexing (OFDM) in visible light communications (VLC) inherits the disadvantage of high peak-to-average power ratio (PAPR) from OFDM in radio frequency (RF) communications. The upper peak power and lower peak power of real-valued VLC-OFDM signals are both limited by the dynamic constraints of light emitting diodes (LEDs). The efficiency and transmitted electrical power are directly related with the upper PAPR (UPAPR) and lower PAPR (LPAPR) of VLC-OFDM. In this paper, we will derive the complementary cumulative distribution function (CCDF) of UPAPR and LPAPR, and investigate the joint distribution of UPAPR and LPAPR.

Visible light communication (VLC) systems can provide illumination and communication simultaneously by way of light emitting diodes (LEDs). The communication function is achieved by employing simple and low-cost intensity modulation and direct detection (IM/DD) schemes. Brightness control and flicker mitigation are two main challenges for the illumination function. Orthogonal frequency division multiplexing (OFDM) has been considered for VLC for its ability to boost data rates. However, OFDM waveforms have high peak-to-average power ratio, and will be clipped if its magnitude is beyond the dynamic range of LEDs. Clipping can cause the performance degradation of communication as well as illumination. In this paper, we will propose an iterative clipping method considering brightness control and flicker mitigation. We will investigate the performance in terms of error vector magnitude (EVM) as well as computational complexity. We will formulate the EVM minimization problem as a convex optimization problem to compare with the iterative clipping method.

In this paper, we study multi-user multi-input single-output (MU-MISO) broadcasting for visible light communication (VLC). VLC differs from radio frequency communication in both baseband signal format and optical power constraints. We propose a precoding and biasing model for MU-MISO transmitter design in indoor VLC. We formulate and solve optimization problems for maximizing max-min fairness or throughput subject to per transmitting unit optical power constraint. We apply linear zero forcing and zero forcing dirty paper coding techniques and compare them in simulations.

Visible light communication (VLC) systems can provide illumination and communication simultaneously via light emitting diodes (LEDs). Orthogonal frequency division multiplexing (OFDM) waveforms transmitted in a VLC system will have high peak-to-average power ratios (PAPRs). Since the transmitting LED is dynamic-range limited, peaks of the OFDM waveform can be clipped causing signal degradation. This same phenomenon also occurs in RF communication system, although in RF systems it is straightforward to quantify the performance in terms of RF power conversion efficiency. Results on quantifying VLC performance are scarce. Specifically, because VLC differs from RF communication in system constraint, baseband signal format, and nonlinearity characteristic of the transmitter, it is not obvious how PAPR is related to illumination-to-communication conversion efficiency in VLC. In this paper, we will attempt to quantify the illumination-to-communication conversion efficiency and clarify how PAPR is related to efficiency in VLC systems. We also present a method to improve the efficiency of VLC OFDM systems.

Relay networks with amplify-and-forward (AF) protocol have attracted attention due to its high performance and low implementation complexity at the relay. To collect full cooperative diversity, the AF relay networks are facing two main issues. One is that the channel state information (CSI) of the source to relay link (i.e., two-hop information) is needed at the destination. The other concern is that the power scaling factor (PSF) and output signals at the relay are unbounded. These two issues make AF less practical in resource constrained networks, e.g., blind and peak power constrained relays. In this paper, we reveal the sufficient and necessary conditions on the PSF for the maximum ratio combining (MRC) receiver with two-hop CSI to achieve full cooperative diversity. Furthermore, we also provide necessary conditions on the PSF design so that MRC with one-hop CSI still collects full cooperative diversity. Based on these design criteria, we show a practical peak power constrained AF strategy so that neither the relay nor the destination node needs the source-relay CSI, yet full cooperative diversity can still be achieved.

A gap between theory and practice in signals and systems courses is often reported at many universities as a key problem in recruiting signals and systems students. On the other hand, instructors often cite a lack of fundamental understanding in mathematics as an issue in this course. Students seem to be discontent with some of the abstraction of the signals and systems courses. In this work-in-progress paper, we describe a new pathways concept we introduced to address these problems by introducing in-depth discussions, several applications and hands-on exercises.

In this paper we present two results on reducing the peak power of orthogonal frequency division multiplexing (OFDM) symbols via constellation extension (CE). The first result is a derivation of the interior-point method (IPM) algorithm needed to find the optimal distortion set, where the distortion is constrained by convex functions. Next we optimize the parameters of a hybrid CE constraint set to minimize the BER. Numerical examples are provided to illustrate the findings.

Optimizing the indices and values of free subcarriers (FSs) can significantly reduce the peak-to-average power ratio (PAR) of orthogonal frequency division multiplexing (OFDM) signals. In this paper, a numerical method is proposed to analyze the average PAR reduction performance of the FS optimization method. Different PAR reduction performance is revealed for different FS index assignments and the optimal single FS index can be determined by the proposed approach.

In this paper, we propose a novel amplify-and-forward relaying strategy for a two-hop single-relay network by incorporating an intentional peak power limit (IPPL). We show that the proposed strategy is not only practical for peak power constrained relay networks, but also helps to simplify the system at both relay and destination. With the proposed IPPL strategy, neither the relay nor the destination node needs the channel state information for the source-relay link, and full cooperative diversity can still be achieved.

In this paper the effects of receiver nonlinearities are examined for clipping channels. The objective of this work is to determine the optimal receiver functions for additive noise clipping channels. In this case the optimal receiver function will be the one that maximizes the signal-to-noise-plus-distortion ratio (SNDR) between the transmitted and received variables. To solve the problem we utilize functional analysis to find a necessary condition for the SNDR-maximizing receiver function. The results are general and can be applied for any noise and signal distribution. Furthermore, the results show that for the example given, the linear receiver is not SNDR-optimal.

In multiple-access multicarrier systems, it is possible to serve multiple users at high data rates from a single base station. In this paper, we propose the multi-channel partial transmit sequences (MCPTS) method for multiple-access OFDM peak-to-average power ratio (PAR) reduction. By applying the PTS phase rotations to each access channel separately and assuming that the rotations can be detected by each user as a channel fading, MCPTS avoids two major disadvantages of standard PTS: i) the phase rotations can be detected without side information, and ii) the set of possible phase rotation values does not need to be finite. In addition, an iterative method of joint MCPTS and power allocation is proposed to minimize the average BER. The results show a significant BER improvement.

Step size and tap length play critical roles in balancing the complexity and steady-state performance of an adaptive filter. For an impulse response with an exponential power decay profile, which models a wide range of practical systems, such as an acoustic echo path, this paper proposes a new variable step-size and tap-length least mean square (LMS) algorithm. In each iteration, the optimal step-size and tap-length are derived by minimizing the mean square deviation (MSD) between the true and the estimated filter coefficients. The proposed algorithm performs better in terms of both convergence rate and steady-state performance than the existing ones. Effectiveness of the proposed algorithm is demonstrated through computer simulations.

This paper addresses signal classification based on an average power statistic for peak-to-average-power ratio (PAR) reduced signals. Specifically, it is assumed that either a QAM or a Complex Gaussian finite-length symbol is transmitted in a noisy, peak-limited channel with known peak power. The goal is determine the whether an uninformed receiver can distinguish between these signal types using an average power statistic. Several methods for transmitting through peak-power channels are examined including optimal clipping and piecewise linear scaling (PWLS) with selected mapping (SLM) PAR reduction. For the analysis, it is necessary to derive the mean power for each of the transmission methods. Accordingly, we show how the harmonic mean PAR, E[1/PAR], is related to the mean power and derive E[1/PAR] in closed form. We find that average power is a accurate discriminator for low-order QAM and Gaussian symbols. For high-order QAM, accurate discrimination is also possible when the noise level is sufficiently low or when enough signal samples are available.

Pilot symbol assisted modulation (PSAM) orthogonal frequency division multiplexing (OFDM) has proven to be a popular technique for high-speed communication through multipath fading channels. In this paper we examine PSAM pilot design optimization in OFDM systems that employ edge null subcarriers for spectral shaping. Specifically, we show that the commonly used even pilot spacing design is suboptimal in terms of symbol estimate mean squared error (MSE) performance when a sufficient number of null subcarriers are present. We pursue a parametric design of the pilot spacings and use convex optimization techniques in order to find a pilot design that results in near-optimal symbol estimate MSE performance. Finally, we present several example PSAM OFDM pilot designs including one example based on the IEEE 802.16 standard to demonstrate performance improvements over the conventional even-spacing pilot design when null edge subcarriers are present.

In this paper we apply a new joint synchronization-pilot sequence (JSPS) optimization design technique to multiple transmitter OFDM systems. One objective in the design of the JSPS for MISO transmissions is to eliminate the requirement for the different preamble fields used for coarse and fine synchronization and channel training. In this work, independent JSPSs are designed for each transmitter in a multiple antenna system, but are transmitted simultaneously from each antenna. Consequently, JSPSs can potentially reduce the overhead of multiple antenna preamble transmissions (improving bandwidth efficiency). The objective of this paper is to determine the performance advantages of joint carrier frequency offset (CFO) and channel estimation using only the pilot portion of the JSPS. By jointly optimizing the position and power of each pilot across the transmitter antennas in Rayleigh fading channels with CFO, we show ≫ 15 dB SNR improvement in the performance of the channel estimator.

Peak-to-average power ratio (PAR) reduction techniques are often employed to increase the power efficiency of orthogonal frequency division multiplexing (OFDM) systems. A recently proposed PAR optimization method demonstrates how the PAR can be minimized when free subcarriers and a certain distortion allowance on the error vector magnitude (EVM) are available. In this paper, we derive the lower bound on the capacity for such a system and investigate the capacity-maximizing number of free subcarriers that should be used.

Linear acoustic echo cancellers are widely employed to enhance the quality of telecommunication systems. However, low-cost audio components may generate significant nonlinear distortions in the acoustic echo path, which degrades the performance of adaptive linear acoustic echo cancellers (AECs), thus motivating the nonlinear AEC research. In this paper, we propose to use a postfilter to further attenuate the nonlinear residual echo following a linear AEC. The postfilter design is based on the power spectral density (PSD) of the nonlinear residual echo. By modeling the nonlinearity in the system using a basis expansion form, the PSD estimate becomes independent of the length of the room impulse response. The performance of the proposed algorithm is illustrated by computer simulations.

A Hammerstein-Wiener system consists of a linear time invariant subsystem sandwiched between two memoryless nonlinear blocks as is the case of an acoustic system with a nonlinear loudspeaker and a nonlinear microphone. We propose to model the memoryless nonlinear blocks of the Hammerstein-Wiener system using a linear combination of nonlinear basis functions, and concentrate on the task of parameter estimation for the nonlinear blocks. An adaptive algorithm is proposed using a pseudo magnitude squared coherence (PMSC) function-based criterion. The proposed method carries out nonlinearity identification without knowing the linear block in the Hammerstein-Wiener system. This is particularly useful for nonlinear acoustic echo cancellation (NAEC) applications, where dealing with the linear and nonlinear blocks together can be computationally challenging due to the long room impulse response. Numerical examples are provided to illustrate the performance of the proposed method.

This paper presents a theoretical analysis of the residual distortions in a linearly interpolated Lookup Table (LUT) predistorter, with both uniform and non-uniform spacings. It is shown that constant linearizer performance across a wide dynamic range can be achieved with a relatively small LUT, when the entries are adequately spaced and linearly interpolated. A closed form expression for the total residual distortion power is also derived. Simulation results have been included to demonstrate the capability of a constant-range, low-resolution LUT predistorter to efficiently mitigate nonlinear distortions across more than 80dB of the top average output power levels for WCDMA transmission.

In this paper we apply a new pilot design optimization technique to the IEEE 802.16a wireless MAN standard. Using the specifications from 802.16a, we demonstrate that significant SER improvements are possible for 802.16a in a Rayleigh fading channel by judiciously choosing where the pilots are placed and the power contained in each pilot. Specifically, for the OFDM mode, we show that up to 13 dB SNR improvement is possible by simply modifying the pilots. For the OFDMA mode we demonstrate that a more modest but still significant improvement of 1.8 dB is possible with proper pilot design.

Selected mapping (SLM) is a distortionless crest factor reduction (CFR) method for orthogonal frequency division multiplexing (OFDM) transmission. With SLM, it is possible to reduce the peak-to-average power ratio (PAR) of an OFDM symbol by several decibels. In this paper, we propose a method for SLM phase sequence detection that does not require side information transmission. We refer to this method as magnitude-scaled SLM, in the sense that it scales the frequency-domain power profile of the OFDM symbol with an envelope function from a set of pre-determined envelope functions. From the envelope of the received symbol, the receiver can detect which envelope and thus which phase sequence was used in the transmission. Also presented in this paper are the theoretical characterizations of the detection error rate (DER) and symbol error rate (SER) in a magnitude-scaled SLM system. Compared with ordinary OFDM without CFR, magnitude-scaled SLM can achieve an order of magnitude SER improvement in a peak-power-limited channel.

Orthogonal frequency division multiplexing (OFDM) is a modern transmission format that has gained much popularity in the past decade. However, a serious drawback of OFDM is the high peak-to-average power ratio (PAR) of its time domain waveforms. Selected mapping (SLM) is a distortionless technique that has good PAR reduction capability; the biggest limitation of SLM however, is the need to transmit side information. In this paper, we assume constant modulus (i.e., phase shift keying - PSK) inputs and propose a novel technique that allows us to carry out SLM without having to transmit any side information and without causing any distortions

Orthogonal frequency division multiplexing (OFDM) is a spectrally efficient multicarrier modulation technique for high speed data transmission over multipath fading channels. However, the price paid for the high spectral efficiency is low power efficiency. OFDM signals suffer from high peak-to-average power ratios (PARs) which lead to power inefficiency in the RF portion of the transmitter. Selected mapping (SLM) is a promising technique to reduce the PAR of an OFDM signal and is distortionless. In this paper, we propose a novel technique which links the index of the phase rotation sequence in SLM to the location of the pilot tones that are used to estimate the channel. Each pilot tone location - phase sequence selection can lead to a different PAR value for the time-domain OFDM signal, and the signal with the lowest PAR value is transmitted. Our proposed method is "blind" in the sense that the optimum pilot tone location - phase sequence index is not transmitted as side information. We describe a novel technique to blindly detect the optimum index at the receiver. PAR reduction performance as well as BER performance of the proposed method in frequency selective fading channels are investigated

Orthogonal frequency division multiplexing (OFDM) is a spectrally efficient multicarrier modulation technique for high speed data transmission over multipath fading channels. However, the price paid for the high spectral efficiency is low power efficiency. OFDM signals suffer from high peak-to-average power ratios (PARs) which lead to power inefficiency in the RF portion of the transmitter. Selected mapping (SLM) is a promising distortionless technique to reduce the PAR of an OFDM signal. In this paper, we propose a novel technique which links the index of the phase rotation sequence in SLM to the location of the pilot tones that are used to estimate the channel. Each pilot tone location-phase sequence selection can lead to a different PAR value for the time-domain OFDM signal, and the signal with the lowest PAR value is transmitted. Our proposed method is "blind" in the sense that the "optimum" pilot tone location-phase sequence index is not transmitted as side information. We describe a novel technique to blindly detect the optimum index at the receiver by taking advantage of the disparity between the pilot tone and information signal powers. PAR reduction performance as well as BER performance of the proposed method in frequency selective fading channels are illustrated.

Orthogonal frequency division multiplexing (OFDM) transmission systems generally have low power efficiency, due to the large peak-to-average power ratio (PAR) of the OFDM signal. Selected mapping (SLM) is a promising technique to reduce the PAR for OFDM. A drawback of SLM is its high computational requirement, which hinders its practical implementation. In this paper, we propose a dynamic, two-buffer structure to reduce the computational requirement without sacrificing the PAR reduction capability. Performance analysis and simulations of the proposed technique are also carried out.

Many components used in communication systems are nonlinear and have a peak power or peak amplitude constraint. Nonlinearity generates distortions and thus signal-to-noise-and-distortion ratio (SNDR) is an appropriate performance measure. In this paper, we are interested in finding the nonlinear mapping that maximizes the SNDR subject to the peak amplitude constraint. The answer is a soft limiter with gain calculated based on the noise power and the probability density function of the input amplitude. We also investigate a bounding relationship between the SNDR and capacity of the nonlinear channel. The results of this paper can be applied for efficient transmission of high peak-to-average power ratio signals or for optimal linearization of nonlinear devices.

Orthogonal frequency division multiplexing (OFDM) transmission with superimposed training is considered in this paper. The superimposed training scheme is promoted for its high bandwidth efficiency, low computational complexity, and possibly improved power amplifier (PA) efficiency. Channel equalization is also straightforward thanks to the OFDM structure. By analyzing the peak-to-average power ratio (PAR) of the superimposed OFDM signal and utilizing a peak power constraint, we demonstrate that it is possible to lose a little in the information signal power, but gain a lot in the power that is devoted to channel sounding.

In this paper, we propose a baseband nonlinear transformation technique to improve the overall communication system performance, under the peak power constraint. A closed-form expression is derived for the signal-to-noise-and-distortion ratio (SNDR) of certain nonlinear transformations. A strategy for SNR-adaptive optimum clipping is proposed. For orthogonal frequency division multiplexing (OFDM), we show that the optimal clipping ratio leads to an SNDR improvement of 5-7 dB and accompanying decrease in symbol-error-rate. By applying an iterative symbol detection and clipping noise mitigation algorithm at the receiver, we demonstrate that clipping in OFDM can lead to large performance gains.

When a non-constant envelope signal goes through a nonlinear power amplifier, spectral regrowth (broadening) appears at the output of the power amplifier. To satisfy regulatory requirements on out-of-band emissions, spectral regrowth must be contained. We derive a novel closed-form expression for the output power spectral density when the power amplifier is quasi-memoryless and cyclostationarity of the digitally modulated input is taken into account. We compare our results with the conventional analysis where stationary input is assumed. We emphasize the importance of paying attention to the cyclostationary nature of the input when excess bandwidth is present.

The detection of tandem repeats is important in biology and medicine as it can be used for phylogenetic studies and disease diagnosis. The paper proposes two techniques for detecting approximate tandem repeats (ATRs) in DNA sequences. First, an evolutionary force heuristic is proposed to merge interspersed perfect tandem repeat sequences into an ATR structure. Next., a more general method is presented using a product spectrum of Fourier nucleotide subsequences to detect hidden periodicity. The Fourier method is sensitive to ATRs and is robust in the presence of substitutions, insertions, and deletions.

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.

The polynomial model is commonly used in predistorter design. However, the conventional polynomial model exhibits numerical instabilities when high-order terms are included. We introduce a novel set of orthogonal polynomial basis functions for predistorter modeling. Theoretically, the conventional and the orthogonal polynomial models are "equivalent", and thus should have the same performance. In practice, however, the two approaches can perform quite differently in the presence of quantization noise and with finite precision processing. Simulation results show that the orthogonal polynomials can alleviate the numerical instability problem associated with the conventional polynomials and generally yield better predistortion linearization performance.

Multipath is a major impairment in a wireless communications environment, and channel estimation algorithms are of interest. We propose a superimposed periodic pilot scheme for finite-impulse response (FIR) channel estimation. A simple first-order statistic is used, and any FIR channel can be estimated. There is no loss of information rate but a controllable increase in transmission power. We derive the variance expression of our linear channel estimate and compare with the Cramer-Rao bound. Numerical examples illustrate the effectiveness of the proposed method.

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.

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 the 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, we model the PA as a Wiener system and construct a Hammerstein predistorter, obtained using an indirect learning architecture. Linearization performance is demonstrated on a 3-carrier UMTS signal.

Power amplifiers (PAs) are important elements in communications systems and they are inherently nonlinear. Nonlinearity generates spectral regrowth (i.e., spectral broadening) in digitally modulated signals which causes adjacent channel interference. In this paper, we present a closed-form expression for the auto-covariance function of the PA output, whose Fourier transform yields the output power spectral density (PSD). The PA input does not need to be Gaussian and the PSD calculation can be carried out using common PA descriptions such as the AM/AM and AM/PM characteristics. We assume that the input is narrow-band, thus PA memory effects, on the order of a symbol period, are not present. The analytical results allow us to predict spectral regrowth without running expensive or time-consuming time-domain simulations; they also lead to a variety of optimization possibilities in transmitter design that includes the PAs.

A comparison is made between the spectral regrowth of quadrature phase shift keyed (QPSK) and offset QPSK (OQPSK) signals as they go through nonlinear amplifications. Contrary to existing approaches that assume the power amplifier input is Gaussian, our analysis is carried out without the Gaussian assumption, by using higher-order statistics. We show that it is possible to assess quantitatively whether and how much OQPSK is beneficial in reducing spectral regrowth. Simple closed form formulas are obtained when the pulse shape filter is time-limited. A particular measure of spectral broadening is also provided.

Communication networks have finite resources (bandwidth, buffer size etc.) that need to be shared among many users. In order to improve the utilization level while providing certain guarantees on the quality of service, the resources have to be allocated intelligently to the users based on the statistical characteristics of the traffic they offer. We propose a new algorithm that is more efficient in allocating resources than existing methods, when the traffic exhibits short and/or long memories. We also provide examples based on synthetic and real traffic data.

Power amplifiers (PAs) are important components in a wireless communications system. Linearity and efficiency are two desirable but conflicting requirements of a PA. All PAs exhibit varying degrees of nonlinearity which causes spectral regrowth and adjacent channel interference. Based on the behavior model of the PA and statistics of the input, it is possible to infer spectral regrowth in the output. Existing analytical results on spectral regrowth assume that the input is Gaussian, which is unrealistic for many digital communications signals. We derive a closed form expression between the covariance function (and hence the power spectrum) of the output and statistics of the input, based on a polynomial behavior model of the PA, without assuming that the input is Gaussian. Such analytical results are useful in finding optimal operating conditions of the PA so that maximum efficiency is achieved without violating the out-of-band emission requirement.

Orthogonal frequency division multiplexing (OFDM) has become increasingly popular due to its potential applications in digital audio broadcasting, digital terrestrial TV broadcasting, and satellite communication. A notable drawback of OFDM systems is their sensitivity to nonlinear distortion. For maximum power efficiency, amplifiers and transmitters of modern communication systems often operate near their saturation regions which leads to nonlinear distortion. We use the special property that the transmitted OFDM symbols are asymptotically white Gaussian to derive an algorithm that identifies the nonlinear channel. A nonlinear equalizer is built to compensate for the undesired nonlinearities. Simulation results show that the nonlinear equalizer outperforms its linear counterpart when nonlinear distortion is present.

The need to recover the original input from the output of a nonlinear system is a common problem in many applications. We propose a new method for Volterra system equalization based on finding the roots of a polynomial of the input. The method is capable of equalizing severe nonlinearities under the assumption that the input comes from a finite symbol set. Numerical simulations demonstrate its performance under a wide range of conditions.

Nonstationary signals appear often in real-life applications and many of them can be modeled as polynomial phase signals (PPS). The high-order ambiguity function (HAF) was first introduced to estimate the parameters of single component PPS. But due to its high nonlinearity, HAF has not been widely used for multi-component PPS which appear, for example, in Doppler radar applications when multiple targets are tracked simultaneously. We present a theory in this paper that HAF is virtually additive for multi-component PPS and illustrate our findings with numerical simulations.

A periodogram is an important tool to reveal hidden periodicities in a given time series but does not tell whether the resulting spectral lines are associated with constant or random amplitude harmonics. Applications dealing with random amplitude models include Doppler spread targets and detection in the presence of fading. We propose to estimate the variance of the harmonic amplitude and then make the decision based on whether the variance can be regarded as zero in a statistical sense. This is a viable approach because any constant has variance zero whereas any real random process has a positive variance. A rigorous statistical test is formulated and illustrated with simulations.

High-order ambiguity function (HAF) is an effective tool for retrieving coefficients of polynomial phase signals (PPS's). The lag choice is dictated by conflicting requirements: a large lag improves estimation accuracy but drastically limits the range of the parameters that can be estimated. By using two (large) coprime lags and solving linear Diophantine equations using the Euclidean algorithm, we are able to recover the PPS coefficients from aliased peak positions without compromising the dynamic range and the estimation accuracy. Separating components of a multicomponent PPS whose phase polynomials have very similar leading coefficients has been a challenging task, but can now be tackled easily with the two-lag approach. Numerical examples are presented to illustrate the effectiveness of our method.

The time-varying tap coefficients of frequency selective fading channels are typically modeled as random processes with low-pass power spectra. However, traditional adaptive techniques usually make no assumption on the channel's time variations and hence do not exploit this information. Kalman filtering methods are derived to track the channel by employing a multichannel autoregressive description of the time-varying taps in a decision-feedback equalization framework. Fitting a model to the variations of the channel's taps is a challenging task because the tap coefficients are not observed directly. A novel linear method is proposed in order to estimate the model parameters from input/output data. The consistency of the proposed method is shown, and some illustrative simulations are presented.

Polyspectral analysis of processes with mixed spectra is considered, and scaled polyperiodograms are introduced to clarify issues related to stationarity, ergodicity, and suppression of additive stationary noise in harmonic retrieval problems. Spectral and polyspectral approaches are capable of retrieving (un)coupled harmonics, not only when the harmonics have constant amplitudes, but also when they are observed in nonzero mean multiplicative noise. Fourier series polyspectra and asymptotic properties of scaled polyperiodograms provide general tools for higher order analysis of time series with mixed spectra. A single record phase coupling detector is derived to obviate the assumption of independent multiple records required by existing methods. The novelties are illustrated by simulation examples.

The authors are interested in estimating the Doppler shift occurred in weather radar returns, which yields precipitation velocity information. Conventional techniques including the pulse pair processor rely heavily on the assumption that the additive noise is white and hence their performance degrades when the noise color is unknown. Because the data length for a given range gate is usually small, the authors employ the high resolution MUSIC algorithm to estimate the Doppler shift. The challenge lies not only in proving that MUSIC is applicable to weather radar signals which are affected by multiplicative noise, but also in showing that MUSIC is robust when the additive noise is colored. The resulting algorithm can also be used to infer wind speed from a small number of lidar observations where the velocity is approximately constant. Assuming linear shear over a longer range, they employ the ambiguity function to estimate the acceleration and instantaneous wind velocity. Real weather radar and lidar data as well as simulated examples are provided to illustrate the performance of the algorithms.

Considers the parameter estimation problem for a class of amplitude modulated polynomial phase signals (PPS), observed in noise. The main contributions of the paper are: (1) The authors prove that the high-order ambiguity function (HAF) is invariant to certain types of amplitude modulation; thus, phase parameter estimation proceeds as in the constant amplitude case. (2) The authors derive the Cramer-Rao bounds for both the amplitude and phase parameters, when the additive noise is white Gaussian. (3) They show that the HAF is almost additive for multi-component PPS. (4) They establish the covariance bounds for the nonlinear least squares estimator when the additive noise is (non) Gaussian, and satisfies some weak mixing conditions.

Self coupled harmonics offer a practical means for testing for the presence of nonlinearities. A computationally attractive method to detect frequency and phase coupling is derived based on a slice of the Fourier series moment polyspectrum, and is capable of handling constant amplitude harmonics as well as harmonics observed in additive and nonzero mean multiplicative noise. The zero-mean case is addressed using cyclic statistics, and contrary to existing approaches, both methods rely on a single record of data and do not assume the additive noise to be Gaussian.>