Opportunistic spectrum access in a cognitive radio network has been a challenge due to the dynamic nature of spectrum availability and possible collisions between the primary user (PU) and the secondary user (SU). To maximize the spectrum utilization, we propose a spectrum access strategy where SU's packets are interleaved with periodic sensing to detect PU's return. We formulate the sensing/probing/access process as a maximum rate-of-return problem in the optimal stopping theory framework and show that the optimal channel access strategy is a pure threshold policy. We consider a realistic channel and system model by taking into account channel fading and sensing errors. We jointly optimize the rate threshold and the packet transmission time to maximize the average throughput of SU, while limiting interference to PU.

Opportunistic spectrum access in a cognitive radio network has been a challenge due to the dynamic nature of spectrum availability and possible collisions between the primary user (PU) and the secondary user (SU). To maximize the spectrum utilization, we propose a spectrum access strategy where SU's packets are interleaved with periodic sensing to detect PU's return. Similar to earlier works on distributed opportunistic scheduling (DOS), we formulate the sensing/probing/access process as a maximum rate-of-return problem in the optimal stopping theory framework and show that the optimal channel access strategy is a pure threshold policy. We consider a realistic channel and system model by taking into account channel fading and sensing errors. We jointly optimize the rate threshold and the packet transmission time to maximize the average throughput of SU, while limiting interference to PU. Our numerical results show that significant throughput gains can be achieved with the proposed scheme compared to other well-known schemes. Our work sheds light on designing DOS protocols for cognitive radio with optimal transmission time that takes into account the dynamic nature of PUs.

We develop channel-aware opportunistic spectrum access strategies for cognitive radio networks consisting of multiple secondary users. In addition to balancing between the cost of foregoing weaker transmission opportunities in pursuit of channels that offer better data rates, we consider collisions between primary users (PUs) and secondary users (SUs), and among the SUs themselves. We derive strategies for both cooperative setting where SUs maximize their sum total of throughputs, as well as non-cooperative, game theoretic setting where each SU tries to maximize its own throughput. We show that the optimal schemes for both scenarios are pure threshold policies, where each SU decides to use or skip transmission opportunities by comparing the channel qualities to a fixed threshold. In the non-cooperative case, we establish the existence of Nash equilibrium and develop best response strategies that can converge to equilibria, with SUs relying only on their local observations. We study the tradeoff between maximal throughput in cooperative setting and fairness in the non-cooperative setting, and schemes based on utility functions and pricing that mitigate this tradeoff. Lastly, we analyze the issue of interference of SUs to the PUs. We show numerical results illustrating the schemes and analysis.

In this work, we develop limited feedback techniques that utilize both Channel State Information (CSI) and Channel Distribution Information (CDI) for communication in multiuser MIMO beamforming networks with SINR constraints on the links. We minimize power in the network using a CDI-based algorithm, and then use limited CSI feedback to improve on this scheme by reducing power consumption further and transmit opportunistically. We study three cases of the CSI feedback channel-with one bit of bandwidth, with infinite bits, and with B bits. We develop feedback techniques for the one-bit and infinite-bit cases, and then derive the optimal quantizer for the B-bit case. Our results show that significant power reduction can be achieved using a small number of bits.

In this work, we look at single user and multiuser Multiple-Input Multiple-Output (MIMO) beamforming networks with Channel Distribution Information (CDI). CDI does not need to be updated every time the channel changes, but only when the statistics of the channel change. Thus, feedback in the network is significantly reduced when compared to CSI schemes. With statistical information, we can only guarantee quality of service for a certain probability of outage in the network. The optimal beamformers and an optimal power control algorithm to minimize the power cost function in the network are presented for the well-known Kronecker model.

With the convergence of multimedia applications and wireless communications, there is an urgent need for developing new scheduling algorithms to support real-time traffic with stringent delay requirements. However, distributed scheduling under delay constraints is not well understood and remains an under-explored area. A main goal of this study is to take some steps in this direction and explore the distributed opportunistic scheduling (DOS) with delay constraints. Consider a network with M links which contend for the channel using random access. Distributed scheduling in such a network requires joint channel probing and distributed scheduling. Using optimal stopping theory, we explore DOS for throughput maximization, under two different types of average delay constraints: 1) a network-wide constraint where the average delay should be no greater than ?; or 2) individual user constraints where the average delay per user should be no greater than am, m = 1,..., M. Since the standard techniques for constrained optimal stopping problems are based on sample-path arguments and are not applicable here, we take a stochastic Lagrangian approach instead. We characterize the corresponding optimal scheduling policies accordingly, and show that they have a pure threshold structure, i.e. data transmission is scheduled if and only if the rate is above a threshold. Specifically, in the case with a network-wide delay constraint, somewhat surprisingly, there exists a sharp transition associated with a critical time constant, denoted by ?*. If a is less than ?*, the optimal rate threshold depends on ?; otherwise it does not depends on a at all, and the optimal policy is the same as that in the unconstrained case. In the case with individual user delay constraints, we cast the threshold selection problem across links as a non-cooperative game, and establish the existence of Nash equilibria. Again we observe a sharp transition associated with critical time constants {?m*}, in the sense that when ?m? am*for all users, the Nash equilibrium becomes the same one as if there were no delay constraints.

The goal of this paper is to explore the benefits of channel diversity in wireless ad hoc networks. Our model is that of a Poisson point process of transmitters, each with a receiver at a given distance. A packet is divided in blocks which are transmitted over different subbands determined by random frequency hopping. At the receiver, a maximum-likelihood decoder is employed to estimate the transmitted packet/codeword. We show that, if L is the Hamming distance of the error correction code and ε is a constraint on the packet error probability, the transmission capacity of the network is proportional to ε1/L, when ε → 0. The proportionality constant depends on the code selection, the packet length, the geometry of the symbol constellation and the number of receive antennas. This result implies that, at the cost of a moderate decoding complexity, large gains can be achieved by a simple interference randomization scheme during packet transmission. We also address practical issues such as channel estimation and power control. We find that reliable channel information can be obtained at the receiver without significant rate loss and demonstrate that channel-inversion power control can increase the transmission capacity.

Orthogonal frequency division multiplexing (OFDM) is noted for its resistance to narrowband interference when equipped with forward error correction. This technique along with erasure insertion is adequate when the the signal-to-interference ratio (SIR) is moderate, around 0 dB, however, when the interference is severe, i.e. SIR = -20 dB, a non-orthogonal interference corrupts a large number of the data subcarriers due to spectral leakage. This situation requires a large number of erasures that compromise the code's error correction capability. The prediction-error filter (PEF) is proposed as an erasure insertion mechanism that localizes the erasures to the tones surrounding the interference, while not affecting the remaining tones. The simulation results indicate excellent performance, for the bit-interleaved coded modulated (BICM) OFDM system using the PEF and BPSK modulation when the SIR = -20 dB in a frequency-selective fading channel.

We present a detection scheme for multiple-symbol DPSK for use in a statistically unknown time-varying channel. The scheme relies on a parametric representation of the time- varying channel, resulting in a reduction in the number of parameters required to be determined by optimizing a maximum likelihood sequence estimation (MLSE) type cost function. We also present a reduced-complexity version of the detection scheme based on sphere decoding. Analysis and simulations show good performance in Rayleigh fading over varying degrees of channel time-variation for an appropriately selected channel parameterization.

In this paper, we propose a physical (PHY)-medium access control (MAC) cross-layer protocol for ad hoc networks with antenna-array-equipped nodes that employ single-antenna transmission and multiple-antenna reception. Our protocol extends the progressive back-off algorithm (PBOA), proposed by Toumpis and Goldsmith, by integrating medium access and power control with optimum receive beamforming (ORB); hence it is named PBOA-ORB. The protocol performance is evaluated via simulations over a single-hop ad hoc network that is subject to a uniform traffic load. It is shown that PBOA-ORB significantly enhances both the aggregate throughput and the energy efficiency of PBOA by harnessing the interference suppression and array gains of receive beamforming. Specifically, for a small number of antennas compared to the number of nodes, the aggregate throughput increases linearly with the number of antennas while the average energy consumption per data packet decreases.

We consider a network where each route comprises a backlogged source, a number of relays and a destination at a finite distance. The locations of the sources and the relays are realizations of independent Poisson point processes. Given that the nodes observe a TDMA/ALOHA MAC protocol, our objective is to determine the number of relays and their placement such that the mean end-to-end delay in a typical route of the network is minimized. We first study an idealistic network model where all routes have the same number of hops, the same distance per hop and their own dedicated relays. Combining tools from queueing theory and stochastic geometry, we provide a precise characterization of the mean end-to-end delay. We find that the delay is minimized if the first hop is much longer than the remaining hops and that the optimal number of hops scales sublinearly with the source-destination distance. Simulating the original network scenario reveals that the analytical results are accurate, provided that the density of the relay process is sufficiently large. We conclude that, given the considered MAC protocol, our analysis provides a delay-minimizing routing strategy for random, multihop networks involving a small number of hops.

Optimization of the transmission range in terms of maximizing information efficiency is studied in this paper for mobile ad hoc networks (MANETs) with frequency-hopped (FH) CDMA and multiple antennas. Realistic channel models are employed to account for path-loss, log-normal shadowing, and Rayleigh fading. The shadowing and fading are assumed time-varying with different time-scales due to mobility and hopping. The receiver employs decision-feedback demodulation for differential unitary space-time modulation and erasure insertion decoding for Reed-Solomon codes [14] [15]. The decoding error probability is derived based on distributions of the multiple access interference power and the signal-to-interference ratio in a dwell for ground propagation model. The trade-off between information efficiency and transmission range is studied in detail and insight is obtained into the impact of various factors, including the spreading gain, modulation and coding schemes, feedback length, erasure insertion, order of spatial diversity, time-variation of the shadowing, and channel statistics such as Doppler frequency and shadowing spread.

The issue of data-aided joint carrier frequency offset (CFO) and channel estimation is investigated in the presence of a rapidly time-varying frequency-selective channel. We derive novel joint CFO/channel estimators for two cases: known and unknown channel statistics. The CFO estimator that makes use of known channel statistics is shown to attain the Cramer-Rao bound. If channel statistics are unknown to the estimator then a parameterization of the time-varying channel is required and this is shown to degrade performance. Theoretical analysis of the derived estimators is provided along with simulation results.

Linear precoding (beamforming) techniques exist that maximize the sum rate in multi-antenna broadcast channels. Such algorithms require accurate channel state information (CSI) at the transmitter and are performance sensitive to erroneous or outdated CSI. The current work focuses on adapting these algorithms to work on the statistics of the channel, rather than channel state, in order to provide more stable performance. This stable beamforming method is shown to require the full spatial correlation matrix thus suffering from high complexity in the feedback channel. Parameterization of the spatial correlation using popular channel models is also considered to make the proposed beamforming practical.

This work explores the performance of a multiple-input multiple-output broadcast channel where both the transmitter and receivers have outdated channel knowledge due to node motion or other time-variations in the communication channel. A performance analysis based on measured channel responses reveals significant throughput degradation for optimal linear and nonlinear precoding strategies unless the channel state information (CSI) is frequently fed back to the transmitter. The paper then develops a linear beamforming precoding strategy based on channel distribution information in the form of a full spatial correlation matrix for each user. This algorithm is shown to provide highly stable communication, with a throughput that is higher than that for optimal precoders operating on outdated CSI, in a time-variant environment, indicating that this approach can operate with significantly reduced feedback frequency. Furthermore, the paper demonstrates the use of the well-known Kronecker and Weichselberger models to parameterize the full correlation matrix to enable further reduction in the amount of feedback data required for implementation of the new beamforming technique.

In this paper, performance of the Alamouti space- time code (STC) [1] and performance of the concatenation between the convolutional code and the Alamouti STC are derived. In order to describe realistic performance issues, we assume that the channel estimates are calculated from linear filters using noisy pilot symbols. We also assume non-quasi- static channels, spatially correlated transmit antennas and finite- depth interleaving. Two types of receivers are investigated for the Alamouti STC, namely, the linear-combining space-time decoder (LC-STD) and the maximum-likelihood space-time decoder (ML- STD). Two types of receivers are investigated for the concatenated system, namely, the LC-STD with the ML convolutional decoder and the joint Alamouti and convolutional ML decoder. The results have shown that the LC-STD is more sensitive to the Doppler spread than the ML-STD. However, since the ML- STD is very sensitive to the channel estimation error, the gains provided by the decoder in fast fading channels will be offset unless an optimized channel estimator is employed. Performance comparisons between the Alamouti systems and the SISO systems indicate that, when the system environment is not ideal, the SISO systems may outperform the Alamouti systems. Lastly, analytical results are compared with simulation results to illustrate the accuracy of the analysis.

In this paper, closed-form expressions for the uncoded bit error probability of closed-loop transmit diversity (CLTD) algorithms with two transmit and one receive antennas and noisy channel state information (CSI) in time-varying Rayleigh fading channels are derived. Two CLTD algorithms considered are the phase-amplitude CLTD (PA-CLTD), where the transmit antennas may transmit with different signal energy, and the phase-only CLTD (PO-CLTD), where the transmit antennas must transmit with the same signal energy. In addition to the uncoded bit error probability, this paper also derives the pairwise error probability when finite-depth interleaved convolutional codes are used with CLTD algorithms. However, due to the complexity of the coded system, the pairwise error probabilities are not in the closed-form expressions. The results have shown that PA-CLTD performs slightly better than PO-CLTD although PA-CLTD requires significantly more feedback information and that, when the Doppler spread is large, the performance of CLTD algorithms may degrade significantly. Moreover, a comparison between PA-CLTD, the Alamouti space-time code and the SISO system indicates that PA-CLTD outperforms the other two systems when the Doppler spread is small and the pilot SNR is large. Finally, the analytical results are compared with results from Monte Carlo simulation and the comparison shows that the analytical results match well with the simulation results.

This paper describes a transformation technique aimed at solving the peak-to-average power ratio (PAPR) problem associated with OFDM (orthogonal frequency-division multiplexing). Constant envelope OFDM (CE-OFDM) transforms the OFDM signal, by way of phase modulation, to a signal designed for efficient power amplification. At the receiver, the inverse transformation - phase demodulation - is applied prior to the conventional OFDM demodulator. The performance of CE-OFDM is analyzed in additive white Gaussian noise (AWGN) and fading channels. CE-OFDM is shown to achieve good performance in dense multipath with the use of cyclic prefix transmission in conjunction with a frequency- domain equalizer (FDE). By way of computer simulation and hardware realization, CE-OFDM is shown to compare favorably to conventional OFDM.

The least-mean square (LMS) decision-feedback equalizer (DFE) was previously shown [1], [2] to possess an extended convergence time in an interference limited environment. In [1] it was shown that the convergence time can be significantly reduced by using the received samples and the training data to initialize (data-aided initialization) the LMS weights with an estimate for the Wiener weights. In this paper, two data- aided initialization techniques for equalization in the presence of severe narrowband interference are discussed and compared. The estimate of the Wiener filter is obtained from data-based averages of the autocorrelation matrix and the cross-correlation vector. The first technique is the Multistage Wiener Filter (MSWF) first proposed by Goldstein, et al. [3]. This algorithm provides a reduced complexity approach by approximating the Wiener filter in a lower dimensional subspace. The second technique is a parametric approximation to the Direct Matrix Inversion (DMI) solution based on the Gohberg-Semencul formula [4], [5] to obtain the inverse in a computationally efficient fashion. Both techniques were compared in terms of complexity (i.e. the number of multiplications required) and BER performance as compared to the theoretical Wiener filter for the DFE. The MSWF requires fewer training symbols than the approximation to the DMI solution in order to approach the BER performance of the theoretical Wiener filter. The parametric approximation to the DMI solution is computationally efficient but exhibits instability due to assumptions made on the structure of the correlation matrix and when the minimum eigenvalue is close to zero at high SNR.

We consider anadhocnetwork where frequency hopping (FH), convolutional coding and multiple antennas are employed in order to combat fading and multiple access (MA) interference. The transmitters are distributed in space according to the Poisson distribution and the corresponding receivers are situated at a fixed distance. Under a channel model that accounts for Rayleigh fading and path-loss, we derive an approximation to the frame-error-probability (FEP). This is in turn used to obtain simple expressions for network metrics of interest, such as thenetworkthroughputandtheinformationefficiency, previously introduced in the literature. A number of interesting observations is made with respect to how the aforementioned metrics are affected by the code diversity order, the choice of multiple- input multiple-output (MIMO) technique and the propagation exponent.

The least mean square (LMS) algorithm is widely assumed to operate around the corresponding Wiener filter solution. It has been observed that an exception to this popular perception occurs when the algorithm is used to adapt a transversal equalizer in the presence of additive narrowband interference. In the latter case, the steady-state LMS behavior does not correspond to the Wiener filter: its mean weights are different from the Wiener weights, and its mean squared error performance may be significantly better than the Wiener performance. Starting from the Butterweck expansion of the weight update equation, we derive a recursive approximation for the mean of the LMS weight vector in steady-state. The analytical approximation is good for all step-sizes where the expansion converges, as supported by the simulation results.

We consider an ad hoc network where frequency hopping (FH) and coding are employed in order to mitigate multiple-access interference. In contrast to previous work, in our model hopping takes place at the symbol level. As a result, different interference levels are encountered across a codeword/packet, creating interference diversity which is exploited through coding. Moreover, the nodes are equipped with multiple antennas which can be used for further error protection or increase of the transmission rate through space-time block coding or spatial multiplexing, respectively. Assuming an infinite network of terminals, modelled as a Poisson random field, the performance is evaluated in terms of the product (spectral efficiency) times (distance), often referred to as information efficiency. With a cross-layer design perspective in mind, results are presented for various combinations of routing strategies, MIMO techniques and code diversity orders.

In a TDD/CDMA network with variable traffic asymmetry across cells, dynamic channel allocation (DCA) enhances resource utilization compared to fixed channel allocation (FCA). However, it also induces crossed-slot intercell interference, which can severely degrade the system performance. To tackle this problem, we propose a scheme that combines a decentralized interference-aware DCA algorithm with space-time LMMSE joint detection at the receivers. Thus, crossed-slot interference is initially mitigated at the resource allocation layer and, then, residual intercell interference is suppressed (along with intersymbol and intracell interference) at the physical layer. The uplink performance of this scheme is evaluated in terms of SINR outage and average throughput via system-level simulations and is compared to that of benchmark random DCA and FCA schemes. The proposed scheme is shown to outperform random DCA and achieve a considerable throughput gain over FCA, that increases with the number of receive antennas.

In this paper, we develop a coded MIMO FH-CDMA transceiver that is robust to partial-band jamming and the near-far problem for ad hoc networks with high mobility. Spatial and frequency diversity are achieved respectively by differential unitary space-time modulation (DUSTM) and coding/interleaving. Decision-feedback demodulation (DFD) and erasure insertion (EI) decoding are employed to mitigate fast Rayleigh fading and interference. A decision-directed adaptive estimator is also developed to estimate the required parameters in DFD and EI. The two proposed EI schemes are based on the Bayesian framework proposed by Baum and Pursley (1992) and a novel threshold test of the effective signal to noise and interference ratio (ESINR), respectively. Decoding error probability of the ESINR based EI is derived analytically. Performance of both EI schemes are examined under various interference conditions, and the effect of EI thresholds is carefully discussed. The Bayesian EI is shown to be insensitive to suboptimal threshold and achieves significantly better performance than error-only decoding. Furthermore, it is shown that analysis of the ESINR based EI scheme predicts the performance of the Bayesian EI when the interference is dominant.

We consider in this paper filtered multitone (FMT) modulation over frequency-selective time-varying fading channels. Due to the phase and amplitude distortion introduced by the fading channel, not only is the orthogonality among different subcarriers destroyed, but also the perfect Nyquist sampling condition of the baseband matched filters is no longer valid. Consequently, interchannel, as well as intersymbol, interference will cause distortions to the transmitted signals. In this paper, the interference caused by the channel frequency selectivity and time variance is quantified by analyzing the demodulated signals at the receiver under several different fading-channel conditions. An analysis of the average carrier-to-interference (C/I) ratio of the FMT system is provided in order to demonstrate the underlying tradeoff between spectral efficiency and system performance. For comparison purposes with other multicarrier communication systems (or modulation techniques), the C/I ratio of the conventional orthogonal frequency-division multiplexing system is also provided and compared with that of the FMT system under the same channel conditions and spectral efficiency. Finally, numerical and simulation results are given that confirm the C/I ratio results obtained.

In this paper, closed-form expressions of the bit error probability of closed-loop transmit diversity (CLTD) schemes with two transmit antennas and noisy channel estimates in time-varying Rayleigh fading channels are derived. Two CLTD schemes considered are the phase-only CLTD (PO-CLTD), where the transmit antennas transmit with the same power, and the phase-amplitude CLTD (PA-CLTD), where the transmit antennas can transmit with different powers. The results have indicated that, with the same channel estimation accuracy, PA-CLTD generally performs slightly better than PO-CLTD. We have also compared the performance of PA-CLTD with the performance of a system without transmit diversity and the performance of a system with the Alamouti space-time code employing the linear-combining decoder. The results have illustrated that, PA-CLTD is outperformed by the other two systems when the pilot SNR is very small and the Doppler spread is large.

In this paper, we consider coded frequency-hopping spread spectrum (FHSS) systems with differential unitary space-time modulation (DUSTM). We investigate the erasure insertion (EI) techniques for improving the decoding error probability, especially in presence of strong partial-band interference (PBI). Conditional likelihood functions are derived for the decision-feedback demodulation and used for EI. The two proposed erasure rules do not require knowledge of the distribution of the noise plus interference power, in contrast to their counterparts in [14]. Instead of assuming the unknown parameters involved in decision-feedback demodulation and EI to be known, a joint estimation-demodulation scheme based on the adaptive recursive least square (RLS) algorithm is proposed. The sensitivity of the proposed EI rules to mismatched thresholds is studied by simulation. Numerical results show that EI can improve the decoding error probability significantly in presence of PBI, even when the required parameters have to be estimated and suboptimal thresholds are used.

We consider the performance of an FMT system with perchannel equalization over frequency-selective time-varying fading channels. Due to the distortion caused by frequency and time selectivity of the fading channel, both ICI and ISI exist in an FMT system and cause performance degradation. By using a per-channel equalizer at the FMT receiver with sufficiently large number of equalizer taps, the ISI can be mitigated significantly, but the ICI still exists. In this paper, the effects of the interference caused by the time-frequency dispersive channel is quantified by analyzing the average system carrier to interference (CIY) ratio of the FMT system under different fading conditions. A closed-form expression for the C/I ratio and its upper bound are provided for the FMT system, which lead to a better understanding of the trade-off between spectral efficiency and system performance degradation. Moreover, comparisons between FMT and OFDM systems under the same channel conditions and spectral efficiency are also provided. Numerical and simulation results of the system C/I ratio further confirm and support the obtained analytical results

Studies on differential unitary space-time modulation are mostly focused on Rayleigh fading channels. In this paper we present new analytic results for the maximum-likelihood demodulator (MLD) and the standard differential demodulator (SDD). The resulting expressions and bounds on the pairwise error probability shed light on the impact of various system parameters and are helpful towards a deeper understanding of the DUSTM in Rician channels. Additional analytic results are also derived for the constellation in the work of Tarokh and Jafarkhani (2000). Unlike in Rayleigh fading, the exact MLD can only be implemented approximately (Cui and Tellambura, 2006). The performance loss of practical demodulator such as the SDD and a prediction-based demodulator relative to the MLD are studied under different Rician fading environments.

In this paper, we derive the Chernoff bound of the pairwise error probability (PEP) and the exact PEP of convolutional codes in a time-varying Rician fading channel. With the assumptions that the channel estimator is a finite impulse response filter and the interleaving depth is finite, we are able to investigate the estimation-diversity tradeoff resulting from the effects of the Doppler spread on the system performance, via the channel estimation accuracy and the channel diversity. In addition, we verify that, in the special case when the pilot signal-to-noise ratio is infinitely large and the channel estimator is well-designed, our analysis leads to the same result as the existing perfect channel-state information analysis. Finally, the analytical results are compared with results from Monte Carlo simulation, and the comparison shows that the analytical results match well with the simulation results.

In this paper, we derive the Chernoff bound of the pairwise error probability (PEP) and the exact PEP of convolutional codes in a time-varying Rician fading channel. With the assumptions that the channel estimator is a finite impulse response filter and the interleaving depth is finite, we are able to investigate the estimation-diversity tradeoff resulting from the effects of the Doppler spread on the system performance via the channel-estimation accuracy and the channel diversity. In addition, we verify that, in the special case when the pilot signal-to-noise ratio is infinitely large and the channel estimator is well-designed, our analysis leads to the same result as the existing perfect channel-state information analysis. Finally, the analytical results are compared with results from Monte Carlo simulation, and the comparison shows that the analytical results match well with the simulation results

The focus of this paper is on the performance of orthogonal frequency division multiplexing (OFDM) signals in mobile radio applications, such as 802.11a and digital video broadcasting (DVB) systems, e.g., DVB-CS2. The paper considers the evaluation of the error probability of an OFDM system transmitting over channels characterized by frequency selectivity and Rayleigh fading. The time variations of the channel during one OFDM symbol interval destroy the orthogonality of the different subcarriers and generate power leakage among the subcarriers, known as inter-carrier interference (ICI). For conventional modulation methods such as phase-shift keying (PSK) and quadrature-amplitude modulation (QAM), the bivariate probability density function (pdf) of the ICI is shown to be a weighted Gaussian mixture. The large computational complexity involved in using the weighted Gaussian mixture pdf to evaluate the error probability serves as the motivation for developing a two-dimensional Gram-Charlier representation for the bivariate pdf of the ICI. It is demonstrated that its truncated version of order 4 or 6 provides a very good approximation in the evaluation of the error probability for PSK and QAM in the presence of ICI. Based on Jakes' model for the Doppler effects, and an exponential multipath intensity profile, numerical results for the error probability are illustrated for several mobile speeds.

We investigate two erasure insertion schemes for a coded slow frequency-hopping system with multiple antennas at both the transmitter and the receiver. The demodulated symbols may become unreliable due to fading, thermal noise, and partial band interference (PBI). Since error correcting codes can correct more erasures than errors, it is often beneficial to erase these unreliable symbols rather than feeding them to the decoder. In this paper, we first extend the Bayesian erasure insertion, originally proposed in C.W. Baum and M.B. Pursley (1992) for FSK modulation, to the case when differential space-time modulation is used. We then propose a simple, suboptimal erasure insertion scheme based on a likelihood ratio threshold test (LRTT). Simulation results show that substantial improvements in decoding error probability can be achieved by the proposed schemes over the non-erasure-insertion scheme, especially when the partial-band interference becomes severe.

Signal clipping has been suggested as an effective peak-to-average power ratio (PAPR) reduction scheme for orthogonal frequency-division multiplexing (OFDM). This paper analyzes clipped M-ary differentially encoded phase-shift keying (M-DPSK) OFDM. The impact of input power backoff (IBO) of a nonlinear power amplifier (PA) is evaluated. An effective PAPR reduction scheme should provide one of the two equivalent enhancements: 1) a reduced error floor at a given backoff, or 2) a reduced required IBO to achieve a target BER. The later is addressed by determining the total degradation (TD) of the system at various IBO. By this measure, it is shown that clipping is ineffective. Moreover, it is shown that clipping PAPR reduction doesn't improve the spectral broadening caused by the PA. The linearity of the amplifier is viewed at various backoff ratios, defined as K = IBO/PAPR. Since K is best viewed statistically, so is the linearity of the PA. As a side note, the formula suggested by A. J. Cann (1980) is shown to be equivalent to the often referenced Rapp solid-state PA model

We consider in this paper filtered multitone (FMT) modulation over frequency-selective time-varying fading channels. Due to the phase and amplitude distortion introduced by the fading channel, not only is the orthogonality among different subcarriers destroyed, but also the perfect Nyquist sampling condition of the baseband matched filters is no longer valid. Consequently, interchannel as well as intersymbol interference will cause distortions to the transmitted signals. In this paper, the interference caused by the time-frequency dispersive channel is quantified by analyzing the demodulated signals at the receiver under several different fading channels conditions. An analysis of the average carrier to interference (C/I) ratio of the filtered multitone system is provided in order to demonstrate the underlying trade-off between spectral efficiency and system performance. For comparison purposes with other multicarrier communication systems (or modulation techniques), the C/I ratio of the conventional OFDM system is also provided and compared with that of the FMT system under the same channel conditions and spectral efficiency. Finally, numerical and simulation results are given that confirm the C/I ratio results obtained

A noncoherent constant envelope orthogonal frequency-division multiplexing (CE-OFDM) receiver is proposed. It is shown that CE-OFDM is naturally noncoherent since the effect of an unknown phase shift at the receiver is eliminated by the matched-filter bank following the front-end phase demodulator. The noncoherent receiver demodulates continuous phase CE-OFDM signals-which produce less adjacent channel interference-with no added complexity. Performance is evaluated in flat fading channels having both Rayleigh and Ricean statistics. Simulation results are compared to analytical approximations1.

In this paper, we derive the theoretical performance of the Alamouti space-time code in time-varying Rayleigh fading channels with noisy channel estimates. The receiver algorithms presented in this paper are the maximum-likelihood (ML) symbol detector with the linear combining scheme, which was suggested by Alamouti (1998), and the ML space-time decoder. The bit error probability for the linear combining scheme and the sequence error probability for the ML space-time decoder are presented as functions of the pilot filter coefficients, the multipath power profile, the normalized Doppler frequency, the pilot SNR and the data SNR. We also compare the bit error performance of the linear combining scheme with the bit error performance of the system without transmit diversity. The results indicate that the Alamouti space-time code with the linear combining scheme is outperformed by the no transmit diversity system at high Doppler frequency or low pilot SNR.

This paper considers an OFDM system over frequency selective time-varying fading channels. The time variations of the channel during one OFDM frame destroy the orthogonality of different subcarriers and result in power leakage among the subcarriers, known as intercarrier interference (ICI), causing a degradation of system performance. In this paper, channel state information is used to minimize the degradation caused by ICI. A simple and efficient polynomial surface channel estimation technique is proposed to obtain the necessary channel state information. Based on the estimated channel information, we describe a MMSE based OFDM detection technique that reduces the degradation caused by ICI distortion. Performance comparisons between conventional OFDM and the proposed MMSE-based OFDM receiver structures under the same channel conditions are provided in this article. Simulation results of the system performance further confirm the effectiveness of the new technique over the conventional OFDM receiver in suppressing ICI in OFDM systems.

This paper describes a feedback assisted stochastic gradient algorithm for adapting the weights of a multiantenna transmitter in a multiuser multiple-input single-output per user (MISO) communication system, which yields both a power delivery (aperture) gain and a fading channel diversity gain from the multiple transmit antennas. Feedback from the receiver is used to attain partial channel state information at the transmitter, which attempts to maximize the power delivered to the receiver. The system utilizes a perturbation probing and update formulation: a vector perturbation probe is transmitted and perturbation sign feedback from the receiver defines the transmitter weight vector additive update. This feedback provides a coarse estimate of the gradient of the delivered power and is used to adapt the multiantenna baseband weights of the transmitter. The second moment update of the algorithm is derived, and the tracking performance of the algorithm applied to a dynamic AR1 fading channel is analyzed, with simulations confirming the analysis. Bit-error rate simulations in a dynamic fading channel show that the algorithm can perform as well or better than previously proposed vector selection feedback, and in slower fading the algorithm substantially outperforms diversity space time coding.

The statistical gain differences between two common spatial combining algorithms: optimum combining (OC) and maximal ratio combining (MRC) are analyzed using a gain ratio method. Using the receive carrier-to-interference plus noise ratio (CINR), the gain ratio ClNR/sub OC/ /CINR/sub MRC/ is evaluated in a flat Rayleigh fading communications system with multiple interferers. Exact analytical solutions are derived for the probability density function (PDF) and the average gain ratio with one interferer. When more than one interferer is present, the PDF of the gain ratio is illustrated using Monte Carlo simulations and its mean value is shown in basic integral form. An upper bound to the gain ratio is derived providing a simple means to determine when OC will exhibit significant gains over MRC.

It has been known for some time that adaptive filters can sometimes provide performance exceeding that of a Wiener filter in cases where there is a difference in frequency between the reference signal and the primary of an adaptive noise canceller (ANC). A recent model to explain this behavior was based on the concept of linking sequences. We evaluate the characteristics of these linking sequences further. It is shown that performance improvement of the adaptive filter is paired with low variation of the linking sequences.

Tracking of highly maneuvering targets with unknown behavior is a difficult problem in sequential state estimation. The performance of predictive-model-based Bayesian state estimators deteriorates quickly when their models are no longer accurate or their process noise is large. A data-driven approach to tracking, the segmenting track identifier (STI), is presented as an algorithm that operates well in environments where the measurement system is well understood but target motion is either or both highly unpredictable or poorly characterized. The STI achieves improved state estimates by the least-squares fitting of a motion model to a segment of data that has been partitioned from the total track such that it represents a single maneuver. Real-world STI tracking performance is demonstrated using sonar data collected from free-swimming fish, where the STI is shown to be effective at tracking highly maneuvering targets while relatively insensitive to its tuning parameters. Additionally, an extension of the STI to allow its use in the most common multiple target and cluttered environment data association frameworks is presented, and an STI-based joint probabilistic data association filter (STIJPDAF) is derived as a specific example. The STIJPDAF is shown by simulation to be effective at tracking a single fish in clutter and through empirical results from video data to be effective at simultaneously tracking multiple free-swimming fish.

The reduction in the average required transmit power in order to achieve the desired system performance is determined when using a receive antenna array employing polarization diversity as opposed to spatial diversity only. Cross-polar-discrimination (XPD) and envelope correlation are used to model the correlation between the horizontal and vertical polarizations. The characteristic function for an M-branch diversity receiver, using maximal-ratio-combining, is used to obtain the analytical expressions for the average required transmit power, assuming Rayleigh fading channels, perfect channel information at the transmitter and the receiver, and perfect fast or average power control. Based on the measurement data of XPD and envelope correlation in an urban environment, two spatially separated dual-polarized antennas are shown to outperform two spatially separated vertical antennas between 2.25-2.4 dB and 4-4.3 dB for the perfect fast power control and the perfect average power control, respectively.

We propose a two-stage adaptive filtering process for canceling narrowband interference from a wideband signal process, based on a reference signal consisting of a Doppler shifted version of the interference. The first stage uses the time-varying behavior of NLMS with large step-size to produce an estimate of the interference signal, in which the Doppler shift is mitigated. The second stage uses NLMS with small step-size, as an approximation to the Wiener filter, in order to modify amplitude and phase of the Doppler-mitigated reference signal so that an estimate of the interference signal is produced suitable for interference cancellation. Simulations with a wideband QPSK signal corrupted by strong sinusoidal interference, for which a Doppler shifted reference is available, show the performance of the proposed approach in terms of signal-to-interference ratio and bit-error rate improvement.

This paper considers the performance degradation of a high QAM orthogonal frequency division multiplexing (OFDM) system over frequency selective time-varying fading channels. The time variation of the channel during one OFDM frame destroys the orthogonality of different sub-carriers and generates power leakage among the sub-carriers, known as inter-carrier interference (ICI). The statistics of the ICI for M-QAM systems are shown to be non-Gaussian distributed. However, the ICI distribution is well approximated by the derived 2-dimensional Gram-Charlier series. Finally, the degradation in the performance of OFDM resulting from Doppler effects over time varying, frequency selective Rayleigh fading channel is obtained by averaging the approximated ICI statistics over the ensemble fading.

This paper describes a feedback assisted stochastic gradient algorithm for transmission tracking of the dominant channel subspaces for multiple-input-multiple-output (MIMO) communications systems. Subspace tracking is introduced as a means of tracking multiple transmission weights, being the MIMO generalization of beam steering in the familiar multiple-input-single-output case. The subspace solution approximates that of water filling (WF) in some cases, without the complete rate/power allocation required by WF. The gain of subspace tracking in low rank systems is demonstrated, particularly, in the case where the number of transmit antennas exceeds the number of receive antennas. Simulations of ergodic capacity show the utility of both subspace tracking in general and of the specific adaptation algorithm, and simulations of frame-error rates show the utility in a specific coding example.

In this paper, we have analyzed the convolutional coded error performance of a 2D-RAKE receiver, in combination with transmit diversity on the downlink of a WCDMA system. The analyses assume correlated fading between receive antenna array elements, and an arbitrary number of independent but nonidentical resolvable multipaths combined by the RAKE receiver in the general Nakagami-m fading channel framework. The closed form expression of pairwise error probability is given in the simple form of a single finite limit integral, with the integrand being an elementary function of array configuration parameters, spatial correlation and operating environment factors. It is shown that the combination of coding and spatial-path combining lead to dramatic performance improvement in various fading environments.

The voice Erlang capacity is analyzed in a multi-antenna combined voice-data CDMA reverse link (RL). The influence of two different spatial combining techniques: optimal combining (OC) and maximal ratio combining (MRC) on the voice Erlangs is evaluated when a single scheduled high data rate (HDR) data channel is shared by users desiring HDR services. The impact of randomly arriving data users on the voice Erlangs is also analyzed. A per rate class rise over thermal metric is defined and used with OC spatial combining. At large HDR values, increases in the voice Erlangs are illustrated when using OC vs. MRC.

This paper provides a framework for the analysis of error rate performance of maximal ratio combining multichannel reception of coherent linearly modulated systems over frequency-selective fading channels. Expressions for the error probability are developed, and the special cases for which closed-form or acceptable efficient numerical solutions are possible are delineated. A new efficient and accurate recursive method for the Ricean fading main resolved path case is presented for coherent quadrature amplitude modulation constellations. The effect of automatic gain control error on analysis of modulation schemes is demonstrated. Finally, numerical examples based on the maritime high-data-rate channel model are provided to demonstrate the usefulness of the framework.

This paper describes the benefits of transmission subspace tracking for multiple input multiple output communications systems, and applies the concepts of previous work on adaptive transmit antenna algorithms to this problem. A specific stochastic gradient technique of subspace or "multi-mode" tracking of the independent modes of the MIMO transfer function and the application to space time coding is considered. The technique provides gains by tracking the active modes when there are more transmit than receive antennas. With the proposed algorithm, the receiver generates binary feedback selecting preferred perturbed weights, which gives the transmitter a gradient estimate useful for subspace tracking. The capacity resulting from this approach is shown by simulation.

The per user carrier-to-interference ratio (CINR) enhancement in the reverse link (mobile to base station) of a CDMA communications system is analyzed using different antenna array spatial combining algorithms: optimum combining (OC) versus maximal ratio combining (MRC) in a multi-rate (combined voice and data users) multi-antenna scenario. Many low data voice users and a single dominant high data user are used to achieve a high degree of colored spatial interference in the analysis. The ratio of the CINR for OC versus MRC is directly analyzed, ie, Z=CINR/sub OC//CINR/sub MRC/ instead of separate analysis of each CINR term: CINR/sub OC/ and CINR/sub MRC/ with later comparison. Exact solutions are derived for the statistics of a per user CINR/sub OC//CINIR/sub MRC/ improvement, as a function of the high-level interference power to background noise, and is compared with CDMA reverse link Monte Carlo simulations.

The reverse link (mobile to base station) average data rate carrying capacity of a CDMA communications system is analyzed comparing different antenna array spatial combining algorithms: optimum combining (OC) versus maximal ratio combining (MRC) in a multiuser system employing multi-rate traffic (combined voice and data users) over Rayleigh fading channels. Typical CDMA power and interference relationships for an embedded multi-cell CDMA reverse link are discussed in the context of spatial OC algorithms and related to the total reverse link data throughput. Other-cell interference and chosen system rise-over-thermal metrics are found to limit the possible gain increase using OC vs. MRC.

The bit-error-rate (BER) performance of a 2D-RAKE receiver, in combination with transmit diversity on the downlink of WCDMA system, is presented. The analyses assume correlated fading between receive antenna array elements, and arbitrary number of independent but nonidentical resolvable multipaths; combined by the RAKE receiver, in the general Nakagami-m (1960) fading channel framework. The impacts of the array configuration (e.g. the number of transmit antennas and receive antennas, the antenna element separation) and the operating environment parameters (such as fading severity, angular spread and path delay profile), on the overall space-path diversity gain can be directly evaluated.

The tracking performance of a transmit antenna weight adaptation algorithm applied in a fading channel is considered. The system uses a stochastic gradient algorithm incorporating gradient sign feedback from a receiving unit to adjust the transmit weights. The feedback is simply a bit indicating which of two normalized perturbed transmission weights delivers greater power to the receiver. A reasonable performance measure is defined and an analytic estimate of the performance in an AR1 vector fading channel is derived and compared to simulations.

This paper presents the average error probability performance in coherent DS-CDMA systems using a 2D-RAKE receiver with an arbitrary number of antennas and arbitrary number of RAKE fingers. In the analysis, we assume a general frequency selective Nakagami-m fading channel with exponential multipath intensity profile. An analytical expression of the average bit-error-rate (BER) is derived, including the effects of the spatial correlation between antenna elements and non-identical fading for different multipaths. The impacts of the receiver configuration (e.g. the spatial diversity order M, the temporal diversity order L and the antenna separation) and the operating environment parameters (such as fading, maximum number of multipath components, angular spread and MIP power decay factor), on the BER performance and the cell capacity are illustrated.

We present an approximate analysis approach to the computation of the probability of error and mean burst error length for a decision feedback equalizer (DFE) that takes into account feedback of decision errors. The method uses a reduced-state Markov model of the feedback process and is applicable to linear modulation formats. We use this technique to analyze a DFE design that mitigates the effects of feedback error by incorporating a soft decision device into the feedback path and a norm constraint on the feedback filter weights. We apply the DFE design and analysis approach to a dispersive multipath propagation environment.

The least-mean-square (LMS) estimator is a nonlinear estimator with information dependencies spanning the entire set of data fed into it. The traditional analysis techniques used to model this estimator obscure these dependencies; to simplify the analysis they restrict the estimator to the finite set of data sufficient to span the length of its filter. Thus the finite Wiener filter is often considered a bound on the performance of the LMS estimator. Several papers have reported the performance of the LMS filter exceeding that of the finite Wiener filter. We derive a bound on the LMS estimator which does not exclude the contributions from data outside its filter length. We give examples of this bound in cases where the LMS estimator outperforms the finite Wiener filter.

This paper investigates the performance of a compact space-time diversity receiver for mobile communication systems. Expressions for the bit error rate and outage mean SNR are derived as a function of the channel covariance matrix. These results define the sensitivity of the performance of such a receiver to the environment (fading characteristics and angular spread) and the antenna array (geometry and coupling).

The least-mean-square (LMS) estimator is a nonlinear estimator with information dependencies spanning the entire set of data fed into it. The traditional analysis techniques which are used to model this estimator obscure this, restricting the estimator to the finite set of data sufficient to span the length of its filter. The finite Wiener filter is thus often considered a bound on the performance of the LMS estimator. Several papers have reported the performance of the LMS filter exceeding that of the finite Wiener filter. We demonstrate a bound on the LMS estimator, which does not exclude the contributions from data outside its filter length, and which demonstrates the ability of the LMS estimator to outperform the finite Wiener filter in certain cases.

An adaptive transversal equalizer based upon the least-mean-square (LMS) algorithm, operating in an environment with temporally correlated interference can exhibit better steady-state mean-square-error (MSE) performance than the corresponding Wiener filter. This phenomenon is a result of the nonlinear nature of the LMS algorithm and is obscured by traditional analysis approaches that utilize the independence assumption. We use a transfer function approach to quantify the MSE performance of the LMS algorithm and demonstrate that the degree to which LMS may outperform the corresponding Wiener filter is dependent on system parameters such as signal-to-noise ratio and the step-size parameter.

This paper presents a recursive method for evaluating the error rate performance of multichannel reception of coherent MPSK systems operating over slowly Ricean fading channels. Each of the multiple channels is assumed to be a bandlimited two-sided discrete path model with complex Gaussian taps. The main path is assumed to be non-zero mean, corresponding to Ricean fading. Maximal ratio combining in the receiver is assumed, and an expression for the received phase density function is developed. A recursive method for solving the resulting error probability expression is then presented. This method is similar to those used for recursive computation of the Marcum Q function, and is both efficient and accurate. The method can be applied for both the flat and frequency selective Ricean fading cases. Examples based on a ship to ship high-data-rate line-of-sight channel model are provided to demonstrate the method.

The effect of both temporal and spatial dispersion on the performance of a combined configuration of a RAKE and a phased array system is analyzed theoretically. The mean power improvement due to an antenna array system, and fading reduction by means of the RAKE configuration, are described in the presence of the spatial and temporal dispersion of multipath waves.

Two-dimensional (2-D) adaptive filtering is a technique that can be applied to many image processing applications. This paper will focus on the development of an improved 2-D adaptive lattice algorithm (2-D AL) and its application to the removal of correlated clutter to enhance the detectability of small objects in images. The two improvements proposed here are increased flexibility in the calculation of the reflection coefficients and a 2-D method to update the correlations used in the 2-D AL algorithm. The 2-D AL algorithm is shown to predict correlated clutter in image data and the resulting filter is compared with an ideal Wiener-Hopf filter. The results of the clutter removal will be compared to previously published ones for a 2-D least mean square (LMS) algorithm. 2-D AL is better able to predict spatially varying clutter than the 2-D LMS algorithm, since it converges faster to new image properties. Examples of these improvements are shown for a spatially varying 2-D sinusoid in white noise and simulated clouds. The 2-D LMS and 2-D AL algorithms are also shown to enhance a mammogram image for the detection of small microcalcifications and stellate lesions.

Multichannel adaptive equalization combines the concepts of spatial diversity and temporal equalization to improve receiver performance in a line-of-sight communication environment. We derive the optimal Wiener filter for conditions common to this environment. We specifically analyze the effect of a CW interference on this solution and demonstrate the dependence of receiver performance on the multichannel adaptive equalizer (MAEQ) spatial-temporal beam pattern.

The paper focuses on the development of an improved 2D adaptive lattice algorithm (2D-AL) and its application to the removal of correlated clutter to enhance the detectability of small objects in images. The two improvements proposed are increased flexibility in the calculation of the reflection coefficients and a 2D method to update the correlations used in the 2D-AL algorithm. The results of the clutter removal is compared to previously published ones for a 2D LMS (TDLMS) algorithm. 2D-AL is better able to predict spatially varying clutter than the TDLMS algorithm since it converges faster to new image properties. Examples of these improvements are shown. The TDLMS and 2D-AL algorithms are also shown to enhance a mammogram images for the detection of small microcalcifications.>

It has been proposed that CDMA systems can be assigned to spectral bands which are presently occupied by narrowband users to further increase spectral capacity. Such CDMA overlay systems could provide new options for efficient utilization of the spectrum with minimal disruption to existing narrowband users, especially if adaptive interference suppression techniques are utilized in the spread spectrum receiver. Previous studies have defined the SNR improvement ratio which can be achieved for tone interferers and for narrowband interferers for which the center frequency of the interference is at the carrier frequency of the CDMA signal. In this paper the bit-error-rate (BER) performance of the mobile-to-base link of a CDMA system for a single narrowband user which occupies a significant portion of the CDMA bandwidth is evaluated. It is shown that the narrowband model used in previous studies does not apply in this case, especially for the large, effective, bandwidths which are characteristic of the interferers in the overlay system. The dependence of the BER on the filter order, the bandwidth of the interference, and its center frequency relative to the CDMA carrier frequency are defined. Additionally the increase in BER for a digital implementation of the adaptive suppression filter relative to the optimal Wiener filter is characterized with respect to the adaptive time constant and the quantization errors due to finite wordlength. It is shown that these implementation errors can be made negligible compared to the errors which are characteristic of the optimal Wiener filter. Analytic results are validated by simulation for typical system parameters.>

This work studies the performance of dimensional least mean square (TDLMS) adaptive filters as prewhitening filters for the detection of small objects in image data. The object of interest is assumed to have a very small spatial spread and is obscured by correlated clutter of much larger spatial extent. The correlated clutter is predicted and subtracted from the input signal, leaving components of the spatially small signal in the residual output. The receiver operating characteristics of a detection system augmented by a TDLMS prewhitening filter are plotted using Monte-Carlo techniques. It is shown that such a detector has better operating characteristics than a conventional matched filter in the presence of correlated clutter. For very low signal-to-background ratios, TDLMS-based detection systems show a considerable reduction in the number of false alarms. The output energy in both the residual and prediction channels of such filters is shown to be dependent on the correlation length of the various components in the input signal. False alarm reduction and detection gains obtained by using this detection scheme on thermal infrared sensor data with known object positions is presented.

The authors compare the performance of the recursive least squares lattice (RLSL) and the normalized step-size stochastic gradient lattice (SGL) algorithms to that of the least mean square (LMS) transversal algorithm for the cancellation of sinusoidal interference. It is found that adaptive lattice filters possess a number of advantages over the LMS transversal filter, making them the preferred adaptive noise cancellation (ANC) filter structure if their increased computational costs can be tolerated. These advantages include faster convergence, notch bandwidths which are independent of the input power, and the generation of less harmonic distortion. The notch bandwidth of each filter structure is related to its respective convergence time constant. Experimental results obtained with the 32-b floating-point lattice development system (LDS) are presented to verify the analytical results.>

A recursive detection scheme for point targets in infrared images is described. Estimation of the background noise is done using a weighted autocorrelation matrix update method and the detection statistic is calculated using a recursive technique. A weighting factor allows the algorithm to have finite memory and deal with nonstationary noise characteristics. The detection statistic is created by using a matched filter for colored noise, using the estimated noise autocorrelation matrix. The relationship between the weighting factor, the nonstationarity of the noise and the probability of detection is described. Some results on one- and two-dimensional infrared images are presented.>

The authors study the behavior of the partial correlation (PARCOR) coefficients of the stochastic gradient adaptive lattice filter in response to a complex linear chirp FM signal in white Gaussian noise. A single-stage model for the behavior of the coefficients is developed, and the recovery error is derived. Also, an accurate model for a two-stage filter is derived.>

The performance of adaptive lattice filters in finite precision real-time hardware is largely unknown because of the complexity of implementing lattice algorithms. The authors show how arithmetic effects can deleteriously manifest themselves in both the stochastic gradient and the least squares adaptive lattice filters. Computer simulations and experimental results are used to verify an analytical analysis describing implementation effects of adaptive lattice filters. It is found that the performance of adaptive lattice filters can be substantially improved by manipulating the time recursive coefficients using direct updating techniques. Results are compared to those obtained from LMS (least mean square) transversal adaptive filters.>

The use of adaptive filters for the enhancement of images is studied. In particular, the enhancement of images where the region of interest has a small spatial extent compared to the noise is considered. A two stage approach for enhancing the desired signal is presented. At each stage, a two dimensional adaptive filter employing the least mean square (LMS) algorithm is used. By properly choosing the adaptation step size, in the first stage the colored noise is whitened, and in the second stage the desired signal is recovered from the white noise. Procedures for selecting the step size are discussed. Computer simulations to support the results are also presented.>

The conditions required to implement real-time adaptive prediction filters that provide nearly optimal performance in realistic input conditions are delineated. The effects of signal bandwidth, input signal-to-noise ratio (SNR), noise correlation, and noise nonstationarity are explicitly considered. Analytical modeling, Monte Carlo simulations and experimental results obtained using a hardware implementation are utilized to provide performance bounds for specified input conditions. It is shown that there is a nonlinear degradation in the signal processing gain as a function of the input SNR that results from the statistical properties of the adaptive filter weights. The stochastic properties of the filter weights ensure that the performance of the adaptive filter is bounded by that of the optimal matched filter for known stationary input conditions.>

This paper evaluates the comparative performance of adaptive and conventional square law detectors for inputs consisting of finite bandwidth signals in white Gaussian noise. The comparative performance of two distinct ALE augmented detector implementations will be provided. Performance is determined on the basis of ROC curves for a range of signal bandwidths, ALE bulk delays, ALE time constants, ALE frequency resolutions, and postdetection integration times for the ALE augmented detectors. These curves are evaluated to determine the best choice of ALE parameters for various input signal conditions, the sensitivity in performance to that choice, and the comparative performance of the conventional and ALE augmented detectors. Monte Carlo simulation is used to generate the ROC curves on which the performance analysis is based.

New analytical and simulation results describing the performance of an adaptive detection processor for narrowband signals are given. The simulation results compare the detection performance of the adaptive processor with an incoherently-averaged, magnitude-squared FFT processor for a class of non-stationary input noise. An analytical derivation of the noise-only probability density function of the adaptive processor's output prior to post-detection integration is presented.

In many applications of Wiener filtering to noise cancellation an external reference noise input is required. However, if an external reference is not available, it is still possible to suppress additive noise using a Wiener linear prediction filter (LPF) provided the signal bandwidth is significantly less than the noise bandwidth. The purpose of this paper is to provide an analytical basis for bounding the performance of a digital LPF when applied to the problem of cancelling broadband additive noise from narrow-band signals.

The optimal minimum-mean-square-error discrete filters are obtained for finite bandwidth signals in noise represented by a rational pole-zero model in the spectral domain. An analytical technique called the method of undetermined coefficients is used to solve the Wiener equation for the optimal prediction coefficients. These coefficients are then used to examine (a) the frequency response of the Wiener prediction filter, and (b) the maximum entropy spectral estimator. Special cases considered include the limiting case of narrow bandwidth signals and large prediction filter lengths.