In this paper we propose new bounds on the achievable information rate for discrete-time Gaussian channels with intersymbol interference (ISI) and independent and uniformly distributed (i.u.d.) channel input symbols drawn from finite-order modulation alphabets. Specifically, we are interested in developing new bounds on the achievable rates for sparse channels with long memory. We obtain a lower bound which can be achieved by practical receivers, based on MMSE channel shortening and suboptimal symbol detection for a reduced-state channel. An upper bound is given in the form of a semi-analytical solution derived using basic information theoretic inequalities, by a grouping of the channel taps into several clusters resulting in a newly defined single-input multiple-output (SIMO) channel. We show that the so obtained time-dispersive SIMO channel can be represented by an equivalent single-input single-output (SISO) channel with a significantly shorter channel memory. The reduced computational complexity allows the use of the BCJR algorithm for the newly defined channel. The proposed bounds are illustrated through several sparse channel examples and i.u.d. input symbols, showing that the upper bound significantly outperforms existing bounds. Performance of our lower bound strongly depends on the channel structure, showing best results for minimum-phase and maximum-phase systems.

We consider a convolutionally coded orthogonal frequency-division multiple access (OFDMA) based cognitive radio system where each user achieves perfect synchronization for its own signal, while different users are asynchronized due to random timing offsets. The presence of asynchronous secondary users introduces potential multiple access interference (MAI) to each primary user's receiver. The strength of the MAI is determined by the secondary users' transmission powers, and their distances and frequency separations to the primary user. Expressions for the primary user's pairwise error probability and average probability of error are derived, and an error floor prediction method is presented. Finally, the trade-off between the MAI to the primary user and the secondary users' performances are investigated through numerical examples and simulations.

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.

The effects of channel estimation errors on the performance of a system employing Tomlinson-Harashima precoding and the QR decomposition, operating over multiple antenna frequency-flat fading channels with decentralized receivers, is evaluated. The QR decomposition of the channel matrix is employed to arrive at an equivalent channel where successive interference cancellation at the transmitter can be used to remove the effect of the multiuser interference. However, in the case of imperfect channel estimation, it is not possible to remove the effect of the multiuser interference due to a mismatch between the precoder and the channel. Consequently, it is necessary to include the estimation error in deriving the probability of symbol error. We also provide simulations to corroborate the analytical results.

The fifteen articles in this special issue are devoted to new equalization techniques for wireless communications, including new the latest theories and applications.

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.

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.

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.

The performance of a pre-Bell Laboratories Layered Space-Time Architecture (BLAST)-decision feedback equalization (DFE) technique with Tomlinson-Harashima precoding and decentralized receivers, operating over multiple-input single-output (MISO) frequency-selective fading channels, is evaluated. First, we derive the probability of symbol error for Tomlinson-Harashima precoding operating over single-input single-output channels with intersymbol interference. We then generalize this result to MISO frequency-selective fading channels with decentralized receivers by using the QR decomposition technique. The effect of optimal ordering of the decentralized receivers, which minimizes the total transmit energy, is investigated. We obtain a closed-form expression for the probability density function of the squared diagonal elements of the upper right triangular matrix belonging to the optimal QR decomposition when two transmit antennas and two receivers are used. We also provide simulations to corroborate the analytical results.

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.

The performance of multicode direct-sequence spread-spectrum multiple-input multiple-output (MIMO) systems in the presence of frequency-selective fading is evaluated. We derive the asymptotic distribution of the multiple-antenna interference when the processing gain is sufficiently large. The probability of error is derived for the conventional RAKE receiver, and its performance is compared for various system configurations. We consider system tradeoffs for both fixed rate and fixed diversity. For a fixed total data rate, we demonstrate the advantage of decreasing the number of transmit antennas while increasing the number of codes, and for a fixed total diversity order, we demonstrate the advantage of decreasing the number of RAKE taps while increasing the number of receive antennas.

Frequency hopping (FH) combined with coding is a popular technique in wireless communication applications. Motivated by the commercial system outlined in [1], this paper investigates the performance of a coherent FH multiple access (FH-MA) cellular system, where hopping patterns are constructed from latin squares. Some of the patterns carry pilot symbols, which the users track to estimate the channel on the data patterns and perform coherent detection. The latin squares construction enables us to analytically evaluate the bit error probability (BEP) over each data pattern, when convolutional codes are employed for error protection. The focus of our work is to precisely determine the effect that frequency and interference diversity, ensuing from FH, have on the coded performance. Regarding frequency diversity, it is shown that the performance can vary widely for different latin squares. Moreover, under pilot-assisted channel estimation, a performance tradeoff is observed, as an increasing frequency selectivity results in more diversity, but also more inaccurate channel state information. With respect to interference diversity, we analyze the performance when the interference power variations are perfectly known or ignored by the receiver. Our results confirm that interference tracking is important in harnessing the error correcting power of convolutional coding.

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.

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

In this paper, we analyze the effect of interference diversity on the capacity of a cellular system that employs frequency hopping, power control and bit-interleaved coded modulation. Interference is created when the hopping patterns of adjacent cells intersect with the patterns of the cell of interest, with a probability that depends on the occupancy of each cell. However, due to frequency hopping and power control, the power of the interference varies randomly across the received symbols creating what is usually named in the literature as interference diversity. We explicitly take into account this randomness and, under a channel model that accounts for fading and path loss, analyze the performance of two receivers; a receiver that tracks the variations of the interference power across the received symbols and a receiver that remains oblivious to these variations. Our results demonstrate under what circumstances the additional complexity of tracking the interference power variations is justified.

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.

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

We investigate the performance of frequency-hopped OFDMA (FIH-OFDMA), where subearriers are assigned to users according to predetermined hopping patterns. Some of the patterns carry pilot symbols, which the users track to estimate their channel and perform coherent detection. We develop a simple theoretical framework in order to evaluate the bit error probability (BEP) over each data pattern, when trellis-coded modulation (TCM) is employed for error protection. Our analytical results illustrate that appropriately constructing the patterns, given the channel parameters, can have a significant effect on the performance experienced by different users of this OFDMA system. An intuitively pleasing trade-off between channel estimation quality and performance enhancement due to frequency diversity is also revealed, as the channel becomes more frequency selective.

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 the deployment of frequency-hopped OFDMA at the downlink of a cellular system. Each user in the cell is assigned a number of subcarriers by the base-station, which change every OFDM symbol according to deterministic hopping patterns. The construction of the hopping patterns is based on orthogonal Latin squares, that guarantee orthogonal intra-cell multiple access and randomize the inter-cell interference. Properties of Latin squares are derived, which enable us to evaluate analytically the performance of two coded modulation schemes, namely TCM and BICM. Our results demonstrate the effect of the channel parameters, the hopping pattern selection, the interleaver depth and the inter-cell interference on the performance of a coded FH-OFDMA system.

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.

We propose a distributed fair scheduling framework for wireless ad hoc networks. Unlike previous works, which assume error-free or predictable channels, our work is based on the signal-to-interference-plus-noise ratio (SINR) model and views channel errors as a result of the interference among the scheduled flows. We show by analysis that under the presented framework long term fairness is guaranteed; furthermore, the framework enables us to maximize throughput and minimize transmit power in a distributed manner.

We propose a distributed fair scheduling framework for wireless ad hoc networks. Unlike previous works, which assume error-free or predictable channels, our work is based on the signal-to-interference-plus-noise ratio (SINR) model and views channel errors as a result of the interference among the scheduled flows. We show by analysis that under the presented framework long term fairness is guaranteed; furthermore, the framework enables us to maximize throughput and minimize transmit power in a distributed manner.

In this paper, we analyze the performance of various receive antenna diversity schemes for use in combination with transmit diversity on the downlink of wideband code-division multiple-access third-generation systems. We consider open loop and closed loop versions of both maximal ratio combining and selection diversity, and study the impact of channel correlation on the performance of these schemes. We also present an analysis of the asymptotic performance of coded systems. The analytical results are compared with simulation results obtained in typical channels.

Serial concatenation of convolutional codes and MSK through an interleaver has a similar structure as turbo codes. Although the union bound, which is an analytical tool to estimate the bit error probability of such systems, is tight for high signal-to-noise ratio (SNR), it diverges for low SNR where the performance of our system is the most appealing. For this reason, we apply improved upper bounding techniques to our system to estimate the performance, at low SNR. We show that by applying these techniques, it is possible to obtain about 0.5dB or more improvement over the union bound in AWGN channel and 1dB or more improvement in fading channels.

This paper addresses the problem of power control in ad hoc networks supporting multicast traffic. First, we present a distributed algorithm which, given the set of multicast transmitters and their corresponding receivers, provides an optimal solution to the power control problem, if there is any. The transmit power levels obtained by solving the optimization problem minimize the network power expenditure while meeting the requirements of the SNR at the receivers. Whenever no optimal solution can be found for the given set multicast transmitters, we introduce a joint scheduling and power control algorithm, which eliminates the strong interferers thus allowing the other transmitters to solve the power control problem. The algorithm can be implemented in a distributed manner; however, it provides a sub-optimal solution since it is based on local information. Simulation results show that the obtained solution is close to the global optimum, when it exists. When there is no optimal solution, the proposed algorithm tries to maximize the number of successful multicast transmission.

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.

Serial concatenation of convolutional codes and CPM through an interleaver has a similar structure as serially concatenated turbo codes. Although the union bound, which is an analytical tool to estimate the bit error probability of such systems, is tight for high signal-to-noise ratio (SNR), it diverges for low SNR where the performance of our system is the most appealing. For this reason, we apply improved upper bounding techniques to our system to estimate the performance at low SNR. We show that by applying these techniques, it is possible to obtain 1 dB or more improvement over the union bound in fading channels.

Multicarrier code-division multiple access (MC-CDMA) combines multicarrier transmission with direct sequence spread spectrum. Different approaches have been adopted which do not assume a perfectly known channel. We examine the forward-link performance of decision-directed adaptive detection schemes, with and without explicit channel estimation, for MC-CDMA systems operating in fast fading channels. We analyze theoretically the impact of channel estimation errors by first considering a simpler system employing a threshold orthogonality restoring combining (TORC) detector with a Kalman channel estimator. We show that the performance deteriorates significantly as the channel fading rate increases and that the fading rate affects the selection of system parameters. We examine the performance of more realistic schemes based on the minimum mean square error (MMSE) criterion using least mean square (LMS) and recursive least square (RLS) adaptation. We present a discussion which compares the decision-directed and pilot-aided approaches and explores the tradeoffs between channel estimation overhead and performance. We find that there is a fading rate range where each method provides a good tradeoff between performance and overhead. We conclude that the MMSE per carrier decision-directed detector with RLS estimation combines good performance in low to moderate fading rates, robustness in parameter variations, and relatively low complexity and overhead. For higher fading rates, however, only pilot-symbol-aided detectors are appropriate.

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 presence of intersymbol interference (ISI), in addition to multiple access interference, severely hampers the performance of a code-division multiple-access (CDMA) communication system. In such a situation, channel coding can be used to obtain better performance, but at the cost of a reduction in rate of flow of information. In this paper, it is shown with the help of simulation results that the chip-interleaved CDMA system effectively combats ISI without requiring additional channel coding. The system differs from the conventional CDMA system in the sense that, the chip sequence resulting from the pseudo noise (PN) sequence modulation is interleaved before transmission. Two receivers are proposed, one based on the turbo equalization method which employs a maximum a posteriori equalizer of exponential complexity and the other based on minimum-mean square error-optimized iterative interference cancellation principles which is of linear complexity. Simulation results are provided which show that error rates close to the no-ISI single-user case can be obtained. The shortcomings of the coded CDMA with turbo detection system in the presence of ISI are also discussed.

Continuous phase modulation (CPM) consists of a large family of signals that are especially suitable for wireless communication. CPM signals have not been represented by discrete points in signal space because the phase of the carrier is time-variant. However, in this paper we present a new method to represent the binary CPM signals by discrete points in signal space by utilizing the amplitude modulated pulse (AMP) representation of the CPM signals. We use this new signal space representation to compute the Euclidean distance for any CPM signal and we compare the performance of CPM signals with each other and with other modulation schemes.

Continuous phase modulation (CPM) consists of a large family of signals that are especially suitable for wireless communication. CPM signals are optimally demodulated applying maximum-likelihood sequence detection (MLSD). However, since MLSD is too complex, great effort has been devoted to reduce the complexity with minimal loss on the performance. A reduced complexity receiver has recently been proposed for this purpose. We compare this new receiver with a previous reduced complexity receiver with respect to the reduction in complexity and, at the same time, the degradation from the optimum performance. We demonstrate that the new receiver achieves better performance at the same complexity.

A formula that computes the maximum number of users supported per base station in a cellular radio network is generalized to consider the frequency reuse number and arbitrary processing gains. The generalization quantifies a cost associated with in-cell interference by accounting for the lack of interference from the desired user on the total interference and by considering the impact of the frequency reuse number on the out-of-cell interference. This interference cost results in an increase in the received Eb/Io relative to FDMA which should be weighted against a reduction in the Eb/Io requirement resulting from using CDMA.

Continuous phase modulation (CPM) signals, which can be written as a sum of amplitude modulated pulses (AMP), are optimally demodulated using maximum-likelihood sequence detection (MLSD). It has been shown that CPM signals can be approximated by a single amplitude modulated pulse. This approximation reduces the complexity of MLSD. We examine the performance of this simplified receiver. The performance criterion used in this paper is the symbol error probability, which is a function of the minimum Euclidean distance (d/sub min//sup 2/)/spl middot/d/sub min//sup 2/ of the simplified receiver is compared to d/sub min//sup 2/ of the optimum receiver both asymptotically and for each observation interval.

We evaluate and compare several data detection schemes used in GSM systems. In particular, we compare the performance of decision feedback equalization (DFE) and nonlinear data directed estimation (NDDE) to that of maximum likelihood sequence estimation (MLSE). Establishing the performance of the basic NDDE detector is a first step in investigating the applicability of block transmission techniques to GSM systems. Our simulation results, obtained both for fading multipath channels and adjacent- and co-channel interference scenarios, suggest that the NDDE offers certain performance advantages over the DFE, and the performance of both detectors is comparable to that of the MLSE for the SNR region of interest in practical systems. Thus, they both represent viable alternatives to the MLSE detector.

We consider wireless communication systems that employ multiple transmitting and receiving antennas to achieve spatial diversity and to increase the data rate through fading channels. In particular, we focus on a system with N transmitting antennas and M receiving antennas. We consider the design and performance evaluation of several detection algorithms for recovering the original data from the received signals on the M antennas. These algorithms include the optimum maximum likelihood detector and suboptimal reduced-complexity detectors such as the MMSE detector and a detector based on maximal ratio combining. We also consider coded systems.

The remarkable performance of turbo codes for low SNRs in AWGN channels has encouraged the application of turbo codes to systems operating in different kind of channels. In this paper we consider an IS-95-based CDMA system operating in a multipath Rayleigh fading channel. We replace the convolutional encoder by a parallel and a serial turbo encoding scheme, and by a serial concatenation of an outer convolutional and an inner parallel turbo code, and instead of the Viterbi decoder we use iterative decoding based on the MAP algorithm. We perform BER and FER comparisons by varying system parameters such as the constraint length of the component convolutional codes, the interleaver lengths, and the wireless channel fading rate. The results obtained show that the concatenated schemes outperform the more complex convolutional scheme even for relatively short interleaving lengths, especially when FER is the desired figure of merit.

In this paper, we evaluate low complexity detectors for use in the GSM system. In particular, we compare the performance of decision feedback equalization (DFE) and nonlinear data directed estimation (NDDE) to that of the optimal maximum likelihood sequence estimation (MLSE). Establishing the performance of the basic NDDE detector is a first step in investigating the applicability of block transmission techniques to the GSM system. Simulation results, obtained both for fading multipath channels and adjacent- and co-channel interference scenarios, show that the NDDE performs just as well as the DFE, and the performance of both low complexity detectors is comparable to that of the MLSE for the SNR region of interest in practical systems.

Multi-carrier CDMA (MC-CDMA) is a hybrid multiple access scheme combining multi-carrier modulation (MCM or OFDM) with direct sequence spread spectrum (DS-SS). Although a common assumption in the analysis of the performance of the various MC-CDMA detectors is that they have perfect knowledge of the fading channel, this assumption is no longer valid as the fading rate (Doppler spread) of the channel increases. We examine the performance of various forms of the minimum mean square error (MMSE) detector operating in a fast fading Rayleigh channel described by a Gauss-Markov state-space model. We show that, although adaptive detection based on the LMS and RLS algorithms is possible without explicit channel estimation, a low complexity detector, termed MMSE per carrier, combined with an RLS channel estimator can achieve better performance as well as increased robustness to the selection of the adaptation parameters.

In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.

In this correspondence we consider the coding for multitrack magnetic recording systems. We provide analytical results related to uncoded and coded multitrack systems which constitute the basis of the code construction. We have designed matched spectral null codes for multitrack recording systems which give coding gains from 3 to 4.8 dB over uncoded systems.

In this paper, we developed a systematic frequency domain approach to analyze adaptive tracking algorithms for fast time-varying channels. The analysis is performed with the help of two new concepts, a tracking filter and a tracking error filter, which are used to calculate the mean square identification error (MSIE). First, we analyze existing algorithms, the least mean squares (LMS) algorithm, the exponential windowed recursive least squares (EW-RLS) algorithm and the rectangular windowed recursive least squares (RW-RLS) algorithm. The equivalence of the three algorithms is demonstrated by employing the frequency domain method. A unified expression for the MSIE of all three algorithms is derived. Secondly, we use the frequency domain analysis method to develop an optimal windowed recursive least squares (OW-RLS) algorithm. We derive the expression for the MSIE of an arbitrary windowed RLS algorithm and optimize the window shape to minimize the MSIE. Compared with an exponential window having an optimized forgetting factor, an optimal window results in a significant improvement in the h MSIE. Thirdly, we propose two types of robust windows, the average robust window and the minimax robust window. The RLS algorithms designed with these windows have near-optimal performance, but do not require detailed statistics of the channel.>

A coherent receiver with a decision-feedback equalizer (DFE) operating on a Rayleigh fading channel under a suitable adaptive algorithm is considered. In the analysis of a DFE, a common assumption is that the receiver has perfect knowledge of the channel impulse response. However, this is not the case in practice, and for a rapidly fading channel, errors in channel tracking can become significant. We analyze theoretically the impact of these errors on the performance of a multichannel DFE. The expressions obtained for the achievable average MPSK bit error probabilities depend on the estimation error covariance. In order to specify this matrix, we focus on a special case when a Kalman filter is used as an optimal channel estimator. In this case, the probability of bit error can be assessed directly in terms of channel fading model parameters, the most interesting of which is the fading rate. Our results show the penalty imposed by imperfect channel estimation, as well as the fading-induced irreducible error rates.>

An integrated course on digital signal processing (DSP) based on theory and engineering practice is described. The course is organized as a unit containing a traditional lecture component on DSP theory interacting with a hardware based laboratory component containing experiments and projects. The innovative aspect of this course is the digital signal processing laboratory. It consists of DSP workstations which are built around a fixed-point digital signal processor. Concepts taught in the lecture component are analyzed in the laboratory so students can learn practical aspects in the context of a real system. The laboratory is organized into three modules and each module is examined in detail. A representative project performed in the laboratory is described.>

Two different approaches for estimating the direction of arrival (DOA) of two coherent signals impinging on a uniform linear array are analyzed. Simple asymptotic expressions for the variance as well as for the bias of the estimated angles are derived. The simplicity of the method allows much insight and an easy analytic comparison is achieved. Examples are also provided.>

Nonlinear equalizers find use in communication applications where the channel distortion is too severe for a linear equalizer to handle. Because of their nonlinear capability and other attractive properties, neural networks have become appealing candidates for equalization problems. The application of neural networks to adaptive equalization problems is investigated. In particular, realization structures (MLP-I, MLP-II) of a multilayer perceptron (MLP) with a backpropagation training algorithm are introduced, and it is shown that they work well for both PAM and QAM signals of any constellation size (e.g., 4-PAM, 8-PAM, 16-QAM, and 64-QAM). It is demonstrated that both MLP structures outperform the least mean square (LMS)-based linear equalizer when channel distortions are nonlinear.>

General order-recursive least-squares estimation employing a sliding window is described. It is shown that time and order updates of any order-recursive sliding window least-squares algorithm can be obtained solely by 3*3 hyperbolic Householder transformations. Applying this general observation to the sliding window least-squares estimation of time-series signals results in a new algorithm: the hyperbolic Householder lattice (HHL) algorithm. This work broadens the range of applications of QR-decomposition (QRD)-based adaptive least-squares algorithms by allowing a sliding window formulation in addition to the known exponentially windowed form.>

One of the main problems in the proposed Northern American digital cellular system (IS-54) is the poor performance of the receiver for fast fading channels. The authors propose to use a novel joint data and channel estimation technique to improve performance. The basic idea of this method was described by N. Seshadri (1990) in the context of blind equalization. Simulation results indicate that this approach solves the problems of decision delay and divergence caused by error decision feedback in conventional maximum likelihood sequence estimation (MLSE). The specified IS-54 requirement of 19 dB at a BER of 3% and a speed of 100 km/h can be met with a margin of 8 dB. This result is 4.5 dB better than the conventional maximum likelihood receiver.>

A formal approach is presented to carry out a performance analysis of subspace-based estimation techniques applied to the problem of the direction of arrival of plane waves. This approach was inspired by the operator formalism, on account of its algebraic simplicity. It is a generalized approach that can be easily modified to analyze any subspace-based technique, as it uses a series expansion of projection operators on the signal and noise subspaces. A perturbation analysis is performed on the operators, thus avoiding a direct use of the eigenvectors and eigenvalues. This allows the analysis to be carried out to any desired order. This is made possible by using an original recurrence formula developed for the higher order terms in the expansion of the projection operators. This method is applied to study the root-min-norm algorithm with uncorrelated signals impinging from distinct directions on a uniform linear array and then extended to the correlated signal scenario. Simulations which verify the analytical derivations are provided.>

A multichannel Givens lattice algorithm is presented, which has a modular structure and is suitable for parallel implementation. The basic processing module requires a 2*2 plane rotation (Givens rotation), which has superior numerical properties due to its circular nature. The application of the multichannel Givens lattice algorithm to channel equalization is also discussed.>

An adaptive algorithm is presented for covariance matrix eigenstructure computation based on the updated computation of the SVD (singular value decomposition) of a data matrix formed with the received data vectors appended as columns. Simulation results show that the algorithm is successful in tracking the eigenstructure of a time-varying covariance matrix in a nonstationary environment. The advantage of the algorithm is that it uses the data vectors X/sub i/ at each iteration to update the eigenstructure instead of a rank one matrix update, thus avoiding the need to double the dynamic range necessary for a given numerical accuracy. The computations for the algorithm are easily mapped on existing systolic arrays with some modifications.>

The relationship between Cadzow's signal subspace algorithm and the spatially smoothed minimum-norm algorithm of Tufts-Kumaresan is investigated. It is shown that Cadzow's algorithm can be realized by subarray averaging lower rank approximations to the array covariance matrix. A data-domain algorithm that is applicable in a correlated signal environment is formulated. This algorithm offers the advantage of lower word length requirements, and obviates the necessity of computing higher order statistics. It may also be extended in a straightforward way to incorporate signal enumeration. Simulation results are given that contrast the performance of this algorithm to the signal eigenvector approach.>

An extension is presented of the work of V.M. Eyubogin (see ibid., vol.36, p.401-9, Apr. 1988) on decision-feedback equalization (DFE) applied to coded systems with interleaving. The authors study the adaptive implementation of the DFE using recursive-least-squares algorithms (RLS). System performance on time-dispersive channels with nulls as well as on channels with relatively small intersymbol interference is investigated. A reference insertion method is used to improve system performance, and a two-stage processing technique is adopted to use the more reliable decisions from the decoder in equalizer coefficient adaptation. Simulation results show that the RLS-implemented DFE systems with coded modulation can successfully combat severe channel distortion while maintaining the coding gain over corresponding uncoded systems.>

The symbol error probability of two selection schemes, namely, maximum signal-to-noise ratio (M gamma ) selection and maximum output (MO) selection, for M-ary multidiversity reception over a Rayleigh fading channel are discussed. The symbol error probability of the MO scheme is lower than that of the M gamma scheme. The more diversity receptions that are used, the larger is the difference. A simple expression of crossover average signal-to-noise ratio (per bit) is presented as a guideline for increasing the number of diversity receptions.>

The effects of a narrowband interference present in a pseudonoise (PN) spread-spectrum system can be minimized by using digital whitening techniques. A new efficient block LS algorithm for the design of an FIR filter with linear phase is derived and used as a whitening filter. Simulations are carried out to demonstrate the effectiveness of the LS optimum linear-phase filter in suppressing a narrowband interference in a PN spread-spectrum system. Comparisons to previously used methods are made. The simulations showed an improvement in the output SNR on the order of 4-5 dB over already existing schemes.>

Investigation of the eigenstructure of the autocorrelation matrix of the received signal in a complex or real fractionally-spaced equalizer indicates that this matrix has a certain number of nontrivial eigenvalues. By using singular value decomposition, it is shown that the excess mean-square error in least-squares adaptive algorithms is proportional to the number of nontrivial eigenvalues, instead of the number of taps. This leads to methods for effectively reducing the misadjustment error.>

The authors address the problem in which time delays are closely-spaced, i.e. the distance between two consecutive time delays is significantly less than the duration of the autocorrelation of the FM signal. A high-resolution estimation method using the cumulant cepstra (polycepstra) of the received sensor data as the basic tool for reconstruction is introduced. The effectiveness of the method is demonstrated for different noise conditions and lengths of data. The results apply to sonar signal processing problems in which the acoustic FM signal is embedded in reverberation noise due to the presence of multipath and observation noise.>

In practical applications of the LMS adaptive transversal filtering algorithm, a delay in the coefficient update is sometimes required. In this paper, the behavior of the Delayed LMS (DLMS) algorithm is studied. A stablility bound for the step size is derived. The relation between the step size and the convergence speed and the effect of the delay on the convergence behavior are also investigated. Computer simulation results are provided and compared with the analytical results.

The effects of a narrowband interference in a PN spread spectrum system can be minimized by employing a whitening filter. The performance of this filter can be improved if its impulse response is symmetrical. In this paper an optimum LS FIR smoother is adopted to perform the whitening process and a new efficient algorithm is presented to compute the smoothers coefficients. To demonstrate the effectiveness of the LS FIR smoother in suppressing a narrowband interference, simulations are carried out and the results are compared with those obtained by previously employed techniques.

The development of systolic array processors is very important for real-time adaptive array processing applications. In this paper a numerically robust algorithm, based on the modified Gram-Schmidt (MGS) method, is presented. The algorithm can be efficiently realized using a systolic architecture and is capable of handling both exponential and finite memory windows in order to cope with time-varying data. Finally, the relation of these algorithms to similar schemes based on the Given's transformation is investigated.

In this paper, we show that it is possible to approximate true division by dividing a number by a power-of-two in the LS lattice algorithm that is based on the new direct-coefficient-update form of the exact least squares (LS) lattice algorithm. The resulting pseudo-LS lattice algorithm is modestly slower in initial convergence than the true LS lattice algorithm, while it has a steady state error similar to the latter. The results are extended to a family of LS estimation algorithms covering a broader scope of applications.

New formulas are presented for direct updating of the reflection coefficients in the a priori and a posteriori forms of the least squares (LS) lattice algorithms. An analysis of the numerical characteristics of the new LS lattice forms is given and a comparison is made with the numerical characteristics of the conventional LS lattice algorithms. Computer simulation results are provided on the numerical accuracy of conventional and new LS lattice algorithms for several values of finite word length.

This paper presents two types of adaptive lattice decisionfeedback equalizers (DFE), the least squares (LS) lattice DFE and the gradient lattice DFE. Their performance has been investigated on both time-invariant and time-variant channels through computer simulations and compared to other kinds of equalizers. An analysis of the self-noise and tracking characteristics of the LS DFE and the DFE employing the Widrow-Hoff least mean square adaptive algorithm (LMS DFE) are also given. The analysis and simulation results show that the LS lattice DFE has the faster initial convergence rate, while the gradient lattice DFE is computationally more efficient. The main advantages of the lattice DFE's are their numerical stability, their computational efficiency, the flexibility to change their length, and their excellent capabilities for tracking rapidly time-variant channels.

This paper provides a quantitative analysis of the tracking characteristics of least squares algorithms. A comparison is made with the tracking performance of the LMS algorithm. Other algorithms that are similar to least squares algorithms, such as the gradient lattice algorithm and the Gram-Schmidt orthogonalization algorithm are also considered. Simulation results are provided to reinforce the analytical results and conclusions.

This paper investigates the numerical accuracy and the numerical stability of adaptive estimation algorithms. A feedback system model is provided to investigate the numerical stability of the algorithms. Simulation results on the comparison of numerical accuracy of LS adaptive algorithms are given. Two new methods are given that improve the numerical accuracy of the adaptive algorithms when a short word length is used.

The paper presents an equalization scheme based on the two-stage equalizer originally introduced by Proakis. Mostly additions are required for implementation of the equalizer structure and the adaptation algorithm. The equalizer can be applied to data transmission Systems which use four-phase modulation, especially in 1200/2400 bit/s modems, thus replacing the fixed equalizer recommended by CCITT. The results presented in the paper deal with the analog and digital implementation of the proposed equalizer. Its performance is compared to the performance of the conventional transversal equalizer, a decision-feedback equalizer, an ideal linear canceller, and an ideal QPSK system.

A generalized least squares lattice algorithm (GLSLA), which is appropriate for multi-channel adaptive filtering and estimation, is presented. This algorithm has all the advantages of a conventional least-squares (LS) lattice algorithm, such as computational efficiency, numerical stability, and the property that successive stages are decoupled. Besides these advantages, it also has the flexibility that the number of stages in each channel may be different. This property does not exist in the conventional LS lattice algorithms. As an application, a decision feedback equalizer (DFE) with different numbers of feedforward and feedback stages is proposed and implemented using the GLSLA. Some results obtained from a computer simulation of the algorithm are also presented.

Results of an investigation of algorithms for estimating and suppressing narrow-band interference in pseudonoise (PN) spread-spectrum digital communication systems are presented. Techniques for determining the coefficients of a linear, interference suppression filter are described, which are based on linear prediction and conventional spectral analysis methods. Numerical results are presented on the characteristics of the linear filter and on its effectiveness in suppressing the interference. The error rate performance of a receiver that employs the interference suppression filter followed by a PN correlator is determined based on the assumption that the combined noise and residual interference at the output of the PN correlator is Gaussian distributed. Performance results obtained by Monte Carlo simulation are also presented and compared with theoretical results.

The error rate performance, obtained on a Rayleigh fading channel, is determined and illustrated graphically for concatenated codes in which the outer code is a dual-kconvolutional code and the inner code is either a Hadamard block code or a block orthogonal code. Comparison of the performance of these two types of concatenated codes is made on the basis of the same bandwidth utilization. It is also illustrated that the concatenated dual-kcode yields a significant improvement in performance relative to the performance achieved with the inner code alone.

The design of a coding/modulation structure for digital communications over a Rayleigh fading channel, the structure of the corresponding decoder, and the error rate performance of the resulting system are considered. Emphasis is on the use of constant weight codes for constructing equal energy waveforms for transmission over the channel. The performance gains that are achieved by the integrated coding/modulation approach relative to conventional methods for obtaining diversity are illustrated via some examples. Of special interest is the use of a concatenated coding technique for forming codes of large distance and hence high diversity. A new decoding algorithm is applied to enable efficient decoding of the concatenated code. An example is included that shows a performance increase of several dB resulting from concatenation.

Adaptive mean-square error (mse) and maximum-likelihood detection (MLD) algorithms for a dual-channel digital communication system in the presence of interchannel interference and white Gaussian noise are presented. The mse algorithm forms estimates of the transmitted symbols from a linear combination of received symbols using weights that minimize the mse between transmitted and estimated symbols. The nonlinear MLD algorithm minimizes the probability of symbol error by maximizing the probability of the received signal samples on the two channels over ail possible transmitted symbol pairs. The probability of error is derived for the two algorithms when quadrature phase-shift keying (QPSK) is used as a modulation technique, and is compared with that of a dual-channel QPSK system having no compensation for the crosstalk.

An adaptive maximum-likelihood sequence estimator for a digital pulse-amplitude-modulated sequence in the presence of finite-duration unknown slowly time-varying intersymbol interference and additive white Gaussian noise is developed. Predicted performance and simulation results for specific channels are given.

An estimate of an upper bound on performance in terms of probability of error is developed for maximum-likelihood sequence estimation over channels for which only the pulse response energy and duration are known. This bound is evaluated for channels with a pulse response duration up to 10 signaling intervals, and the related minimum-distance channel codes are presented.

A tutorial paper on an adaptive receiver that is suitable for high-speed digital signaling over slowly time-varying, band-limited channels which have impulse responses that are unknown at the receiver is presented. The receiver utilizes a steepest-descent technique for adjusting its parameters to existing channel conditions. A treatment of the speed of adaptation of the receiver is included.

In studies of sequential detection of radar signals, the parameter of primary interest is the length of the sequential test, denoted byn. Since this test length is a random variable, moments and/or probability distribution functions ofnare desirable. A procedure is described in this communication for obtaining exact probability distribution functionsP(n)and exact average values ofn,E(n), when the input to the sequential processor is discrete radar data (radar data in quantized form). This procedure is based upon the representation of the sequential test as a Markov process. The results are quite general in that they apply to multilevel quantization of the data. However, the procedure appears especially attractive when the number of levels is small as is usually the case when dealing with discrete radar data. The procedure for determining exact distribution functions and average values ofnpresented herein is compared with the Wald-Girshick approach for obtainingP(n)andE(n), and the superiority of the former approach in computational convenience is indicated.