Orthogonal spreading codes play an essential role in code-division multiple-access (CDMA) systems by eliminating multiple-access interference (MAI). In this paper, a novel orthogonal spreading code has been proposed for spectrally-encoded (SE) CDMA, a.k.a., spread-time (ST) CDMA with arbitrary pulse shape. It has been shown that it is possible to retain the orthogonality of the code in the presence of tail truncation by time windowing and in a general multipath fading channel in which users experience different frequency selectivity just by modifying the user codewords. Simulation results show that the proposed codes can achieve single user performance when the code length is twice the number of users.

We consider the effects of the frequency variation of frequency selective fading channels on adaptive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The magnitude of this variation has important effects on system performance and design as well as applications to temporal variation, feedback delay and channel estimation.We first examine the variation of the eigenvalues and eigenvalue sums across the frequency bins of a MIMO OFDM system focusing on the changes in the ordered eigenvalues and the eigenvalue sum or link gain between two distinct frequency bins. Here we derive distributions and moments for changes in the link gain and maximum eigenvalue and autocorrelation functions for the link gain and maximum eigenvalue as well as simple approximate results for the ordered eigenvalue differences. We then consider variations in performance via the level crossing rates (LCRs) of the bit error rates (BERs) across the frequency bins of the MIMO OFDM system operating over a Rayleigh fading channel. Each eigenmode constitutes a random process in the frequency domain and we compute the LCR for the BER of transmission down the eigenchannels of the MIMO OFDM channel. We finally verify our analysis using Monte Carlo simulations.

We develop a practical adaptive equalizer structure for time reversal-space time block-coded amplify-and-forward relaying systems, which eliminates the need for a separate decoding block requiring explicit channel estimation. The adaptive equalizer length is also independent of the data block length, making it particularly suitable for frequency selective fading channels with short delay spreads. We derive the minimum mean square error (MMSE) solution and, using the resulting structure, we develop a block recursive least squares (RLS) adaptive algorithm. We use computer simulations to compare two new adaptive equalizer structures for an amplify-and-forward relay network based on Protocols I and III proposed by Nabar et al. We show that both adaptive equalizers work well, but the equalizer tailored for Protocol I outperforms that for Protocol III.

In this paper we consider an adaptive modulation system with multiple-input multiple-output (MIMO) antennas in conjunction with orthogonal frequency division multiplexing (OFDM) operating over frequency selective Rayleigh fading environments. In particular, we consider a type of beamforming with a maximum ratio transmission, maximum ratio combining (MRT-MRC) transceiver structure. For this system we derive a central limit theorem for various block-based performance metrics. This motivates an accurate Gaussian approximation to the system data rate and the number of outages per OFDM block. In addition to data rate and outage distributions, we also consider the subcarrier SNR as a random process in the frequency domain and compute level crossing rates (LCRs) and average fade bandwidths (AFBs). Hence, we provide fundamental but novel results for the MIMO OFDM channel. The accuracy of these results is verified by Monte Carlo simulations, and applications to both performance analysis and system design are discussed.

In this paper we consider transmit and receive selection methods designed to achieve high channel capacities in a single-user MIMO link. A variety of radio channels are considered, including i.i.d. Rayleigh, correlated Rayleigh and Ricean fading environments. Also considered is the presence of imperfect channel state information (CSI) and a simplified waterfllling scheme. In all cases, we evaluate the performance of optimal selection, simple norm-based selection and other benchmark selection techniques. The major contribution is a general approach to analyzing the capacity of the norm-based selection schemes via a simple power scaling factor. We are able to assess the impact of different channels, imperfect CSI and power allocation using this power scaling factor. Furthermore, the analysis is valid for all scenarios: transmit selection, receive selection and joint transmit-receive selection. Results are shown which compare the capacity performance over a wide range of cases. A notable conclusion is that optimal selection, which is computationally intensive, is outperformed at low signal-to-noise- ratios by the simple norm-based approach with power allocation.

Spectrally encoded (SE) CDMA systems, a. k. a. spread time (ST) CDMA systems, have several advantages over their frequency-time dual, direct-sequence CDMA such as the abilities to shape the transmitted spectrum and to avoid narrow-band interference. However, no orthogonal spreading code has been proposed to efficiently avoid multiple-access interference (MAI). In this paper, we propose a novel orthogonal spreading code for SE-CDMA. We study undesirable channel conditions under which the orthogonality property of the code could be lost. We propose a chip normalizing scheme (CNS) to restore the orthogonality property of the code in these cases. Our simulation results show that the encoded system can achieve the performance of interference-free channels. Furthermore, using our CNS the users can achieve a higher bit rate at the same bit error rate as the unnormalized case.

For MIMO broadcast systems the effects of shadowing on the channel capacity and the fairness of the system in sharing the resources amongst multiple users are important issues that need to be addressed. In this paper we consider a variety of capacity-approaching algorithms for MIMO broadcast channels. We compare the performance of these algorithms in terms of their ability to approach the sum-capacity and their fairness in sharing the channel resources amongst the multiple users. We also model distance-based attenuation effects and shadowing, yielding valuable insights into the relative performances of the algorithms under varying SNR conditions. Using a novel approach of mapping the broadcast channel to an "equivalent' single-user channel followed by power scaling, we derive closed-form analytical approximations for the capacity of MIMO broadcast channels. For the more evenly distributed SNR case our approximations are quite accurate, suggesting an analytical lower bound for the well known iterative waterfilling solution. Finally, our Monte Carlo simulations comparing the algorithms point to an inherent tradeoff between sum-capacity and fairness.

We propose a practical adaptive equalizer structure for space-time block coded systems operating over frequency selective fading channels. Specifically, we develop a time domain block equalizer for time reversal-space time block coded transceivers, which eliminates the need for a separate decoding block requiring explicit channel estimation. The block equalizer length is also independent of the data block length, making it particularly suitable for short delay spread channels. We develop new normalized least mean square (NLMS) and recursive least squares (RLS) adaptive algorithms for this block structure. We use computer simulations to compare our new equalizer with an existing frequency domain equalizer. We show that our time domain equalizer requires far fewer equalizer taps, and our equalizer running the RLS algorithm outperforms in terms of both dynamic convergence behavior and symbol error rate performance. Using the flexibility of the new equalizer, we finally show that a frame structure evenly distributing the training among the blocks yields better performance for fast time-varying channels than frame structures that are constrained by frequency domain equalization.

The condition number is a well known indicator of the spatial selectivity of a MIMO wireless channel. The objective of this paper is to examine the temporal behavior of this metric using a Markov model construction. Specifically, we have developed two methods to calculate analytically the transition probabilities between Markov states. These methods involve the joint density for the channel eigenvalues at two adjacent time instances and the level crossing rates (LCR) of the condition number. We then use our Markov model to investigate the behavior of dual-mode antenna selection schemes in an i.i.d. Rayleigh fading channel.

In this letter, the joint probability density function (PDF) for the eigenvalues of a complex Wishart matrix and a perturbed version of it are derived. The latter version can be used to model channel estimation errors and variations over time or frequency. As an example, the joint PDF is used to calculate the transition probabilities between modulation states in an adaptive MIMO system. This leads to a Markov model for the system. We then use the model to investigate the modulation state entering rates (MSER), the average stay duration (ASD), and the effects of feedback delay on the accuracy of modulation state selection in mobile radio systems. Other applications of this PDF are also discussed.

Tomlinson-Harashima precoding (THP) and blind equalization are often viewed as incompatible equalization techniques. In this paper, we give multiple scenarios where the THP-blind equalization combination might arise. With this motivation we set out to answer the question, can a blind equalizer successfully acquire a THP-shaped signal? By bounding the kurtosis of the THP-shaped signal, we show that THP actually aids the initial convergence of blind equalization. We find that, as the symbol constellation size increases, the THP-shaped signal kurtosis approaches that of a uniform distribution, not a Gaussian. We then verify our analytical results using a Monte Carlo simulation of a VDSL channel.

Line selection (LS), tone selection (TS), and joint tone-line selection (JTLS) partial crosstalk cancellers have been proposed to reduce the online computational complexity of far-end crosstalk (FEXT) cancellers in DMT DSL. However, in contrast to perfect crosstalk cancellers, partial crosstalk cancellers should also provide a low pre-processing complexity when crosstalk profile changes rapidly in time. In this paper, we propose two novel fast classes of JTLS algorithms, namely, a family of sub-sort JTLS algorithms and the Lagrange JTLS. The computational complexity of our algorithms is much lower than that of the optimal greedy algorithm. Simulation results show that the performances of the proposed sub-sort algorithms are very close to the optimal greedy algorithm. More importantly, our Lagrange JTLS algorithm is optimal for the DSL channels we consider.

Singular Value Decomposition (SVD) techniques are well-known for providing an elegant transceiver architecture, that can realize the intrinsic spatial links of a MIMO channel. Such a scheme is also referred to as eigen-beamforming or eigenmode transmission. The system performance is, however, closely related to the quality of the channel information at both ends of the link. Hence, we focus on the effect of feedback time delay, which causes the transmitter to use outdated channel information in timevarying fading channels. In this paper, we derive an analytical expression for the instantaneous SINR of eigenmode transmission with a feedback time delay T. Furthermore, this expression implies a novel metric that gauges the system performance sensitivity to time-variations of the steering vectors (eigenvectors of the channel correlation matrix) at the transmitter.

In this paper we consider transmit and receive selection methods designed to achieve high channel capacities in a single-user MIMO link. A variety of radio channels are considered, including i.i.d. Rayleigh, correlated Rayleigh and Ricean fading environments. Also considered is the presence of imperfect channel state information (CSI) and a simplified waterfilling scheme. In all cases, we evaluate the performance of optimal selection, simple norm based selection and other benchmark selection techniques. The major contribution is a general approach to analyzing the capacity of the selection schemes via a simple power scaling factor. We are able to assess the impact of different channels, imperfect CSI and power allocation using this power scaling factor. Furthermore, the analysis is valid for all scenarios: transmit selection, receive selection and joint transmit-receive selection. Results are shown which compare the capacity performance over a wide range of cases. A notable conclusion is that optimal selection, which is computationally intensive, is outperformed at low SNR by the simple, norm based approach with power allocation.

Loop loss and crosstalk are the main impairments in DSL. Recently, novel crosstalk rejection and reduction techniques have been proposed to achieve the maximum capacity of the DSL channel. The performance of these techniques depends strongly on the degree of coordination among the users. In this paper, we consider maximizing the throughput of DSL when the users are coordinated at different levels. Moreover, we propose a novel centralized power allocation algorithm by generalizing a recently proposed iterative spectrum balancing (ISB) algorithm. Our generalized ISB (GISB) algorithm provides a superior performance to the ISB with polynomial complexity in the number of users. This complexity is much lower than that of the optimal spectral balancing (OSB) algorithm. Moreover, it can be selected adaptively based on the available processing power

The two single-carrier line codes which have recently been considered for VDSL standards are quadrature amplitude modulation (QAM) and carrierless amplitude/phase modulation (CAP). They have the same signal constellation and transmitted spectral shape. However, experiments have shown that the equalizer convergence rates for QAM and CAP can be different. These convergence rates can impact both the training sequence length requirements and the equalizer tracking ability for time-varying channels. We investigate a variety of equalizer architectures and algorithms and study the training sequence equalizer convergence behavior of QAM- and CAP-based VDSL systems by using both theoretical analysis and Monte Carlo computer simulations. We show that the particular equalizer structure and channel have important effects on the convergence behavior. Based on our simulations for various VDSL test loops, we recommend using the CAP matched filtered phase-splitting equalizer due to its good convergence speed and relatively low complexity

In this paper we derive a generalized method to compute the error probabilities of singular value decomposition-based receivers for a MIMO system with uncoded transmission. The method can be used for a wide class of flat fading environments, including i.i.d. and semi-correlated Rayleigh and i.i.d. Ricean channels. Although we apply the method to equal-power BPSK, it can easily be extended to higher order M-PSK and M-QAM signal constellations and adaptive "water-filling" schemes. The error probability curves derived from closed-form formulas and simulations demonstrate very close agreement. We also compare the error performances of CI, MMSE and ZF receivers with the SVD receiver.

A linear adaptive filter is one of the simplest methods to reject narrowband interference in spread spectrum systems and yields a significant increase in the received signal-to-noise ratio (SNR). In many scenarios, the interference is time varying. Therefore, characterizing the ability of the adaptive filter to track dynamically the interferer is of great interest. In this, paper, we study in parallel the dynamic convergence behaviors of the classical linear predictor and linear interpolator adapted by the LMS and normalized LMS algorithms using two analytical methods: the independence method and the small step-size method. We verify our theoretical MSE trajectories using computer simulations.

MIMO systems using adaptive transmission down the eigenchannels require the level crossing rate of the eigenvalues to compute adaptation rates and possibly feedback rates. Examples of such systems include MIMO systems using singular value decomposition (SVD) transmission. Similarly, the average fade durations of the eigenvalues give the average length of time that a particular constellation is used in adaptive modulation. Other systems which require the minimum eigenvalue to be above a certain threshold (for example, channel inversion) can also use these level crossing rates in system analysis. Hence, in this paper we derive approximate level crossing rates for the eigenvalues in the baseline case of an uncorrelated Rayleigh fading channel. Our results are remarkably accurate and compact and further improvements are also discussed.

In CDMA systems by exploiting the binary nature of the CDMA signal, adaptive nonlinear filters can significantly outperform their linear counterparts at rejecting narrowband interference (NBI). Because the NBI is time varying in many scenarios, we characterize the ability of adaptive nonlinear filters to track dynamically the NBI. We study the dynamic convergence behavior of the nonlinear predictor proposed by Vijayan and Poor, adapted by the LMS and normalized LMS algorithms using two analytical methods: the independence method and the small step-size method. We verify our theoretical mean square error trajectories using Monte Carlo simulations

Constellation shaping introduced to maximize channel capacity is detrimental to the performance of many cost function-based blind equalization algorithms including the constant modulus algorithm (CMA). We propose a new multimodulus algorithm closely related to CMA, but robust against changes in the statistical nature of the signal due to constellation shaping. While CMA behaves properly only for sub-Gaussian distributions, the algorithm we develop is applicable to a broad class of distributions including Gaussian and super-Gaussian.

Blind equalizers do not require a training sequence to start up or to restart after a communications breakdown, making them particularly useful in applications such as broadcast and point-to-multipoint networks. We study in parallel the dynamic convergence behavior of three blind equalization algorithms: the multimodulus algorithm (MMA), the constant modulus algorithm (CMA), and the reduced constellation algorithm (RCA). Using a conditional Gaussian approximation, we first derive the theoretical mean-squared-error (MSE) trajectory for MMA. This analysis leads to accurate but somewhat cumbersome expressions. Alternatively, we apply a Taylor series approximation to derive MSE trajectories for MMA, CMA, and RCA. This approach yields simpler but somewhat less accurate expressions. For the steady-state operation, however we derive even simpler formulas that accurately predict the asymptotic MSE values. We finally study the convergence rates of the three blind algorithms using their theoretical MSE trajectories, computer simulations, and a laboratory experiment.

We propose a dual-mode receiver capable of blindly demodulating both carrierless amplitude modulation/phase modulation (CAP) and quadrature amplitude modulation (QAM) line codes. Our work is motivated by some emerging broad-band access standards which require a receiver that can first blindly start up, then blindly distinguish between CAP and QAM, and finally decode the signal. The "brute force" solution to this problem would be to implement CAP and QAM receivers in parallel. However, we propose a single novel receiver based on a single equalizer that accommodates both line codes, yielding significant computational savings. We describe the receiver architecture, blind start-up methods, and line code identification algorithms, as well as computer simulations and a laboratory experiment to verify the theoretical receiver behavior.

Some emerging broadband access standards require a receiver that can first blindly start up, then blindly distinguish between carrierless amplitude modulation/phase modulation (CAP) and quadrature amplitude modulation (QAM), and finally decode the signal. The "brute force" solution to this problem would be to implement CAP and QAM receivers in parallel. However, we propose a novel dual-mode receiver based on a single equalizer which accommodates both line codes, yielding significant computational savings. We describe the receiver architecture, blind start-up methods, and line code identification algorithms, as well as computer simulations and a laboratory experiment to verify the theoretical receiver behavior.

Non-Gaussian signals arise in a wide variety of applications, including sonar, digital communications, seismology, and radio astronomy. In this tutorial overview, a hierarchical approach to signal modeling and detector design for non-Gaussian signals is described. In addition to being of interest in applications, this problem serves as a paradigm within which most of the areas of active research in statistical signal processing arise. In particular, the methodologies of nonlinear signal processing, higher order statistical analysis, signal representations, and learning algorithms, all can be juxtaposed quite naturally in this framework.>