Orthogonal delay-Doppler (DD) division multiplexing (ODDM) modulation has recently emerged as a promising paradigm for ensuring reliable communications in doubly-selective channels. This work investigates the spectra and orthogonality characteristics of analog (direct) and approximate digital implementations of ODDM systems. We first determine the time and frequency domain representations of the basis functions for waveform in analog and approximate digital ODDM systems. Thereafter, we derive their power spectral densities and show that while the spectrum of analog ODDM waveforms exhibits a step-wise behavior in its transition regions, the spectrum of approximate digital ODDM waveforms is confined to that of the ODDM sub-pulse. Next, we prove the orthogonality characteristics of approximate digital ODDM waveforms and show that, unlike analog ODDM waveforms, the approximate digital ODDM waveforms satisfy orthogonality without the need of additional time domain resources. Additionally, we examine the similarities and differences that implementations of approximate digital ODDM share with the other variants of DD modulations, focusing on the domain changes the symbols undergo, the type of pulse shaping and windowing used, and the domains and the sequence in which they are performed. Finally, we present numerical results to validate our findings and draw further insights.

In this paper, we investigate the design of low-complexity, high-performance transmission and detection schemes for the emerging affine frequency division multiplexing (AFDM) waveform in doubly selective channels. We first propose the time-domain zero-padding (TZP-)AFDM transmission frame, which simplifies time-domain input-output (IO) relation, while preserving the spectral efficiency and retaining a relatively compact discrete affine Fourier transform (DAFT)-domain IO relation via aphase-rotated overlap-add(PROLA) technique. Based on the derived IO relations, we develop a novel two-stage detector. In the first stage, low-complexity, initial linear minimum mean square error (MMSE) detection is performed in the time domain, with statistics efficiently computed and passed to the second stage. For the second stage, we introduce several iterative MMSE detection schemes that offer a trade-off between error performance and detection complexity. In particular, our cross-DAFT-and-time-domain iterative detector enhances error performance while exploiting the time-domain IO relation to reduce complexity. As an alternative, a DAFT-domain iterative detector is proposed for the second stage utilizing the DAFT-domain IO relation derived, which further improves the error performance albeit with increased complexity. Simulation results show that the proposed TZP-AFDM and detectors achieve superior error performance, higher spectral efficiency and lower computational overhead compared to existing approaches.

Delay-Doppler (DD) domain modulation such as orthogonal DD division multiplexing (ODDM) has been recently explored for communications over doubly selective channels. This paper derives equivalent sampled (on-grid) DD (ESDD) channel models for the effective discrete-time channels in ODDM systems over highly-spread off-grid physical channels with delay and Doppler shifts that can exceed the subpulse spacing and subtone spacing, respectively, of the DD orthogonal pulse (DDOP). The derived ESDD models account for i) off-grid delay and Doppler shifts present in practical physical channels, ii) sample-wise pulse shaping at the transmitter, and iii) matched filtering and windowing at the receiver. We then investigate the supports of the ESDD models and their implications on the input-output (IO) relation of ODDM adopting more general pulses and windows over highly-spread physical channels. In particular, we show that the digital sequences of ODDMcouple finelywith on-grid discrete-time DD channels, which leads to compact IO relation. We also analyze the folding and aliasing of the ESDD channel and their influence on the fading effect and predictability of effective channels experienced by the DD-domain symbols of ODDM. Based on the results, we identify conditions under which the ESDD channels can be estimated directly from embedded DD-domain pilots in a single ODDM frame. Finally, numerical results are provided to further demonstrate the findings of this paper.

The orthogonal delay-Doppler (DD) division multiplexing (ODDM) modulation has been proposed as a promising paradigm for ensuring reliable communications in doublyselective channels. Although ODDM functions as a multicarrier modulation on the DD plane, academia and industry are more accustomed to understanding and altering the time and frequency resources of signals and waveforms. Recognizing this, in this work, we investigate the time and spectral occupancies of the transmitted signals in both analog (direct) and digital (approximate) implementations of ODDM systems. We begin by explicitly determining the basis functions for both ODDM systems in time and frequency domains, and highlight their phase term difference in the time domain and their envelope difference in the frequency domain. We then derive the spectral responses of their transmit signals. We reveal that while the spectral response of signals in analog ODDM systems exhibits a step-wise behavior in its transition regions, the spectral response of signals in digital ODDM systems is confined to that of the ODDM sub-pulse. Finally, through numerical results, we verify our findings and show that out-of-band-emission of ODDM systems can be further improved by increasing the duration of the ODDM sub-pulse.

This paper examines orthogonal delay-Doppler (DD) division multiplexing (ODDM) systems over highly-spread channels characterized by delay and Doppler shifts which can exceed, respectively, the sub-pulse separation and sub-tone separation of the DD orthogonal pulse employed by ODDM. We first derive an equivalent sampled DD (ESDD) channel model with on-grid delay and Doppler shifts specified by the sampling interval and frame duration of the transmission scheme. Our model accounts for off-grid delay and Doppler present in practical channels, samplewise pulse shaping at the transmitter, and matched filtering and windowing at the receiver. By examining their interaction, we show that the time-domain sequences of ODDM implemented approximately (digitally) using discrete Fourier transform (DFT) and inverse DFT (IDFT) and the discrete-time on-grid DD channel are finely coupled, and this leads to compact input-output (IO) relation for ODDM over on-grid channels. We then leverage the ESDD model to describe the IO relation of ODDM adopting more general pulses and windows over highly-spread off-grid channels, which reveals the potential folding (aliasing) of the ESDD channel and its implication on the signal model. We finally present numerical results. It is observed that pulses with shorter duration and windows with lower sidelobes in their spectrum lead to sparser ESDD channels.

In pursuit of reliable performance for high-mobility integrated sensing and communication (ISAC) scenarios, the orthogonal delay-Doppler division multiplexing (ODDM) modulation can be leveraged to exploit the inherent channel sparsity in the delay-Doppler (DD) domain. In this letter, we propose a joint target localization and channel estimation method for ODDM-ISAC systems that employs a multi-pilot training frame to enhance parameter estimation with accumulated signal energy. By exploiting the block-circulant-like structure of the equivalent sampled DD domain (ESDD) channel matrix, multiple pilots are strategically arranged within a training frame. To facilitate effective energy accumulation from different pilots, a phase compensation strategy is devised, which improves the accuracy of parameter estimation for target localization and channel reconstruction. Moreover, the feasibility of the proposed method is theoretically analyzed when the actual delay and Doppler shift are on or off the quantized DD grid, respectively. Simulation results validate the effectiveness of the proposed method for both target localization and channel estimation.

The orthogonal delay-Doppler division multiplexing (ODDM) modulation is a recently proposed multi-carrier modulation that features a realizable pulse orthogonal with respect to the delay-Doppler (DD) plane’s fine resolutions. In this paper, we investigate the performance of ODDM systems with imperfect channel estimation considering three detectors, namely the message passing algorithm (MPA) detector, iterative maximum-ratio combining (MRC) detector, and successive interference cancellation with minimum mean square error (SIC-MMSE) detector. We derive the post-equalization signal-to-interference-plus-noise ratio (SINR) for MRC and SIC-MMSE and analyze their bit error rate (BER) performance. Based on this analysis, we propose the MRC with subtractive dither (MRC-SD) and soft SIC-MMSE initialized MRC (SSMI-MRC) detector to improve the BER of iterative MRC. Our results demonstrate that soft SIC-MMSE consistently outperforms the other detectors in BER performance under perfect and imperfect CSI. While MRC exhibits a BER floor above$10^{-5}$, MRC-SD effectively lowers the BER with a negligible increase in detection complexity. SSMI-MRC achieves better BER than hard SIC-MMSE with the same detection complexity order. Additionally, we show that MPA has an error floor and is sensitive to imperfect CSI.

In this study, we design novel approximately mutually unbiased bases (AMUBs) sequences with arbitrary lengths and large family sizes for massive connection systems. Sequences with low correlations are highly demanded for many wireless communications systems, including Industrial Internet of Things (IIoT) systems for various applications. While many sets of sequences have been designed in the past decades, the requirement of large family size, i.e., the number of available sequences for massive connection systems has not yet been addressed. It is well known that mutually unbiased-based (MUB) sequences process desired correlation properties with large family sizes. However, the family size based on the current construction methods is limited by the length of the MUB sequences. In real applications, the longer length may lead to higher overhead and affect the overall transmission rate. This drawback makes MUB sequences have limited applications for industrial massive connection systems. In this article, we modified the original sequences generator of MUB from a quadratic polynomial to a cubic polynomial to further increase the family size. To generate AMUB sequences with arbitrary lengths, we then proposed a construction method based on the exponential sums over finite fields, and optimized the continuous peak-to-average power ratio (PAPR) of the proposed AMUB sequences for real applications. Given the dimension of MUB M, the proposed method can increase M times the number of available sequences. Meanwhile, the length restrictions in MUB sequence construction are removed. Theoretical cross-correlation (CC) bounds are provided and show low correlations of the proposed sequences. The low CC, PAPR, and increased family size of the proposed sequences are then verified by numerical results.

This paper investigates the characteristics and performance of orthogonal delay-Doppler division multiplexing (ODDM) modulation over doubly selective physical channels with general delay and Doppler. Assuming that the implementation of the ODDM is based on IDFT/DFT and sample-wise pulse shaping/receiver filtering, we study the input-output (IO) relation for ODDM and characterize the equivalent sampled delay-Doppler (ESDD) domain channel in terms of the parameters of the physical channel and the DD plane orthogonal pulse (DDOP). The established IO relation can describe the patterns of inter-symbol-interference (ISI) and inter-carrier-interference (ICI) for more general delay and Doppler shifts of the physical channel. Based on the results, we also examine the influence of the transmitter configuration on the sparsity of the ESDD channel and on the resulting performance-complexity tradeoff of ODDM. We further introduce a pilot-assisted method of estimating the physical channel parameters by leveraging the derived IO relation and the root-MUSIC algorithm. We also present a low-complexity symbol detector for ODDM systems based on conjugate gradients (CG). Simulation results under various settings show that the error performance of ODDM based on the estimate of the physical channel approaches that with perfect channel state information (CSI) at a low-to-medium signal-to-noise ratio (SNR), but has an increased gap from the perfect CSI case when the SNR increases.

This paper studies the estimation of cascaded channels in passive intelligent reflective surface (IRS)-aided multiple-input multiple-output (MIMO) systems employing hybrid precoders and combiners. We propose a low-complexity solution that estimates the channel parameters progressively. The angles of departure (AoDs) and angles of arrival (AoAs) at the transmitter and receiver, respectively, are first estimated using inductive matrix completion (IMC) followed by root-MUSIC-based super-resolution spectrum estimation. Forward-backward spatial smoothing (FBSS) is applied to address the coherence issue. Using the estimated AoAs and AoDs, the training precoders and combiners are then optimized and the angle differences between the AoAs and AoDs at the IRS are estimated using the least squares (LS) method followed by FBSS and the root-MUSIC algorithm. Finally, the composite path gains of the cascaded channel are estimated using on-grid sparse recovery with a small-size dictionary. The simulation results suggest that the proposed estimator can achieve improved channel parameter estimation performance with lower complexity as compared to several recently reported alternatives, thanks to the exploitation of the knowledge of the array responses and low-rankness of the channel using low-complexity algorithms at all the stages.

This letter studies the estimation of structured clutter covariance matrix (CCM) for space–time adaptive processing (STAP)-based airborne multiin multiout (MIMO) radar with limited training data. The Kronecker-product-expansion structure of the CCM is considered, where each term involves two Kronecker product operators. By exploiting the low-rankness of two permutations of the CCM, we propose a novel estimator based on least squares penalized by two nuclear norms. The estimator is also extended by considering the linear structures of the CCM. We examine the structure of the proposed solution and demonstrate its superior performance through simulation studies.

This article investigates regularized estimation of Kronecker-structured covariance matrices (CMs) for polarization radar in sea clutter scenarios where the data are assumed to follow the complex elliptically symmetric (CES) distributions with a Kronecker-structured CM. To obtain a well-conditioned estimate of the CM, we add penalty terms of Kullback–Leibler divergence to the negative log-likelihood function of the associated complex angular Gaussian (CAG) distribution. This is shown to be equivalent to regularizing Tyler’s fixed-point equations by shrinkage. A sufficient condition that the solution exists is discussed. An iterative algorithm is applied to solve the resulting fixed-point iterations, and its convergence is proven. In order to solve the critical problem of tuning the shrinkage factors, we then introduce two methods by exploiting oracle approximating shrinkage (OAS) and cross-validation (CV). The proposed estimator, referred to as the robust shrinkage Kronecker estimator (RSKE), is shown to achieve better performance compared with several existing methods when the training samples are limited. Simulations are conducted for validating the RSKE and demonstrating its high performance by using the IPIX 1998 real sea data.

This paper considers the best channel selection for reduced-dimension space-time adaptive processing (STAP) in the presence of multiple targets. An algorithm based on semidefinite programming (SDP) is proposed to achieve the best channel selection by optimizing the worst case of the detection performance of the different targets. Compared with some existing algorithms which only consider the single-target case, the proposed algorithm can provide considerable performance improvements for detecting several different targets. Simulations are conducted for validating the proposed method and demonstrating their high performance.

As training samples are not always target-free in space-time processing for airborne radar, the traditional methods usually use the sample covariance matrix (SCM) as the test covariance matrix (TCM) to censor contaminated training samples. However, the SCM cannot represent the property of the cell under test (CUT) accurately, resulting in low selection efficiency. To deal with this problem, this letter proposes a novel training sample selection method based on covariance matrix whitening. Specifically, we utilize the reconstructed subaperture's clutter covariance matrix (RSCCM) of the CUT as the TCM. The RSCCM is only determined by the CUT and can characterize the CUT directly. Then, we use the RSCCM to whiten the subaperture's covariance matrix of the training sample. A criterion for selecting the training samples is derived based on the maximum eigenvalue of the whitened subaperture's covariance matrix, which is related to the energy of the outliers and more stable than the statistic of the generalized inner product method. Simulations are conducted to evaluate the performance of the proposed method.

This article considers the waveform design problem for airborne multiple-input-multiple-output (MIMO) radar systems with space-time adaptive processing (STAP). We choose the mutual information between the received signal and the target impulse response as the design metric to achieve enhanced detection performance under the influences from neighboring range cells. In order to solve the resulting optimization problem, we first decompose the objective function into two parts and consider their optimization individually. We optimize the first part by relaxing it using an upper bound and optimize the second part using a simple optimization procedure based on the majorization-minimization (MM) algorithm. The alternation direction method of multipliers (ADMM) framework is then adopted to derive the overall solution, where the MM algorithm is employed again to handle the fourth-order term of the waveform vector. Numerical results are provided to show that the proposed algorithm has better detection performance than that of the existing methods.

Employing low-resolution analog-to-digital converters (ADCs) coupled with large antenna arrays at the receivers has drawn considerable interests in the millimeter wave (mm-wave) system. Since mm-wave channels are sparse in angular dimensions, exploiting the structure could reduce the number of measurements while achieving acceptable performance at the same time. Motivated by the variational Bayesian line spectral estimation (VALSE) algorithm which treats the angles as random parameters, in contrast to previous works which confine the estimate to the set of grid angle points and induce grid mismatch, this paper proposes the grid-less quantized variational Bayesian channel estimation (GL-QVBCE) algorithm for antenna array systems with low resolution ADCs. Numerical results show the near optimal performance of GL-QVBCE by comparing with the Cramèr Rao bound (CRB) and the state-of-art methods.

Water demand forecast is the basis of urban intelligent water supply, because the system is limited by nonlinear changes in the process of water consumption, the traditional prediction model has great impact in accuracy and stability. Even small changes in temperature and holidays periods can lead to abnormal changes in urban water use. To solve these problems, a hybrid model combining convolutional neural network and bidirectional long and short term memory network was adopted in this study. Corresponding corrective model is established for special situations such as weather natural changes and holidays. In order to extract the features of water quantity and climate data, these features are input into the Bi-LSTM network to predict the usage of urban water. This paper carries out a correlation analysis of historical water data and climatic factors that cause an impact on the usage of urban water. The previous five days water usage data and the daily maximum temperature were selected as the basis for the holiday correction model and the temperature correction model. Comparing the different models before and after correcting the deviation, the prediction results have been improved. The present work was compared with results of long-term and short-term memory networks (LSTM), bidirectional long-term memory networks (Bi-LSTM), CNN, sparse autoencoder (SAEs), and CNN-LSTM, hence the prediction error is reduced by using the CNN-Bi-LSTM model. Finally, under the same training period, the training time and convergence of the six models were analyzed. The training time of CNN-Bi-LSTM is less than LSTM, Bi-LSTM, CNN, and CNN-LSTM, but larger than SAEs. The training convergence of CNN-Bi-LSTM was set in 125 times, which is smaller than the training times of the other five models.

This paper studies the influence of signal detection schemes on the energy efficiency (EE) of uplink multiple-input-multiple-output (MIMO) systems with low-resolution analog-to-digital converters (ADCs). Assuming equal transmission rates for all users, we derive the optimal power allocation and their analytical approximations for zero-forcing (ZF) and ZF successive interference cancellation (ZF-SIC) receivers. Both the cases with perfect channel state information (CSI) and with imperfect CSI are considered. The EE with different receivers is compared. The results indicate that for uplink massive MIMO systems with low-resolution ADCs, the radio-frequency circuit power consumption can be significant because a large number of antennas are required to compensate for the loss due to quantization errors while the number of base station antennas needed with the ZF-SIC receiver is significantly smaller than that with the ZF receiver. Meanwhile, the increase of power consumption of signal processing with ZF-SIC can be moderate, due to the fact that the receiver weights are reused in a coherent block and the dimensionality is reduced. Consequently, the ZF-SIC receiver is able to improve the overall EE for massive MIMO systems with practical ADCs. We also conduct an approximation analysis for a multi-cell scenario with the pilot contamination and inter-cell-interference considered.

Inverse covariance matrix, a.k.a. precision matrix, has wide applications in signal processing and is often estimated from training samples. The quality of estimation can be poor when the sample support is low. Banding/tapering are effective regularization approaches for covariance and precision matrix estimation but the bandwidth must be properly chosen. This paper investigates the bandwidth selection problem for banding/tapering-based precision matrix estimation. Exploiting a regression analysis interpretation of the precision matrix, we design a data-driven cross-validation (CV) method for automatically tuning the bandwidth. The effectiveness of the proposed method is demonstrated by numerical examples under a quadratic loss.

This letter proposes a new approach for knowledge-aided estimation of structured clutter covariance matrices (CCMs) in airborne radar systems with limited training data. First, we model the CCM in space-time adaptive processing (STAP) as a sum of low-rank Kronecker products. We then apply a permutation operation to convert the Kronecker factors into linear structures and propose a novel CCM estimation method under the maximum-likelihood framework. Employing a proximal gradient algorithm, the proposed method simultaneously exploits the knowledge about the clutter and the Kronecker structure of the CCM. We finally evaluate the performance of the proposed method using real data from airborne STAP.

Linear signal estimation based on sample covariance matrices (SCMs) can perform poorly if the training data are limited and the SCMs are ill-conditioned. Diagonal loading (DL) may be used to improve robustness in the face of limited training data. This paper introduces two leave-one-out cross-validation schemes for choosing the DL factor. One scheme repeatedly splits the training data with respect to time, while the other repeatedly splits the out-of-training data with respect to space. We derive computationally efficient implementations and compare them with the oracle choice in terms of the mean squared error.

This letter introduces condition number-constrained approximation to matrices used for signal estimation and detection. Under a Frobenius norm criterion, the closed-form solution to the optimal approximation is derived, which can be found efficiently for arbitrary condition number constraints. The resulting approximation techniques are applied to the imperfectly estimated covariance and channel matrices used for estimating transmit signals in communication systems. With an appropriately chosen value of condition number, the robustness of the linear and decision-feedback estimators (DFE) against model mismatch can be significantly improved.

Linear equalization can be applied to combat intersymbol interference (ISI) and cross-antenna interference (CAI) for communication systems over multipath channels. If the channel estimation is imperfect, the receiver uses a mismatched model of the system. Regularized equalization based on Krylov subspace expansion can be applied to improve robustness and reduce complexity for large systems. In this paper, we study the convergence behavior, stopping criteria, and preconditioner design for Krylov subspace methods. We show that the optimal rank can be chosen using a decision-aided estimate of the mean-squared error (MSE). However, due to the semi-convergence behavior, conventional preconditioners may fail to provide gains. To overcome this issue, we introduce regularized preconditioners, which cluster only the largest eigenvalues of the system matrix in Krylov subspace methods.

This paper deals with different techniques for linear equalization of multipath channels with imperfect channel estimation (CE). We develop a unified framework based on Krylov subspace expansion, which allows us to compare the performance of the conjugate gradient (CG) method, diagonal loading (DL), and a hybrid scheme. Our analysis shows that the DL method generally outperforms its alternatives, but at the cost of higher complexity. However, we also demonstrate that a proper implementation of the low-complexity CG method can also approach the performance of DL. Finally, we show that preconditioning degrades performance when the CE is poor.

This paper considers large multiple-input multiple-output (MIMO) communication systems with linear precoding and linear minimum mean-squared error (LMMSE) equalization based on the iterative conjugate gradient (CG) algorithm. Convergence of the CG algorithm is fast when the eigenvalues of the received signal's covariance matrix are clustered, suggesting that mean-squared error and receiver complexity can be managed with judicious precoder design. In order to accelerate convergence of an iterative CG receiver, we incorporate constraints on two measures of eigenvalue clustering into the precoder design. Closed-form solutions to the optimal precoders are derived using majorization theory and convex optimization techniques. We show that if there are constraints on receiver complexity, the proposed precoders can improve performance for large MIMO systems operating over slowly time-varying fading channels.

This paper considers linear precoding for time-varying multiple input multiple-output (MIMO) channels. We show that linear minimum mean-squared error (LMMSE) equalization based on the conjugate gradient (CG) method can result in significantly reduced complexity compared with conventional approaches. This reduction is achieved by incorporating a condition number constraint into the precoder optimization framework, which leads to clustered eigen values of the measurement covariance matrix. The cost is a small increase in MSE compared to the optimal precoder.

This paper studies the design and analysis of large multiple-input multiple-output (MIMO) systems with linear precoding and Krylov subspace receivers. We design precoders that can improve performance with low-rank receivers. We then introduce a tool based on potential theory to analyze the convergence behavior of the mean-squared error (MSE). The effectiveness of the proposed precoder and the superexponential convergence of the MSE are demonstrated1.

This paper deals with the clipping method used in orthogonal frequency-division multiplexing (OFDM) systems to reduce the peak-to-average power ratio (PAPR). An iterative soft compensation method is proposed to mitigate the clipping distortion, which can outperform conventional treatments. The impact of signaling schemes on the residual clipping noise power is studied via the symbol variance analysis. It is found that superposition coded modulation (SCM) can minimize the residual clipping noise power among all possible signaling schemes. This indicates that SCM-based OFDM systems are more robust to clipping effect than other alternatives when soft compensation is applied. It is also shown that a multi-code SCM scheme can further reduce the clipping effect and its overall performance can be quickly evaluated using a semi-analytical evolution method. Numerical examples are provided to verify the analysis.

We study superposition coded modulation (SCM) with iterative linear minimum-mean-square-error (LMMSE) detection. We show that SCM offers an attractive solution for highly complicated transmission environments with severe interference. We analyze the impact of signaling schemes on the performance of iterative LMMSE detection. We prove that among all possible signaling methods, SCM maximizes the output signal-to-noise/ interference ratio (SNIR) in the LMMSE estimates during iterative detection. Numerical examples are used to demonstrate that SCM outperforms other signaling methods when iterative LMMSE detection is applied to multi-user/multi-antenna/multipath channels.

We apply clipping to superposition coded modulation (SCM) systems to reduce the peak-to-average power ratio (PAPR) of the transmitted signal. The impact on performance is investigated by evaluating the mutual information driven by the induced peak-power-limited input signals. It is shown that the rate loss is marginal for moderate clipping thresholds if optimal encoding/decoding is used. This fact is confirmed in examples where capacity-approaching component codes are used together with the maximumaposterioriprobability (MAP) detection. In order to reduce the detection complexity of SCM with a large number of layers, we develop a suboptimal soft compensation (SC) method that is combined with soft-input soft-output (SISO) decoding algorithms in an iterative manner. A variety of simulation results for additive white Gaussian noise (AWGN) and fading channels are presented. It is shown that with the proposed method, the effect of clipping can be efficiently compensated and a good tradeoff between PAPR and bit-error rate (BER) can be achieved. Comparisons with other coded modulation schemes demonstrate that SCM offers significant advantages for high-rate transmissions over fading channels.

In this paper, we study the iterative detection problem for a coded system with multi-ary modulation. We show that, with iterative linear minimum-mean-square-error (LMMSE) detection, superposition coded modulation (SCM) can provide performance superior to that with other traditional signaling schemes used in trellis coded modulation (TCM) and bit-interleaved coded modulation (BICM). This finding provides a useful guideline for system design considering inter-symbol interference (ISI) and other forms of interference. Simulation results are provided to illustrate the efficiency of the iterative LMMSE detection with different signaling schemes.

This paper studies orthogonal frequency-division multiplexing (OFDM) systems employing coded modulation. Clipping is applied to reduce the peak-to-average-power-ratio (PAPR) of the transmit signal. A soft compensation method is proposed to combat the clipping effect. It is shown that the proposed method can outperform conventional clipping effect mitigation methods. The impact of signaling schemes of the coded modulation on system performance is investigated. The average variance analysis and numerical results demonstrate that superposition coded modulation (SCM) together with the proposed detection technique provides a simple and efficient solution to clipped OFDM transmission.

This paper presents a peak-power-limited superposition coding scheme based on clipping. A low-complexity soft compensation algorithm (SCA) for combating the clipping effect is investigated. It can be easily combined with soft-input soft-output (SISO) decoding algorithms in an iterative manner. Various numerical results show that the SCA can effectively mitigate the performance loss due to clipping.

In this paper, we present an unequal power allocation technique to increase the throughput of code-division multiple-access (CDMA) systems with chip-level interleavers. Performance is optimized, respectively, based on received and transmitted power allocation. Linear programming and power matching techniques are developed to provide solutions to systems with a very large number of users. Various numerical results are provided to demonstrate the efficiency of the proposed techniques and to examine the impact of system parameters, such as iteration number and interleaver length. We also show that with some very simple forward error correction codes, such as repetition codes or convolutional codes, the proposed scheme can achieve throughput reasonably close to that predicted by theoretical limit in multiple access channels.