Multi-scale Multi-lag Channel Research Articles

Cyclostationarity of Communication Signals in Underwater Acoustic Channels

The effect of underwater acoustic propagation on the cyclostationary features of communication signals is modeled and analyzed. Two kinds of channels are considered: the multiscale-multilag channel, over which mobile and wideband acoustic systems usually communicate, and the dispersive channel resulting from low-frequency modal propagation in shallow water. It is shown that multiscale-multilag channels transform cyclostationary signals into a sum of velocity and acceleration-dependent time-warped cyclostationary processes. This time-warping is carefully taken into account to efficiently recover the cyclostationary features. On the other hand, it is found that low-frequency dispersive channels preserve the original periodicity but attenuate the shorter cycles and spread the correlations. To illustrate the theoretical results, applications with simulated and real data are also presented. Specifically, the problem of estimating time-varying Doppler scales is addressed for multiscale-multilag channels as well as the detection of signals with unique cyclostationary signatures. The example of blind symbol-rate estimation applied to covert communications in dispersive channels is also discussed. Special attention is paid to phase-shift keying (PSK), quadrature amplitude modulation (QAM), orthogonal frequency-division multiplexing (OFDM), and direct-sequence spread-spectrum (DSSS) signals. Accompanying supplementary material provides the MATLAB code used for the estimation and detection examples.

Power Allocation for OFDM Over Multi-scale Multi-lag Channels

Underwater acoustic (UWA) signal is wideband in nature and suffers doubly selective fading in time and frequency. In the presence of relative motion, a typical UWA channel can be described by a multiscale multilag (MSML) model. To compensate the scaling effect of UWA channels, many UWA communication systems employ a signal-resampling operation by a single scale at the front end of the receiver. For orthogonal frequency division multiplexing systems, since the path scales are different from each other, the resampling can alleviate but not clean out the intercarrier interference (ICI) resulting from the MSML channel. In this paper, we first describe the resampled signal by an equivalent MSML model with residual time scales, which are much smaller than that of the original MSML channel. With the given statistical parameters of the equivalent MSML channel, the closed-form expressions of the average subchannel gains and ICI coefficients are derived. Based on the ICI coefficients, we derive the analytical expression of a lower bound on the average achievable rate of the system as a function of the power allocation. We then investigate the power allocation to improve the lower bound on the achievable rate. Our key idea is that, on subcarriers whose ICIs dominate the additive noise, nothing is transmitted to avoid low energy efficiency. After proving that the ICI coefficient increases monotonically as the subcarrier frequency rises, we propose an ON–OFF uniform power allocation method, in which subcarriers with odd indices keep inactive starting from a certain index to avoid ICI. The performance of the proposed power allocation is evaluated via numerical simulations, whose results show that the proposed method outperforms the existing methods when the residual time scales cannot be neglected.

A Novel Approach for the Estimation of Doubly Spread Acoustic Channels Based on Wavelet Transform

In this paper, the estimation of doubly spread underwater acoustic (UWA) channels is investigated. The UWA channels are characterized by severe delay spread and significant Doppler effects, and can be well modeled as a multi-scale multi-lag (MSML) channel. Furthermore, exploiting the sparsity of UWA channels, MSML channel estimation can be transformed into the estimation of parameter sets (amplitude, Doppler scale factor, time delay). Based on this, the orthogonal matching pursuit (OMP) algorithm has been widely used. However, the estimation accuracy of OMP depends on the size of the dictionary, which is related with both delay spread and Doppler spread. Thus it requires high computational complexity. This paper proposes a new method, called wavelet transform (WT) based algorithm, for the UWA channel estimation. Different from OMP algorithm which needs to search in both time domain and Doppler domain, WT-based algorithm only needs to search in time domain by using the Doppler invariant characteristic of hyperbolic frequency modulation (HFM) signal. The performance of the proposed algorithm is evaluated by computer simulations based on BELLHOP. The simulation results show that WT-based algorithm performs slightly better than OMP algorithm in low signal to noise ratio (SNR) while can greatly reduce computational complexity.

Parameter Estimation for Multi-Scale Multi-Lag Underwater Acoustic Channels Based on Modified Particle Swarm Optimization Algorithm

The wideband underwater acoustic multipath channel can be modeled as a multi-scale multi-lag (MSML) channel because signals from different paths might experience different Doppler scales. This brings great challenge to channel parameter estimation. In this paper, we propose a novel algorithm for parameter estimation of MSML channels. This new algorithm is a modified particle swarm optimization (MPSO) algorithm, which can estimate the parameters of the Doppler scale, the time delay, and the amplitude simultaneously for each individual path. Comparing to PSO algorithm, MPSO algorithm uses a multipath list to record positions and fitness values of particles whose fitness values are selected as lbest s, and uses these lbest s to update particles’ velocities at each iteration. As for training sequence, we employ the zero correlation zone sequence which has excellent correlation properties. Computer simulation is used to evaluate the proposed algorithm in comparison with the matching pursuit (MP)-based method and the fractional Fourier transform (FrFT)-based method. Simulation results confirm that the proposed MPSO algorithm outperforms both MP-based method and FrFT-based method in estimation accuracy as well as computation complexity.

Multi-Scale Multi-Lag Channel Estimation Using Low Rank Approximation for OFDM

This paper considers the estimation of multi-scale multi-lag (MSML) channels. The MSML channel model is a good representation for wideband communication channels, such as underwater acoustic communication and radar. This model is characterized by a limited number of paths, each parameterized by a delay, Doppler scale, and attenuation factor. Herein, it is shown that an OFDM signal after passing through the MSML channel exhibits a low rank representation. This feature can be exploited to improve the channel estimation. By characterizing the received signal, it is shown that the MSML channel estimation problem can be adapted to a structured spectral estimation problem. The challenge is that the unknown frequencies are very close to each other due to the small values of Doppler scales. This feature can be employed to show that the data matrix is approximately low-rank. By exploiting structural features of the received signal, the Prony algorithm is modified to estimate the Doppler scales (close frequencies), delays and channel gains. Two strategies using convex and no-convex regularizers to remove noise from the corrupted signal are proposed. These algorithms are iterative based on the alternating direction method of multipliers. A bound on the reconstruction of the noiseless received signal provides guidance on the selection of the relaxation parameter in the optimizations. The performance of the proposed estimation strategies are investigated via numerical simulations, and it is shown that the proposed non-convex method offers up to 7 dB improvement in low SNR and the convex method offers up to 5 dB improvement in high SNR over prior methods for the MSML channel estimation.

Optimal Bayesian Resampling for OFDM Signaling Over Multi-scale Multi-lag Channels

Underwater acoustic (UWA) communication channels are ultra-wideband in nature and experience long delay spreads and significant Doppler effects. The typical UWA channel distortion can be described by a multi-scale, multi-lag (MSML) channel model. Many UWA communication systems employ resampling by a single-scale at the front-end to compensate for the scale effects of UWA channels. In this letter, the optimal resampling parameter for OFDM signaling over MSML channels is investigated from a Bayesian perspective. The resampling parameter is selected to minimize the inter-carrier interference (ICI) resulting from the MSML channel for OFDM signaling. The exact interference energy is computed, but is intractable for optimization, thus, an upper bound is employed for optimization. Numerical results verify the tightness of the bound and quantify the performance of the Bayesian approach. As expected, the proposed method outperforms previous deterministic methods for resampling in MSML channels, which in turn outperform the classical packet-length-based approach, and is more effective in ICI mitigation.

Multi-Rate Block Transmission Over Wideband Multi-Scale Multi-Lag Channels

Many linear time-varying (LTV) channels of interest can be well-modeled by a multi-scale multi-lag (MSML) assumption, especially when wideband transmissions with a large bandwidth/carrier-frequency ratio are employed. In this paper, communications over wideband MSML channels are considered, where conventional communication methods often fail. A new parameterized data model is proposed, where the continuous MSML channel is approximated by discrete channel coefficients. It is argued that this parameterized data model is always subject to discretization errors in the baseband. However, by designing the transmit/receive pulse intelligently and imposing a multi-branch structure on the receiver, one can eliminate the impact of the discretization errors on equalization. In addition, to enhance the bandwidth efficiency, a novel multi-layer transmit signaling is proposed, which is characterized by multiple data rates on different layers. The inter-layer interference, induced by the multi-layer transmitter, can also be minimized by the same design of the transmit/receive pulse. As a result, the effective channel experienced by the receiver can be described by a block diagonal matrix, with each diagonal block being strictly banded. Such a channel matrix structure enables the use of several existing low-complexity equalizers viable.

Iterative equalization for OFDM systems over wideband Multi-Scale Multi-Lag channels

OFDM suffers from inter-carrier interference (ICI) when the channel is time varying. This article seeks to quantify the amount of interference resulting from wideband OFDM channels, which are assumed to follow the multi-scale multi-lag (MSML) model. The MSML channel model results in full channel matrices both in the frequency and time domains. However, banded approximations are possible, leading to a significant reduction in the equalization complexity. Measures for determining whether a time-domain or frequency-domain approach should be undertaken are provided based on the interference analysis, and we propose to use the conjugate gradient (CG) algorithm to equalize the channel iteratively. The suitability of a preconditioning technique, that often accompanies the CG method to accelerate the convergence, is also discussed. We show that in order for the diagonal preconditioner to function properly, optimal resampling is indispensable.