Christian R. Berger

Sparse Channel Estimation for Multicarrier Underwater Acoustic Communication: From Subspace Methods to Compressed Sensing

In this paper, we present various channel estimators that exploit the channel sparsity in a multicarrier underwater acoustic system, including subspace algorithms from the array precessing literature, namely root-MUSIC and ESPRIT, and recent compressed sensing algorithms in form of Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP). Numerical simulation and experimental data of an OFDM block-by-block receiver are used to evaluate the proposed algorithms in comparison to the conventional least-squares (LS) channel estimator. We observe that subspace methods can tolerate small to moderate Doppler effects, and outperform the LS approach when the channel is indeed sparse. On the other hand, compressed sensing algorithms uniformly outperform the LS and subspace methods. Coupled with a channel equalizer mitigating intercarrier interference, the compressed sensing algorithms can handle channels with significant Doppler spread.

Application of compressive sensing to sparse channel estimation

Compressive sensing is a topic that has recently gained much attention in the applied mathematics and signal processing communities. It has been applied in various areas, such as imaging, radar, speech recognition, and data acquisition. In communications, compressive sensing is largely accepted for sparse channel estimation and its variants. In this article we highlight the fundamental concepts of compressive sensing and give an overview of its application to pilot aided channel estimation. We point out that a popular assumption - that multipath channels are sparse in their equivalent baseband representation - has pitfalls. There are over-complete dictionaries that lead to much sparser channel representations and better estimation performance. As a concrete example, we detail the application of compressive sensing to multicarrier underwater acoustic communications, where the channel features sparse arrivals, each characterized by its distinct delay and Doppler scale factor. To work with practical systems, several modifications need to be made to the compressive sensing framework as the channel estimation error varies with how detailed the channel is modeled, and how data and pilot symbols are mixed in the signal design.

Signal Processing for Passive Radar Using OFDM Waveforms

Passive radar is a concept where illuminators of opportunity are used in a multistatic radar setup. New digital signals, like digital audio/video broadcast (DAB/DVB), are excellent candidates for this scheme, as they are widely available, can be easily decoded to acquire the noise-free signal, and employ orthogonal frequency division multiplex (OFDM). Multicarrier transmission schemes like OFDM use block channel equalization in the frequency domain, efficiently implemented as a fast Fourier transform, and these channel estimates can directly be used to identify targets based on Fourier analysis across subsequent blocks. In this paper, we derive the exact matched filter formulation for passive radar using OFDM waveforms. We then show that the current approach using Fourier analysis across block channel estimates is equivalent to the matched filter, based on a piecewise constant assumption on the Doppler-induced phase rotation in the time domain. We next present high-resolution algorithms based on the same assumption: first we implement MUSIC as a 2-D spectral estimator using spatial smoothing; then we use the new concept of compressed sensing to identify targets. We compare the new algorithms and the current approach using numerical simulation and experimental data recorded from a DAB network in Germany.

Iterative sparse channel estimation and decoding for underwater MIMO-OFDM

We propose a block-by-block iterative receiver for underwater MIMO-OFDM that couples channel estimation with multiple-input multiple-output (MIMO) detection and low-density parity-check (LDPC) channel decoding. In particular, the channel estimator is based on a compressive sensing technique to exploit the channel sparsity, the MIMO detector consists of a hybrid use of successive interference cancellation and soft minimum mean-square error (MMSE) equalization, and channel coding uses nonbinary LDPC codes. Various feedback strategies from the channel decoder to the channel estimator are studied, including full feedback of hard or soft symbol decisions, as well as their threshold-controlled versions. We study the receiver performance using numerical simulation and experimental data collected from the RACE08 and SPACE08 experiments. We find that iterative receiver processing including sparse channel estimation leads to impressive performance gains. These gains are more pronounced when the number of available pilots to estimate the channel is decreased, for example, when a fixed number of pilots is split between an increasing number of parallel data streams in MIMO transmission. For the various feedback strategies for iterative channel estimation, we observe that soft decision feedback slightly outperforms hard decision feedback.

Sparse channel estimation for multicarrier underwater acoustic communication: From subspace methods to compressed sensing

In this paper, we present various channel estimators that exploit the channel sparsity in a multicarrier underwater acoustic system, including subspace algorithms from the array precessing literature, namely root-MUSIC and ESPRIT, and recent compressed sensing algorithms in form of Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP). Numerical simulation and experimental data of an OFDM block-by-block receiver are used to evaluate the proposed algorithms in comparison to the conventional least-squares (LS) channel estimator. We observe that subspace methods can tolerate small to moderate Doppler effects, and outperform the LS approach when the channel is indeed sparse. On the other hand, compressed sensing algorithms uniformly outperform the LS and subspace methods. Coupled with a channel equalizer mitigating intercarrier interference, the compressed sensing algorithms can handle channels with significant Doppler spread.

Detection, Synchronization, and Doppler Scale Estimation with Multicarrier Waveforms in Underwater Acoustic Communication

We propose a novel method for detection, synchronization, and Doppler scale estimation for underwater acoustic communication using orthogonal frequency division multiplex (OFDM) waveforms. The method involves transmitting two identical OFDM symbols together with a cyclic prefix, while the receiver uses a bank of parallel self-correlators matched to different Doppler scaling factors on waveform dilation or compression. We characterize the receiver operating characteristic in terms of probability of false alarm and probability of detection, and analyze the impact of Doppler scale estimation accuracy on the data transmission performance. We have tested the proposed method with real data from an experiment at Buzzards Bay, MA, Dec. 15, 2006. Using only one OFDM preamble, the proposed method achieves performance similar to an existing method that uses two linearly-frequency-modulated (LFM) waveforms, one as a preamble and the other as a postamble. Avoiding the need of buffering the whole data packet before data demodulation, the proposed method enables online receiver operation.

Progressive Inter-Carrier Interference Equalization for OFDM Transmission Over Time-Varying Underwater Acoustic Channels

Multicarrier modulation in the form of orthogonal-frequency-division-multiplexing (OFDM) has been intensively pursued for underwater acoustic (UWA) communications recently due to its ability to handle long dispersive channels. Fast variation of UWA channels destroys the orthogonality of the sub-carriers and leads to inter-carrier interference (ICI), which degrades the system performance significantly. In this paper, we propose a progressive receiver dealing with time-varying UWA channels. The progressive receiver is in nature an iterative receiver, based on the turbo principle. However, it distinguishes itself from existing iterative receivers in that the system model for channel estimation and data detection is itself continually updated during the iterations. When the decoding in the current iteration is not successful, the receiver increases the span of the ICI in the system model and utilizes the currently available soft information from the decoder to assist the next iteration which deals with a channel with larger Doppler spread. Numerical simulation and experimental data collected from the 2008 Surface Processes and Acoustic Communications Experiment (SPACE08) show that the proposed receiver can self adapt to channel variations, enjoying low complexity in good channel conditions while maintaining excellent performance in adverse channel conditions.

Optimizing Joint Erasure- and Error-Correction Coding for Wireless Packet Transmissions

To achieve reliable packet transmission over a wireless link without feedback, we propose a layered coding approach that uses error-correction coding within each packet and erasure-correction coding across the packets. This layered approach is also applicable to an end-to-end data transport over a network where a wireless link is the performance bottleneck. We investigate how to optimally combine the strengths of error- and erasure-correction coding to optimize the system performance with a given resource constraint, or to maximize the resource utilization efficiency subject to a prescribed performance. Our results determine the optimum tradeoff in splitting redundancy between error-correction coding and erasure-correction codes, which depends on the fading statistics and the average signal to noise ratio (SNR) of the wireless channel. For severe fading channels, such as Rayleigh fading channels, the tradeoff leans towards more redundancy on erasure-correction coding across packets, and less so on error-correction coding within each packet. For channels with better fading conditions, more redundancy can be spent on error-correction coding. The analysis has been extended to a limiting case with a large number of packets, and a scenario where only discrete rates are available via a finite number of transmission modes.

Frequency-Domain Oversampling for Zero-Padded OFDM in Underwater Acoustic Communications

Although time-domain oversampling of the received baseband signal is common for single-carrier transmissions, the counterpart of frequency-domain oversampling is rarely used for multicarrier transmissions. In this paper, we explore frequency-domain oversampling to improve the system performance of zero-padded OFDM transmissions over underwater acoustic channels with large Doppler spread. We use a signal design that enables separate sparse channel estimation and data detection, rendering a low complexity receiver. Based on both simulation and experimental results, we observe that the receiver with frequency-domain oversampling outperforms the conventional one considerably in channels with moderate and large Doppler spreads, and the gain increases as the Doppler spread increases. Although a raised-cosine pulse-shaping window can be used to improve the system performance relative to a rectangular window at the expense of data rate reduction, the performance gain is much less than that brought by frequency-domain oversampling in the considered OFDM system for Doppler spread channels.

Comparison of basis pursuit algorithms for sparse channel estimation in underwater acoustic OFDM

Recently it has been shown that sparse channel estimation, implemented with orthogonal matching pursuit (OMP) and basis pursuit (BP) algorithms, has impressive performance gains over alternatives that do not take advantage of the channel sparsity, for underwater acoustic (UWA) communications. We in this paper compare the performance and complexity of three popular BP algorithms, namely l1 ls, SpaRSA, and YALL1, using both simulation and experimental data for underwater orthogonal frequency division multiplexing (OFDM) systems with both single and multiple transmitters. We find that all BP solvers achieve similar block-error-rate performance, considerably outperforming OMP. In terms of complexity, both SpaRSA and YALL1 reduce the runtime by about one order of magnitude relative to l1 ls, catching up with OMP. The efficient BP solvers such as SpaRSA and YALL1 are thus appealing to be implemented in real-time underwater OFDM modems.