Filtered Multitone Modulation Underwater Acoustic Communications Using Low-Complexity Channel-Estimation-Based MMSE Turbo Equalization

In minimum mean squared error (MMSE) based turbo equalization, the decoder's extrinsic information is used as the MMSE equalizer's prior information. In order to improve the performance, the combined prior information which consists of the whole decoder's extrinsic information and the partial decoder's full information in the last iteration, is used by the MMSE equalizer. Meanwhile, the MMSE equalizer is lead by matched filter as a preprocessor to reduce the complexity. The extrinsic information transfer (EXIT) chart analysis and simulation results show that the performance of the proposed scheme is much better than that of the conventional turbo equalizer.

This paper presents some experimental results on both the channel estimation based minimum mean square error Turbo equalizer (CE MMSE-TEQ) and the direct-adaptation turbo equalizer (DA-TEQ) in single-input single-output (SISO) underwater acoustic (UWA) channels. For CE MMSE-TEQ, we compare the soft-decision feedback Turbo equalizer (SDFE), the bidirectional soft-decision feedback Turbo equalizer (Bi-SDFE) and the classic linear Minimum Mean Square Error (MMSE) Turbo equalizer in terms of bit error rate (BER) performance. For DA-TEQ, the recently proposed soft-decision direct-adaptation TEQ (Soft DA-TEQ) is evaluated with the same set of experimental data. Both QPSK and multilevel modulations (8PSK and 16QAM) have been tested with the symbol rate of 9.77 ksymbols/s. Experimental results show that the CE-TEQs are more robust in SISO underwater acoustic transmission under harsh channel conditions. Especially, with low pilot overheads, the recently proposed Bi-SDFE achieved low BER performance in all cases.

Multipath channels often exhibit sparse structures in multicarrier underwater acoustic (MC-UWA) communication systems. Conventional linear channel estimators, such as least squares (LS) and minimum mean square error (MMSE) are considered as optimal solutions under the assumption of rich multipath. However, they often result in low spectral efficiency due to neglect of the sparsity in multipath channels. In this paper, we propose a novel sparse channel estimation method with compressive sensing. The proposed estimator has better estimation performance and low complexity when compared with the LS estimator. Simulations verified the proposed method with respect to the mean square error (MSE) and the computational complexity. Key words: Underwater acoustic (UWA), orthogonal frequency division multiplexing (OFDM), sparse multipath, compressive sensing (CS), sparse channel estimator.

A filter-bank modulation technique called filtered multitone (FMT) and its application to data transmission for very high-speed digital subscriber line technology are described. The proposed scheme leads to significantly lower spectral overlapping between adjacent subchannels than for known multicarrier techniques such as discrete multitone (DMT) or discrete wavelet multitone. FMT modulation mitigates interference due to echo and near-end crosstalk signals, and increases the system throughput and reach. Signal equalization in an FMT receiver is accomplished in the form of per-subchannel symbol-spaced or fractionally spaced linear or decision-feedback equalization. The problem of channel coding for this type of modulation is also addressed, and an approach that allows combined removal of intersymbol-interference via precoding and trellis coding is described. Furthermore, practical design aspects regarding filter-bank realization, initial transceiver training, adaptive equalization, and timing recovery are discussed. Finally, simulation results of the performance achieved by FMT modulation for very high-speed digital subscriber line systems, where upstream and downstream signals are separated by frequency-division duplexing, are presented and compared with DMT modulation.

Turbo equalization schemes based on minimum mean square error (MMSE) criteria available in the literature for multiple-input multiple-output (MIMO) systems are computationally expensive, as they require a relatively large matrix inversion. In this paper, we propose a low complexity turbo equalization (TE) scheme with successive interference cancellation for orthogonal frequency division multiplexing (OFDM) based MIMO receiver systems (TE-SIC-MIMO). TE-SIC-MIMO leverages on the soft feedback symbol estimate to selectively remove the intercarrier interference (ICI) and co-antenna interference (CAI) from the received data, thus turning the system matrix into an easily invertible form. Extrinsic Information Transfer (EXIT) chart analysis supplemented with numerical simulation results shows that TE-SIC-MIMO performance under static and rapidly time varying multipath conditions is mostly on par with MMSE turbo equalization scheme available in the literature, that is based on a sub-matrix of the system matrix at signal-to-noise ratios (SNR) of practical interest. However, the computation complexity of TE-SIC-MIMO turns out to be much lesser than the TE scheme considered.

The single-carrier frequency-division multiple access (SC-FDMA) or the discrete Fourier transform (DFT) pre-coded orthogonal frequency-division multiple access (OFDMA) technique has been adopted in the uplink transmission of the long term evolution (LTE) terrestrial communication standard, for its lower peak-to-average power ratio (PAPR) and similar receiver complexity, compared with OFDM. It is, however, rarely investigated in underwater acoustic (UWA) communications. This paper presents an SC-FDMA transceiver scheme for multiple-input, multiple-output (MIMO) UWA communications, and studies the performance of turbo equalization on the receiver side. The signalling of the pilot symbols bypasses the DFT precoding module, so the channel estimation and the carrier frequency offset (CFO) estimation are performed in a similar way as in a conventional OFDM system. A recently proposed high-performance frequency-domain turbo equalization technique is adopted for detecting the data symbols, which suffer inter-symbol interference (ISI) due to the DFT spreading operation. Experimental results clearly show the performance gain attributed to the turbo equalization, especially for high-order modulations.

This letter proposes a new frequency domain turbo equalization algorithm based on nonlinear minimum-mean- squared-error (MMSE) estimation. The conceptual basis of the proposed equalizer is the probabilistic data association (PDA) filtering. It is shown that by performing internal equalizer iterations, of which structure is resulted from the algorithm derivation according to the PDA concept, the convergence properties, analytical and verified by simulations, can be significantly improved over conventional MMSE turbo equalization techniques. Results of the simulations conducted to demonstrate the superiority of the proposed algorithm and to verify the accuracy of the analysis are presented in this letter.

This paper proposes using direct adaptation (DA)-based turbo equalization in multiple-input-multiple-output (MIMO) filtered multitone (FMT) time reversal (TR) acoustic communications to jointly suppress noise, residual co-channel interference (CCI) and intersymbol interference (ISI) after the TR process. Soft information-based adaptive decision feedback equalization (ADFE) adjusted according to the recursive expected least squares (RELS) algorithm, including interference cancellation and decoding, is used to construct the DA-based turbo equalization. In the proposed method, soft information is exchanged between soft symbols with soft decisions of decoding iteratively, and interference suppression is proceeded successively and iteratively until the performance is stable. The principle of the proposed method is analyzed, and based on the acoustic channel responses measured in a real experiment, the performance is assessed in relation to that of anther two methods. Compared with the MIMO-FMT TR underwater acoustic communication using interference suppression without error control coding (ECC), the proposed method performs better, benefitting from the ECC included in turbo equalization. Additionally, compared with the MIMO-FMT TR underwater acoustic communication using interference suppression based on hard decision equalization and decoding, the proposed method exhibits superior performance by exploiting soft information.

This paper addresses a novel frequency-domain (FD) derivation of the Minimum Mean Square Error (MMSE) Turbo Equalizer for ST-BICM systems. The receiver consists of a FD MMSE Equalizer and a Time Domain (TD) decoder with iterative information exchange between the two functions. In particular, we propose a FD MMSE equalizer derivation improved from previous approaches, in that feedback and feedforward filters are directly derived in the frequency-domain. The accuracy of the proposed approach is confirmed by comparing the lower bound of the iterative equalizing process with the corresponding analytical results proposed in previous paper. Simulations over multi-path Rayleigh block fading channels show that the resulting algorithm exhibits similar performance with that of the corresponding TD MMSE equalization. The problem of finding the TD filter achieving the best compromise between minimum impulse response length and performance is considered.

In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.

Severe time-dispersion of the channel is one of the limiting factors for high data rate acoustic communications in shallow water. To overcome the large time spread, the research community has devoted enormous effort in the design of high efficient, low complexity equalizers. The goal of these equalizers is to convert the time-dispersive channel into a unit-tap impulse function. In another research direction, code division multiple access (CDMA) and orthogonal frequency division multiplexing (OFDM) systems are designed to combat the multi-path effect. However, using OFDM or CDMA alone to combat the multi-path effect often forces system designers to reduce the data rate in such severe time-dispersive channels. In this paper, we propose to adopt a class of generalized equalizers to generate an effective channel with a desired length. These equalizers are referred to as channel-shortening equalizers. Then, other advanced modulation schemes, such as OFDM and CDMA, can be employed to overcome the remaining time-dispersion of the channel. Compared to the unit-tap equalization, channel-shortening equalizers can provide quality performance at low computation cost. Examples of current channel-shortening equalizers are based on minimum mean-squared error (MMSE) and maximum shortening signal-to-noise ratio (MSSNR) criteria. In this paper, these algorithms are compared in the context of underwater acoustic communications. Their performance, complexity, and implementation in acoustic communications are investigated. In the digital subscriber line (DSL) channel, where channel-shortening equalizers are often applied to, MSSNR algorithms perform better than MMSE algorithms. However, we show that the MMSE algorithm is more suitable for the underwater acoustic channels with lower complexity and robustness to noise. With the MMSE method, a channel-shortening equalizer with 20 taps can convert a typical 120-tap acoustic channel into a 33-tap shortened channel. Using data obtained from the Kauai experiment, June-July 2003, it shows that the mean of the effective signal-to-interference ratio (SIR) achieves 15.7 dB. For the same channel, the optimum unit-tap equalization needs more than 200 taps to achieve the same effective SIR

This paper investigates low complexity detection for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems with co-channel interference (CCI). We firstly derive minimum mean square error (MMSE) detection based on sorted QR decomposition (SQRD) and modified MMSE SQRD detection for MIMO-OFDM systems with CCI. Although better performance can be achieved by the new detectors than liner MMSE (LMMSE) detection, the computational complexity is still high due to the required matrix inversion operation. In order to overcome such an issue and design low complexity detection method for MIMO-OFDM systems with CCI, then, we propose an improved MMSE SQRD detector by utilizing a regularization method. The simplification of the regularization parameter calculation in the proposed method is then discussed. Simulation results show that the error performance of the proposed method approaches modified MMSE SQRD detection in presence of CCI, while keeping a much lower complexity.

A novel filter bank modulation scheme is proposed. This architecture is based on the Filtered Multitone (FMT) modulation concept where well frequency confined prototype pulses are deployed. However, in the proposed scheme linear convolutions are replaced by circular convolutions. We refer to this new scheme as Cyclic Block Filtered Multitone Modulation (CB-FMT). Both the synthesis and the analysis filter banks in CB-FMT can be efficiently implemented in the frequency domain via the concatenation of Fast Fourier Transforms (FFTs). Furthermore, it is possible to design the prototype pulse so that the system is orthogonal and it does not experience any inter-symbol and inter-carrier interference in ideal conditions. To cope with the interference introduced by a frequency selective fading medium, simple frequency domain equalization can be used. Numerical results show that CB-FMT can provide better performance than FMT and OFDM in frequency selective fading with comparable or lower complexity.

In this study, various techniques of UWA (Underwater Acoustic, UWA) channel estimation for underwater MIMO-OFDM system are studied. Dual turbo channel estimation algorithm based on channel puncture technique is proposed. In order to judge the criteria of channel compensation, difference between the raw received signal and the re-coded information signal is carried out. The uncertain sub-channels are punched by using channel puncture technique and replaced by the responses estimated by MMSE (Minimum Mean Square Error, MMSE) or OMP (Orthogonal Matching Pursuit, OMP) algorithms. Compared with the conventional existing algorithms, the proposed algorithm can effectively reduce the occupancy of pilots, offer confined error propagation and significantly increase the stability of the system with Monte Caro simulation. The results of in-tank-experiment further indorse the reliable performance with improved efficiency of 1.51 bits/s/Hz.

Formulations of the turbo equalization approach to iterative equalization and decoding vary greatly when channel knowledge is either partially or completely unknown. Maximum aposteriori probability (MAP) and minimum mean-square error (MMSE) approaches leverage channel knowledge to make explicit use of soft information (priors over the transmitted data bits) in a manner that is distinctly nonlinear, appearing either in a trellis formulation (MAP) or inside an inverted matrix (MMSE). To date, nearly all adaptive turbo equalization methods either estimate the channel or use a direct adaptation equalizer in which estimates of the transmitted data are formed from an expressly linear function of the received data and soft information, with this latter formulation being most common. We study a class of direct adaptation turbo equalizers that are both adaptive and nonlinear functions of the soft information from the decoder. We introduce piecewise linear models based on context trees that can adaptively approximate the nonlinear dependence of the equalizer on the soft information such that it can choose both the partition regions as well as the locally linear equalizer coefficients in each region independently, with computational complexity that remains of the order of a traditional direct adaptive linear equalizer. This approach is guaranteed to asymptotically achieve the performance of the best piecewise linear equalizer, and we quantify the MSE performance of the resulting algorithm and the convergence of its MSE to that of the linear minimum MSE estimator as the depth of the context tree and the data length increase.