Open Access

Iterative Sparse Channel Estimation and Decoding for Underwater MIMO-OFDM

  • Jie Huang1Email author,
  • Jianzhong Huang1,
  • Christian R. Berger2,
  • Shengli Zhou1 and
  • Peter Willett1
EURASIP Journal on Advances in Signal Processing20102010:460379

DOI: 10.1155/2010/460379

Received: 1 November 2009

Accepted: 8 April 2010

Published: 16 May 2010

Abstract

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.

1. Introduction

Multi-input multi-output (MIMO) techniques have been recently applied in underwater acoustic (UWA) systems to drastically improve the spectral efficiency. Experimental results have been reported in [19] for single-carrier systems, and in [6, 1015] for multicarrier systems, in the form of orthogonal frequency division multiplexing (OFDM).

As we consider MIMO-OFDM in UWA channels, we specify related work: a block-by-block receiver has been developed in [10], where Maximum A Posteriori (MAP) and zero forcing (ZF) detectors are used for MIMO detection following least-squares- (LS-) based channel estimation. Receivers for both spatial multiplexing and differential space time coding have been developed in [11]. Adaptive MIMO detectors have been proposed in [13, 14], where channel estimates based on the previous data block are used for demodulation of the current block after being combined with phase tracking. All the receivers in [10, 11, 13, 14] are noniterative. In [12], an iterative receiver has been presented for MIMO-OFDM that iterates between MIMO detection and channel decoding.

In this paper, we propose an iterative receiver that couples channel estimation, MIMO detection and channel decoding. The differences from [12] are the following.
  1. (1)

    Channel estimation is included in the iteration loop so that refined channel estimates become available along the iterations.

     
  2. (2)

    The LS channel estimator is replaced by a more advanced channel estimator recently tested in [16], that exploits the sparse nature of UWA channels.

     

When channel estimation is included in the iteration loop, data symbols estimated in the previous round can be utilized as additional training symbols to improve the channel estimation accuracy. We investigate different feedback strategies, including hard decision feedback, soft decision feedback, and their variants that discard unreliable feedback symbols through a thresholding mechanism. We compare the performance using numerical simulation and experimental data collected from the RACE08 and SPACE08 experiments. Iterative receiver processing leads to impressive performance gains relative to a noniterative receiver.

Note that iterative channel estimation and decoding has been heavily investigated in the literature of wireless radio communications. For example, references [1719] have considered different hard and soft decision feedback strategies with pilot symbol assisted modulation (PSAM) over time-selective flat-fading channels. References [20, 21] have considered cross-entropy-based hard decision feedback. Specifically to UWA communications, iterative channel estimation and channel decoding has been studied and tested with real data in [22], where only single transmitter OFDM and hard decision feedback are considered. The main contributions of this paper are the followings.
  1. (1)

    Development of an iterative receiver for underwater MIMO-OFDM, improving upon an existing receiver [12].

     
  2. (2)

    Extensive performance testings based on experimental data, showing impressive results for underwater MIMO-OFDM with very high spectral efficiencies.

     

The rest of this paper is organized as follows. Section 2 introduces the system model. Section 3 presents the details on the iterative receiver. Simulation results are reported in Section 4. Experimental results are reported in Sections 5 and 6 with data collected in RACE08 and SPACE08 experiments, respectively. We conclude in Section 7.

2. System Model

2.1. MIMO-OFDM Transmission

We use zero-padded (ZP) OFDM, as in [12, 23]. Let https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq1_HTML.gif denote the OFDM symbol duration and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq2_HTML.gif the guard interval. The duration of the overall OFDM block is https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq3_HTML.gif and the subcarrier spacing is https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq4_HTML.gif . The https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq5_HTML.gif th subcarrier is at frequency
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ1_HTML.gif
(1)

where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq6_HTML.gif is the carrier frequency and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq7_HTML.gif subcarriers are used so that the bandwidth is https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq8_HTML.gif .

For an MIMO-OFDM system with https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq9_HTML.gif transmitters, we use spatial multiplexing to transmit https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq10_HTML.gif parallel data streams. Specifically, within each OFDM block, https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq11_HTML.gif independent bit streams are separately encoded with a nonbinary low-density parity-check (LDPC) code [24]. Let https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq12_HTML.gif denote the encoded information symbols, for example, quadratic phase-shift-keying (QPSK) or quadratic amplitude modulation (QAM), to be transmitted on the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq13_HTML.gif th subcarrier by the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq14_HTML.gif th transmitter. The nonoverlapping sets of active subcarriers https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq15_HTML.gif and null subcarriers https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq16_HTML.gif satisfy https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq17_HTML.gif ; the null subcarriers are used to facilitate Doppler compensation at the receiver [23]. The signal transmitted by the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq18_HTML.gif th transmitter is given by
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ2_HTML.gif
(2)
where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq19_HTML.gif describes the zero-padding operation, that is,
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ3_HTML.gif
(3)
Accounting for all the overheads due to guard interval, channel coding, pilot, and null subcarriers, the overall spectral efficiency in terms of bits per second per Hz (bits/s/Hz) is
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ4_HTML.gif
(4)

where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq20_HTML.gif is the code rate, https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq21_HTML.gif is the constellation size, and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq22_HTML.gif is the set of data subcarriers (excluding pilot tones). With bandwidth https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq23_HTML.gif , the data rate is https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq24_HTML.gif bits per second.

2.2. Receiver Preprocessing

The same receiver preprocessing as in [12] is applied. The received signal can be resampled to compensate a dominant Doppler effect if necessary. After resampling each receiver assumes one common Doppler shift on all transmitted data streams, and uses the energy on the null subcarriers as an objective function to search for the best Doppler shift estimate [12]. Doppler shift compensation is done at each receiver separately.

Let https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq25_HTML.gif denote the output on the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq26_HTML.gif th subchannel at the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq27_HTML.gif th receiver, after the ZP-OFDM demodulation on the received block after Doppler compensation. As in [12], we use the following channel input-output model:
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ5_HTML.gif
(5)

where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq28_HTML.gif is the frequency response between the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq29_HTML.gif th transmitter and the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq30_HTML.gif th receiver at the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq31_HTML.gif th subcarrier, and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq32_HTML.gif is the additive noise at the demodulator output, which includes both the ambient noise and the residual intercarrier interference (ICI).

3. Iterative Sparse Channel Estimation and Decoding

The proposed iterative receiver processing with https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq33_HTML.gif transmitters and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq34_HTML.gif receivers is shown in Figure 1, where the line represents feedback from the LDPC decoder. We next specify the key modules in the iteration loop: sparse channel estimation, MIMO detection, and channel decoding.
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Fig1_HTML.jpg
Figure 1

Iterative channel estimation and decoding for MIMO-OFDM.

3.1. Sparse Channel Estimation

For each transmitter-receiver pair, we assume a baseband channel with https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq35_HTML.gif distinct paths, with each path characterized by a complex amplitude https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq36_HTML.gif and a delay https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq37_HTML.gif , (c.f. [16]):
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ6_HTML.gif
(6)
such that
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ7_HTML.gif
(7)

where we omit the transmitter and receiver index for compact notation.

Define https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq38_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq39_HTML.gif as column vectors containing https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq40_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq41_HTML.gif across subcarriers, respectively. We have
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ8_HTML.gif
(8)

3.1.1. Overcomplete Delay Dictionary

To formulate the compressed sensing problem, we need to use a large, but finite, dictionary. We discretize https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq42_HTML.gif based on the assumption that after synchronization all arriving paths fall into the guard interval, and we choose the time resolution as a fraction, https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq43_HTML.gif , of the baseband sampling stepsize https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq44_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq45_HTML.gif is the oversampling factor. In other words, we consider
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ9_HTML.gif
(9)
where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq46_HTML.gif is less than https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq47_HTML.gif but larger than the channel delay spread. With this we construct a matrix as
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ10_HTML.gif
(10)
and rewrite (8) as
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ11_HTML.gif
(11)

where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq48_HTML.gif contains the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq49_HTML.gif possible delays corresponding to the dictionary columns. Since commonly https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq50_HTML.gif is sparse, that is, it has a limited number of nonzero entries.

Now, we include the transmitter and receiver subscripts, and define https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq51_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq52_HTML.gif as column vectors whose https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq53_HTML.gif th elements are the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq54_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq55_HTML.gif , respectively. The vector https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq56_HTML.gif contains known symbols (pilots and symbol estimates from the LDPC decoder). We then have
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ12_HTML.gif
(12)

where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq57_HTML.gif is a diagonal matrix with the elements of vector https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq58_HTML.gif on its main diagonal, and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq59_HTML.gif contains the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq60_HTML.gif possible delays corresponding to the dictionary columns for the channel from the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq61_HTML.gif th transmitter to the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq62_HTML.gif th receiver.

For a more compact notation, define
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ13_HTML.gif
(13)
where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq63_HTML.gif stands for transpose. We then rewrite (12) as
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ14_HTML.gif
(14)

which depends on the pilots and known symbol estimates https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq64_HTML.gif via the matrix https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq65_HTML.gif .

3.1.2. Basis Pursuit Formulation

Sparse channel estimation can be formulated as a convex optimization problem using what is commonly referred to as https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq66_HTML.gif -regularization. This approach is called Basis Pursuit (BP), see for example, [25, 26]. Specifically, BP seeks the solution of
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ15_HTML.gif
(15)
where the parameter https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq67_HTML.gif controls the sparsity of the solution https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq68_HTML.gif . Note that for a complex vector https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq69_HTML.gif , its https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq70_HTML.gif -norm is defined as
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ16_HTML.gif
(16)

An efficient implementation for the complex valued version of BP has been suggested in [26, Section VI.D]. Adopting BP-based sparse channel estimation in multicarrier underwater acoustic communications has been presented in [16], where impressive performance gains over a LS-based channel estimator have been reported. The complexity of BP-based sparse channel estimation, specifically for underwater OFDM systems, is studied in [27].

3.2. MIMO Detection

After estimating the path weights and delays, the frequency response at the data subcarriers can be calculated using (7). At each subcarrier, we stack the received data from https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq71_HTML.gif receiving-elements [c.f. (5)] as
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ17_HTML.gif
(17)
Let https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq72_HTML.gif denote the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq73_HTML.gif channel matrix whose ( https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq74_HTML.gif )-element is https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq75_HTML.gif , and let https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq76_HTML.gif contain https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq77_HTML.gif transmitted symbols on the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq78_HTML.gif th subcarrier. The matrix-vector channel model for each subcarrier is
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ18_HTML.gif
(18)

where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq79_HTML.gif is the additive noise. We assume that the noise on different receivers is uncorrelated and Gaussian distributed.

To demodulate https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq80_HTML.gif from (18), we use the MIMO detector of [12] which consists of a hybrid use of successive interference cancellation and soft minimum mean-square error (MMSE) demodulation; see [12] for details.

3.3. Nonbinary LDPC Decoding

With the outputs from the MMSE equalizer, nonbinary LDPC decoding as in [24] is performed separately for each data stream. The decoder outputs the decoded information symbols and the updated a posterior/extrinsic probabilities, which are used in the next iteration of channel estimation and equalization. During the decoding process, if all the parity check conditions of one data stream are satisfied, the decoder declares successful recovery of this data stream. In this case we assume that all symbols of this data stream are known without uncertainty.

To use feedback in channel estimation or MIMO detection, we need estimates of the unknown data and a measure of the uncertainty left in these estimates. Based on the previous round of decoding, the LDPC decoder outputs a posterior probabilities for each symbol, as well as probabilities based on extrinsic information only. While the extrinsic information is used in the MIMO symbol detection [12], the a posterior probabilities are used to improve channel estimation. Next we investigate different feedback strategies for channel estimation.

3.4. Feedback Strategies

We consider two categories of feedback strategies, namely, hard decision feedback and soft decision feedback. In each category we investigate full feedback and threshold-controlled feedback where the former uses all symbols for feedback and the latter uses only reliable symbols for feedback.

Let https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq81_HTML.gif denote the a posterior probability where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq82_HTML.gif are the constellation symbols. There are three main feedback strategies in the literature [1719], varying by the definition of https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq83_HTML.gif —the estimate of https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq84_HTML.gif for channel estimation.

Full Hard Decision Feedback

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ19_HTML.gif
(19)

Controlled Hard Decision Feedback

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ20_HTML.gif
(20)

where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq85_HTML.gif stands for the entropy calculated from https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq86_HTML.gif which is the counterpart of the log-likelihood-ratio (LLR) of binary codes and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq87_HTML.gif is the threshold which lies in https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq88_HTML.gif . In other words, only when the symbol estimate is considered reliable enough, a hard decision is made for feedback.

Full Soft Decision Feedback

One has
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ21_HTML.gif
(21)

In this paper, we further consider a new feedback strategy by applying a threshold on the soft information, where only symbols with the absolute value of their soft estimates larger than a threshold are used.

Controlled Soft Decision Feedback

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Equ22_HTML.gif
(22)

where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq89_HTML.gif is the maximum absolute value of all constellation symbols and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq90_HTML.gif is the threshold which lies in https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq91_HTML.gif . Here the threshold is applied to the symbols from https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq92_HTML.gif transmitters jointly. We have also investigated the strategy when a threshold is applied on the symbols from each transmitter individually. The individually controlled feedback strategy has comparable (or worse) performance than the jointly controlled version.

4. Simulation Results

Consider an OFDM system with the following specifications: carrier frequency https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq93_HTML.gif  kHz, https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq94_HTML.gif subcarriers, symbol duration https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq95_HTML.gif  ms, and guard time https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq96_HTML.gif  ms. The bandwidth is then https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq97_HTML.gif  kHz. It has https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq98_HTML.gif pilot tones and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq99_HTML.gif null subcarriers for edge protection and Doppler estimation, leaving https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq100_HTML.gif data subcarriers. The data within each OFDM symbol is encoded using a rate https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq101_HTML.gif nonbinary LDPC code from [24], and modulated using either QPSK or 16-QAM. These parameters are used in the signal design for the SPACE08 experiment [16, 28].

We consider MIMO systems with https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq102_HTML.gif or https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq103_HTML.gif transmitters. With https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq104_HTML.gif , the data rates are 10.4 kb/s and 20.8 kb/s for QPSK and 16-QAM modulations, respectively. With https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq105_HTML.gif , the data rates are 15.6 kb/s and 31.2 kb/s for QPSK and 16-QAM modulations, respectively. The https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq106_HTML.gif pilots are divided into nonoverlapping sets among all transmitters so that each transmitter has roughly the same number of pilots. The pilot patterns are randomly drawn, rendering irregular positioning [12]. This is usually seen as advantageous in compressed sensing theory, as it can guarantee identifiability of active channel taps with high probability [25].

For the simulation scenario we generate https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq107_HTML.gif discrete fading paths, where the interarrival times are exponentially distributed with a mean of 1 ms. The amplitude of each path is Rayleigh distributed, with decreasing variance as the delay increases. As each OFDM symbol is encoded separately, we use block-error-rate (BLER) as the figure of merit. In the simulation, each OFDM symbol experiences an independently generated channel. The pilot symbols are drawn from the QPSK constellation whereas the data symbols are drawn from QPSK or 16-QAM constellations. The pilots are scaled to ensure that about one third of the total transmission power is dedicated to channel estimation regardless of the number of transmitters. We simulate the BLER performance at different SNR levels, where SNR is the signal to noise power ratio on the data subcarriers.

In Figure 2 we compare hard decision and soft decision feedback strategies with operating SNR fixed as 2.75 dB for https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq108_HTML.gif , and 16-QAM modulation. Note that https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq109_HTML.gif corresponds to full hard decision feedback and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq110_HTML.gif corresponds to full soft decision feedback. As https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq111_HTML.gif (or https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq112_HTML.gif ) increases from 0 to 1, the number of feedback symbols drops all the way from the maximum down to zero. We observe from Figure 2 that a decent number of feedback symbols is necessary to achieve good performance, which means that we need to choose a small value of https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq113_HTML.gif or https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq114_HTML.gif (less than 0.4 in Figure 2). In general, controlled soft decision feedback performs better than hard decision feedback when the threshold https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq115_HTML.gif or https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq116_HTML.gif is small. We also observe that both soft and hard decision feedback strategies are not sensitive to the threshold when it is below a certain value (e.g., https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq117_HTML.gif in the setting of Figure 2).
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Fig2_HTML.jpg
Figure 2

BLER peformance (a) and number of feedback symbols (b) for hard and soft feedback with varying threshold https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq118_HTML.gif or https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq119_HTML.gif ; SNR of 2. 75 dB.BLER peformanceNumber of feedback symbols

In Figures 3, 4, 5, and 6 we compare different receivers for two MIMO-OFDM systems where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq120_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq121_HTML.gif in Figures 3 and 4, https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq122_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq123_HTML.gif in Figures 5 and 6. The maximum number of iterations for performing iterative updating between sparse channel estimation, MIMO detection and nonbinary LDPC decoding is 10, where we update both the channel estimation and the MIMO detection in each iteration.
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Fig3_HTML.jpg
Figure 3

Simulation results, https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq124_HTML.gif , QPSK.

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Fig4_HTML.jpg
Figure 4

Simulation results, https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq125_HTML.gif , 16-QAM.

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Fig5_HTML.jpg
Figure 5

Simulation results, https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq126_HTML.gif , QPSK.

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Fig6_HTML.jpg
Figure 6

Simulation results, https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq127_HTML.gif , 16-QAM.

The receivers considered are as follows.
  1. (i)

    "Non-iterative" receiver as in [10], but with the LS channel estimator replaced by the BP estimator.

     
  2. (ii)

    "Turbo-equalization" receiver as in [12], but with the LS channel estimator replaced by the BP estimator.

     
  3. (iii)

    The proposed iterative receiver with "controlled soft decision feedback" with different thresholds.

     
  4. (iv)

    The proposed iterative receiver with "full hard decision feedback" (in all subsequent figures, "Non-iterative," "Turbo-equalization," "Soft feedback," and "Hard feedback" are used as legends for different receivers).

    Also we include a case with full channel state information (CSI) which still iterates between MIMO detection and LDPC decoding, but has a perfect channel estimate.

     

Figures 36 show that employing a turbo equalization receiver gains about 0.5–1 dB over a noniterative receiver, Including channel estimation in the iteration loop leads to gains of about 1 dB for https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq128_HTML.gif and 1.5 dB for https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq129_HTML.gif . This seems intuitive, as with an increasing number of transmitters there are less pilots available per data stream, making the "additional pilots" from feedback more valuable. The gap between the proposed receivers and the full CSI case is approximately between 0.5 dB and 1 dB.

In Figure 4 the iterative receiver with full hard decision feedback performs slightly worse than the iterative receivers with soft decision feedback. This gap gets more pronounced when the number of transmitters increases as shown in Figures 5 and 6.

5. Experimental Results: RACE08

The RACE08 experiment was held in the Narragansett Bay, Rhode Island, in March 2008. The water depth in the area is between 9 and 14 meters. The system parameters are the same as in the numerical simulation, except for a different bandwidth of https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq130_HTML.gif  kHz. The corresponding symbol duration and subcarrier spacing are https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq131_HTML.gif  ms and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq132_HTML.gif  Hz, respectively. More detailed description of the RACE08 experiment can be found in [12, 29].

During the experiment, each transmission file was transmitted twice every four hours, leading to 12 transmissions each day. A total of 124 data sets were successfully recorded on each array within 13 days from the Julian date 073 to the Julian date 085. We focus on three days of the experiment, Julian dates 81–83, and receiver S3, which was located 400 m away from the transmitter. We consider 16-QAM and two MIMO setups: one with two transmitters and one with three transmitters. These setups have also been studied in [12] with the turbo-equalization receiver.

The performance results with two transmitters are plotted in Figure 7 and the performance results with three transmitters are plotted in Figure 8. We combine an increasing number of hydrophones to vary effective SNR and to illustrate performance differences. The spacing between consecutive hydrophones is 12 cm. The maximum number of iterations for performing iterative updating between sparse channel estimation, MIMO detection, and nonbinary LDPC decoding is 6. We report the results with the proposed iterative processing with full hard decision feedback and soft decision feedback with https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq133_HTML.gif or https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq134_HTML.gif . Generally an iterative receiver can gain significantly over a noniterative receiver. Besides, all feedback strategies, including full hard decision and soft decision feedback have similar performance on this data set, showing a sizable gain over turbo-equalization.
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Fig7_HTML.jpg
Figure 7

Experimental results from the RACE08 experiment on MIMO-OFDM with https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq135_HTML.gif and 16-QAM. Julian date 81 Julian date 82 Julian date 83

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Fig8_HTML.jpg
Figure 8

Experimental results from the RACE08 experiment on MIMO-OFDM with https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq136_HTML.gif and 16-QAM. Julian date 81 Julian date 82 Julian date 83

In Table I, we also include results for two setups not available in [12]: (i) https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq137_HTML.gif , 64-QAM and (ii) https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq138_HTML.gif , 16-QAM, having spectral efficiencies of 5.28 and 4.69 bits/s/Hz, respectively. The results are based on Julian date 83 only, and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq139_HTML.gif receive-elements are used. Although data stream one performs poorly due to a transducer issue (see discussion in [12]), the other data streams can be decoded at reasonable levels.

Remark 1.

This paper does not include performance results with the LS channel estimator. It has been shown in [16] that the BP-based channel estimator outperforms the LS counterpart considerably. Also, comparing with the turbo equalizer based on the LS channel estimator [12], the turbo equalizer based on the BP channel estimator has considerably better performance. Specifically, in Table III of [12], the turbo-equalization receiver achieves BLER of https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq140_HTML.gif using twelve phones, for MIMO-OFDM with two transmitters and 16-QAM. Figure 7 in this paper shows that zero BLER is achieved using even less than twelve phones for turbo equalization using the BP channel estimator. Finally, we note that the MIMO-OFDM settings in Table 1 cannot be decoded by the turbo-equalization receiver if coupled with the LS channel estimator as in [12].
Table 1

Performance results with high data rates from RACE08; twelve receivers used.

 

Spectral efficiency

Data streams

Average BER

Average BLER

3IMO, 64-QAM

5.28 bits/s/Hz

Stream 1

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq141_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq142_HTML.gif

  

Stream 2

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq143_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq144_HTML.gif

  

Stream 3

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq145_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq146_HTML.gif

4IMO, 16-QAM

4.69 bits/s/Hz

Stream 1

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq147_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq148_HTML.gif

  

Stream 2

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq149_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq150_HTML.gif

  

Stream 3

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq151_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq152_HTML.gif

  

Stream 4

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq153_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq154_HTML.gif

6. Experimental Results: SPACE08

The SPACE08 experiment was held off the coast of Martha's Vineyard, MA, from Oct. 14 to Nov. 1, 2008. The water depth is about 15 meters. The spacing between consecutive hydrophones is 12 cm. The detailed description of the SPACE08 experiment can be found in [28, 29].

We focus on receivers S3 and S5 that were located 200 m and We consider recorded data from three consecutive days, Julian date 297 to Julian date 299. For each day, there are twelve recorded files consisting of twenty OFDM symbols each. On the Julian date 298, the five files recorded during the afternoon were severely distorted and therefore unusable; we focus on the remaining seven files recorded during the morning and evening. Due to the more challenging environment, we only consider the small-size QPSK constellation. The transmission signal model for SPACE08 has the same setup as the simulation setup in Section 4. The data rates for the MIMO system using QPSK modulation are 10.4 kb/s and 15.6 kb/s, when https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq155_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq156_HTML.gif , respectively.

Performance results are plotted in Figure 9 for https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq157_HTML.gif and in Figure 10 for https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq158_HTML.gif . The maximum number of iterations for performing iterative updating between sparse channel estimation, MIMO detection, and nonbinary LDPC decoding is 6 and we use full soft decision and hard decision feedback. For https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq159_HTML.gif , we observe a sizable gain using updated channel estimates, while all iterative receivers gain significantly over the noniterative receiver. For the https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq160_HTML.gif setup, the gain of updated channel estimates is more pronounced, matching previous observations in numerical simulation.
https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Fig9_HTML.jpg
Figure 9

Experimental results from the SPACE08 experiment with https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq161_HTML.gif , QPSK, for S3 (200 m) and S5 (1000 m).

https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_Fig10_HTML.jpg
Figure 10

Experimental results from the SPACE08 experiment with https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq162_HTML.gif , QPSK, for S3 (200 m) and S5 (1000 m).

Remark 2.

For the simulation results in Section 4, we plot the BLER performance as a function of SNR. For the experimental results in Sections 5 and 6, we plot the BLER performance as a function of the number of phones used at the receiver. One common practice to show the performance dependance on SNR based on experimental data is to add recorded ambient noise to the received signals. In this paper, we have not pursued such an approach, which could be explored in the near future.

7. Conclusion

In this paper, we have developed an iterative receiver for underwater MIMO-OFDM that couples sparse channel estimation, MIMO detection, and channel decoding. Various types of feedback information have been considered to improve the sparse channel estimator using the Basis Pursuit algorithm. We tested the proposed receiver extensively using numerical simulation and experimental data for MIMO-OFDM with very large spectral efficiencies. We find that including channel estimation in the iterative loop leads to significant gains in performance. These gains are more pronounced if less pilots are available for channel estimation, for example, when a fixed number of pilots is split between parallel data streams. For the various feedback strategies for iterative channel estimation, we observe that soft decision feedback slightly outperforms hard decision feedback in most cases.

Declarations

Acknowledgments

This work was supported by the NSF Grant CNS-0721834, the ONR Grants N00014-07-1-0805 (YIP), and N00014-09-1-0704 (PECASE). Part of this work was presented at the MTS/IEEE OCEANS Conference, Biloxi, MS, USA, Oct. 2009.

Authors’ Affiliations

(1)
Department of Electrical and Computer Engineering, University of Connecticut
(2)
Department of Electrical and Computer Engineering, Carnegie Mellon University

References

  1. Kilfoyle DB, Preisig JC, Baggeroer AB: Spatial modulation experiments in the underwater acoustic channel. IEEE Journal of Oceanic Engineering 2005, 30(2):406-415. 10.1109/JOE.2004.834168View ArticleGoogle Scholar
  2. Song HC, Roux P, Hodgkiss WS, Kuperman WA, Akal T, Stevenson M: Multiple-input-multiple-output coherent time reversal communications in a shallow-water acoustic channel. IEEE Journal of Oceanic Engineering 2006, 31(1):170-178. 10.1109/JOE.2005.850911View ArticleGoogle Scholar
  3. Roy S, Duman TM, McDonald V, Proakis JG: High-rate communication for underwater acoustic channels using multiple transmitters and space-time coding: receiver structures and experimental results. IEEE Journal of Oceanic Engineering 2007, 32(3):663-688.View ArticleGoogle Scholar
  4. Tao J, Zheng YR, Xiao C, Yang TC, Yang W-B: Time-domain receiver design for MIMO underwater acoustic communications. Proceedings of the MTS-IEEE Oceans Conference, September 2008, Quèbec, CanadaGoogle Scholar
  5. Zhang J, Zheng YR, Xiao C: Frequency-domain equalization for single carrier MIMO underwater acoustic communications. Proceedings of the MTS-IEEE Oceans Conference, September 2008, Quèbec, CanadaGoogle Scholar
  6. Qu F, Yang L: Basis expansion model for underwater acoustic channels? Proceedings of the MTS-IEEE Oceans Conference, September 2008, Quèbec, CanadaGoogle Scholar
  7. Song A, Badiey M, McDonald VK: Multi-channel combining and equalization for underwater acoustic MIMO channels. Proceedings of the MTS-IEEE Oceans Conference, September 2008, Quèbec, CanadaGoogle Scholar
  8. Ling J, Yardibi T, Su X, He H, Li J: Enhanced channel estimation and symbol detection for high speed mutli-input multi-output underwater acoustic communications. Journal of Acoustical Society of America 2009, 125(5):3067-3078. 10.1121/1.3097467View ArticleGoogle Scholar
  9. Zhang J, Zheng YR, Xiao C: Frequency-domain turbo equalization for MIMO underwater acoustic communications. Proceedings of the MTS-IEEE Oceans Conference, May 2009, Bremen, GermanyGoogle Scholar
  10. Li B, Zhou S, Stojanovic M, Freitag L, Huang J, Willett P: MIMO-OFDM over an underwater acoustic channel. Proceedings of the MTS-IEEE Oceans Conference, October 2007, Vancouver, CanadaGoogle Scholar
  11. Emre Y, Kandasamy V, Duman TM, Hursky P, Roy S: Multiinput multi-output OFDM for shallow-water UWA communications. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '08), 2008, Paris, FranceGoogle Scholar
  12. Li B, Huang J, Zhou S, et al.: MIMO-OFDM for high rate underwater acoustic communications. IEEE Journal of Oceanic Engineering 2009, 34(4):634-644.View ArticleGoogle Scholar
  13. Carrascosa P, Stojanovic M: Adaptive MIMO detection of OFDM signals in an underwater acoustic channel. Proceedings of the MTS-IEEE Oceans Conference, September 2008, Quèbec, CanadaGoogle Scholar
  14. Stojanovic M: Adaptive channel estimation for underwater acoustic MIMO OFDM systems. Proceedings of the IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop (DSP/SPE '09), January 2009, Marco Island, Fla, USA 132-137.Google Scholar
  15. Qu F, Yang L: Rate and reliability oriented underwater acoustic communication schemes. Proceedings of the IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop (DSP/SPE '09), January 2009, Marco Island, Fla, USA 144-149.Google Scholar
  16. Berger CR, Zhou S, Preisig JC, Willett P: Sparse channel estimation for multicarrier underwater acoustic communication: from subspace methods to compressed sensing. IEEE Transactions on Signal Processing 2010, 58(3):1708-1721.MathSciNetView ArticleGoogle Scholar
  17. Valenti MC, Woerner BD: Iterative channel estimation and decoding of pilot symbol assisted turbo codes over flat-fading channels. IEEE Journal on Selected Areas in Communications 2001, 19(9):1697-1705. 10.1109/49.947034View ArticleGoogle Scholar
  18. Niu H, Ritcey JA: Iterative channel estimation and decoding of pilot symbol assisted LDPC coded QAM over flat fading channels. Proceedings of the 37th Asilomar Conference on Signals, Systems and Computers, November 2002, Pacific Grove, Calif, USA 1: 2265-2269.Google Scholar
  19. Niu H, Shen M, Ritcey JA, Liu H: A factor graph approach to iterative channel estimation and LDPC decoding over fading channels. IEEE Transactions on Wireless Communications 2005, 4(4):1345-1350.View ArticleGoogle Scholar
  20. Wu J, Vojcic BR, Wang Z: Turbo decoding complexity reduction by symbol selection and partial iterations. Proceedings of the 50th Annual IEEE Global Telecommunications Conference (GLOBECOM '07), November 2007, Washington, DC, USA 3910-3914.Google Scholar
  21. Wu J, Vojcic BR, Wang Z: Cross-entropy based symbol selection and partial iterative decoding for serial concatenated convolutional codes. Proceedings of the 42nd Annual Conference on Information Sciences and Systems (CISS '08), March 2008, Princeton, NJ, USA 1104-1107.Google Scholar
  22. Kang T, Iltis RA: Iterative carrier frequency offset and channel estimation for underwater acoustic OFDM systems. IEEE Journal on Selected Areas in Communications 2008, 26(9):1650-1661.View ArticleGoogle Scholar
  23. Li B, Zhou S, Stojanovic M, Freitag FL, Willett P: Multicarrier communication over underwater acoustic channels with nonuniform Doppler shifts. IEEE Journal of Oceanic Engineering 2008, 33(2):198-209.View ArticleGoogle Scholar
  24. Huang J, Zhou S, Willett P: Nonbinary LDPC coding for multicarrier underwater acoustic communication. IEEE Journal on Selected Areas in Communications 2008, 26(9):1684-1696.View ArticleGoogle Scholar
  25. Donoho DL: Compressed sensing. IEEE Transactions on Information Theory 2006, 52(4):1289-1306.MathSciNetView ArticleMATHGoogle Scholar
  26. Kim S-J, Koh K, Lustig M, Boyd S, Gorinevsky D:An interior-point method for large-scale https://static-content.springer.com/image/art%3A10.1155%2F2010%2F460379/MediaObjects/13634_2009_Article_2804_IEq163_HTML.gif -regularized least squares. IEEE Journal on Selected Topics in Signal Processing 2007, 1(4):606-617.View ArticleGoogle Scholar
  27. Huang J-Z, Berger CR, Zhou S, Huang J: Comparison of basis pursuit algorithms for sparse channel estimation in underwater acoustic OFDM. Proceedings of the MTS-IEEE Oceans Conference, May 24–27, 2010, Sydney, AustraliaGoogle Scholar
  28. Berger CR, Zhou S, Chen W, Huang J: A simple and effective noise whitening method for underwater acoustic OFDM. Proceedings of the MTS-IEEE Oceans Conference, October 2009, Biloxi, Miss, USAGoogle Scholar
  29. Freitag L, Singh S: Performance of micro-modem PSK signalling under variable conditions during the 2008 RACE and SPACE experiments. Proceedings of the MTS-IEEE Oceans Conference, October 2009, Biloxi, Miss, USAGoogle Scholar

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© Jie Huang et al. 2010

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