Open Access

Canceling Interferences for High Data Rate Time Reversal MIMO UWB System: A Precoding Approach

EURASIP Journal on Wireless Communications and Networking20112011:959478

DOI: 10.1155/2011/959478

Received: 3 December 2010

Accepted: 9 February 2011

Published: 8 March 2011

Abstract

An ultra-high data rate time reversal (TR) multiple-input multiple-output (MIMO) ultra-wideband (UWB) communication system with space-time precoding is proposed. When the symbol duration is set to approach the duration of UWB monocycles, the data rate is close to the limit, resulting in the severe intersymbol interference (ISI). The zero-forcing (ZF) criterion-based space-time precoding presented in this paper eliminates both ISI and multistream interference (MSI) caused by spatial multiplexing at the sampling time. With less demand for the degree of freedom (the number of antennas) than other existing schemes, the proposed scheme enables the data rate to reach the order of Gbps without losing bit error rate (BER) performance. Since TR signal preprocessing and the proposed precoding both require the channel state information (CSI), a simple but effective channel estimation algorithm is also proposed to evaluate the impact of channel estimation on the proposed scheme.

1. Introduction

Ultra-wideband (UWB) impulse radio communications, as a promising candidate for location-aware indoor communications, wireless sensor networks (WSN) and wireless personal area network (WPAN), has received significant attention in both academia and industry in recent years [1, 2]. The most attractive feature of UWB is its potential to offer great capacity in theory as compared with the narrowband systems. However, the conventional UWB system shows much lower data rate than expectation. This is because capturing the energy of dense multipath channel [3] and combating severe intersymbol interference (ISI) caused by large maximum excess delay of the channel [4] will increase receiver complexity which limits both detection performance and data rate under the condition that receivers with high complexity are not preferred in UWB short-range applications. To reduce receiver complexity, noncoherent scheme is developed to bypass the complicated treatments on UWB channel, whereas the deterioration of detection performance and the reduction of data rate are inevitable [5]. On the other hand, the system complexity can be shifted from the receiver to the transmitter, where the power and computation resources are generally enough to implement signal processing. Since preprocessing the signal before transmission may cope with the deteriorating effects of the channel, the receiver can keep a simple structure without losing detection performance and data rate. In particular, signal preprocessing scheme is desirable in the networks where a central node with sufficient power and computation resources serves many distributed nodes with extremely stringent limits on complexity and power consumption [6].

A time reversal (TR) (TR is also referred to as pre-Rake diversity combining [7]) preprocessing-based system with minimum mean-squared error (MMSE) equalizer is firstly applied to combat ISI in UWB communications [8]. TR preprocessing is that the transmitter takes the time reversed channel impulse response (CIR) as a filter to prefilter the original signal before transmission. If the prefiltered signal is radiated into the channel, it convolves with the CIR and leads to a strong peak at the output of the channel at one particular instant. As a result, the receiver can be simplified significantly and meanwhile makes full use of the energy from all paths of the channel. Recently, the TR-based UWB system and its variations have been investigated in [914].

Multiple-input multiple-output (MIMO) technique, employing multiple antennas at the transmitter and receiver, is capable of increasing data transmission rate by spatial multiplexing without expanding the bandwidth. In order to transmit parallel data streams simultaneously (spatial multiplexing), the multistream interference (MSI) of MIMO channel must be mitigated. The potential of TR-based UWB system with multiple antennas to increase data rate is studied in [9]. In [10], a TR-based scheme for MSI suppression is proposed for MIMO-UWB system without considering ISI. (To be exact, the schemes in [10] are proposed for multiuser UWB system, which consists of an access point with multiple transmit antennas and several single-antenna radio terminals. Obviously, it is equivalent to a MIMO-UWB system without cooperation among receive antennas.) Further, TR is proposed to cope with both MSI and ISI in MIMO-UWB system in [11]. It is worthwhile to note that the interferences are not absolutely eliminated by TR in [10, 11] though they are mitigated to a certain extent, which becomes the principal factor to cause error for the large signal-to-noise ratio (SNR) and results in the deterioration of bit error rate (BER) performance ultimately.

In this paper, we propose an ultra-high data rate TR-MIMO-UWB system with space-time precoding. Multiple antennas can increase data rate, whereas the occurrence of MSI degrades the system performance. The ultra-high data rate UWB transmission usually requires extremely short symbol, thus ISI is very strong. In order to implement a TR-based UWB system, the channel state information (CSI) must have been available at transmitter. Therefore, the interferences (MSI and ISI) of TR-MIMO-UWB system should be canceled by using CSI at transmitter rather than at receiver. In [15, 16], the precoding scheme, which is extensively applied in narrowband system, has been employed to eliminate the MSI of TR-MIMO-UWB system. Since the effect of ISI is not taken into account, their system performances are degenerating rapidly as symbol duration is shorted. In this work, the space-time precoding matrix based on zero-forcing (ZF) criterion is originally derived, which is independent on the degree of freedom (the number of antenna). The proposed space-time precoding can effectively eliminate both ISI and MSI, and it is beneficial to achieve the high data rate of TR-MIMO-UWB system up to the order of Gbps without losing BER performance.

Since TR signal preprocessing requires the CSI, a simple but effective channel estimation algorithm for TR-MIMO-UWB system is also presented in this work. In [13, 14], the authors utilize a feedback channel to send the estimated channel information from the receiver to the transmitter. Because the UWB channel is characterized by dense multipath, that is, the number of multipath is large, the required bandwidth for the feedback channel is huge. Hence, the implementation of feedback channel is unfeasible. The proposed channel estimation exploits the reciprocity of the UWB channel which has experimentally been demonstrated in [12]. That is to say that the receiver sends training symbols, and the channel estimation algorithm is performed at transmitter. As the channel estimation algorithm is introduced to acquire CSI, the imperfection of CSI inevitably presents at this more practical UWB system. Since the proposed scheme can more effectively use the CSI to cancel the interferences, it shows more robustness to the error of channel estimation.

The rest of this paper is organized as follows. The system model of ultra-high data rate TR single-input single-output (SISO) UWB is described in Section 2, and the TR-MIMO-UWB system with space-time precoding is proposed in Section 3. In Section 4, we address the channel estimation problem for TR-MIMO-UWB system. Section 5 presents the simulation results. Finally, conclusions are drawn in Section 6.

Notation 1.

The boldface letters denote vector or matrix. https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq1_HTML.gif is a matrix of size https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq2_HTML.gif with all entries being zeros. https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq3_HTML.gif represents convolution operation. https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq4_HTML.gif stands for integer floor operation. https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq5_HTML.gif returns https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq6_HTML.gif transformed into a column vector with one column stacked onto the next. https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq7_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq8_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq9_HTML.gif stand for the Euclidian norm, the transpose and the inverse of matrix https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq10_HTML.gif , respectively.

2. System Model of TR-SISO-UWB

In this section, a peer-to-peer TR-SISO-UWB system is described. The UWB impulse radio signal with binary pulse amplitude modulation (BPAM) is
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ1_HTML.gif
(1)
where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq11_HTML.gif is the monocycle pulse waveform with very short duration https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq12_HTML.gif and normalized energy, https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq13_HTML.gif is the symbol duration which is assumed to be an integer multiple of the pulse waveform duration, https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq14_HTML.gif is the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq15_HTML.gif th binary symbol and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq16_HTML.gif denotes the bit energy. https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq17_HTML.gif is prefiltered by the time reversed CIR before transmission, then the transmitted signal is
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ2_HTML.gif
(2)
where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq18_HTML.gif is the estimate of the UWB channel impulse response https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq19_HTML.gif and
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ3_HTML.gif
(3)

is the transmitted waveform for one binary symbol.

The dense multipath environment, such as the industrial and indoor office [17], is considered in this paper, and the CIR https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq20_HTML.gif is modeled as
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ4_HTML.gif
(4)

where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq21_HTML.gif is the Dirac delta function, https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq22_HTML.gif is the number of resolvable multipath components (MPCs), https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq23_HTML.gif is the fading coefficient of the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq24_HTML.gif th MPC, and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq25_HTML.gif is the minimum multipath resolution, which is equal to the duration of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq26_HTML.gif ( https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq27_HTML.gif ), as any two paths whose relative delay is less than https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq28_HTML.gif are not resolvable. The maximum excess delay of the channel is denoted by https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq29_HTML.gif . In conventional UWB systems, the symbol duration https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq30_HTML.gif is usually set large enough ( https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq31_HTML.gif ) to avoid or alleviate ISI. However, in this paper, https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq32_HTML.gif is set much smaller than https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq33_HTML.gif ( https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq34_HTML.gif ) to achieve an ultra-high data rate. It can be found that the waveform duration of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq35_HTML.gif is https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq36_HTML.gif , and thus the transmitted waveform for one symbol overlaps that of other symbols.

The transmitted signal is radiated into the channel, and it convolves with the CIR. The received signal is
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ5_HTML.gif
(5)
where
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ6_HTML.gif
(6)
is the correlation function between https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq37_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq38_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq39_HTML.gif is the zero-mean additive white Gaussian noise (AWGN) with two sided power spectral density (PSD) https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq40_HTML.gif . Substituting https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq41_HTML.gif and (4) into (6), we have
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ7_HTML.gif
(7)
Since the dense multipath channel is regarded as an equally spaced model, (7) is actually a sequence of delta functions with regular spacings. This channel model is employed for the only purpose of facilitating the analysis for ISI. And if more general channel model is involved, the validity of our proposal is still supported. If https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq42_HTML.gif is the perfect estimation of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq43_HTML.gif , the peak of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq44_HTML.gif is https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq45_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq46_HTML.gif due to channel energy normalization. A simple filter is designed to capture the desired energy at the positions of peak as follows:
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ8_HTML.gif
(8)
where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq47_HTML.gif is the decision statistic for https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq48_HTML.gif is the noisy component, and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq49_HTML.gif is the ISI component for https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq50_HTML.gif . For the purpose of analyzing the interference pattern at receiver, we define the received waveform https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq51_HTML.gif for one symbol as
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ9_HTML.gif
(9)
The process that signal transmits from transmitter to receiver in the absence of noise is illustrated in Figure 1. Since the duration of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq52_HTML.gif ranges from https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq53_HTML.gif to https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq54_HTML.gif , any symbol is interfered by its following https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq55_HTML.gif symbols and preceding https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq56_HTML.gif symbols at receiver, where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq57_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq58_HTML.gif . From (5), https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq59_HTML.gif can be considered as an equivalent channel impulse response (ECIR), and we define discrete form of the equivalent channel as a https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq60_HTML.gif vector https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq61_HTML.gif , where
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ10_HTML.gif
(10)
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq62_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq63_HTML.gif , is the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq64_HTML.gif th sampling value of ECIR. Using the discrete form of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq65_HTML.gif , the ISI component in (8) can be expressed as
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ11_HTML.gif
(11)
It can be observed in (11) that the concerned interferences are only dependent on the sampling value of the ECIR, yet they do not relate to the value of ECIR at any other time.
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Fig1_HTML.jpg
Figure 1

The process that signal transmits from the transmitter to receiver in the absence of noise. (a) Signal at the output of transmitter. (b) The process of transmitted signal convolving with CIR. (c) The received waveform for one symbol. (d) The discrete form of ECIR. (e) Received waveforms are interfered by each other.

3. TR-MIMO-UWB with Space-Time Precoding

3.1. System Description

A TR-MIMO-UWB communication system includes a transmitter equipped with https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq66_HTML.gif antennas and a receiver equipped with https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq67_HTML.gif antennas. https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq68_HTML.gif parallel data streams are transmitted simultaneously. In typical indoor environments, the UWB channel is quasistatic [17, 18]. That means UWB channels remain invariant over a block of symbols duration, but they are allowed to change from block to block. Therefore, block transmission is adopted in the proposed scheme. We consider a block of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq69_HTML.gif bit binary symbols, which is represented by https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq70_HTML.gif column vectors https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq71_HTML.gif for https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq72_HTML.gif . The https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq73_HTML.gif column vectors are stacked in one https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq74_HTML.gif column vector which is https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq75_HTML.gif .

The https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq76_HTML.gif space-time precoding matrix is denoted by https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq77_HTML.gif . After using https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq77_HTML.gif to prefilter https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq79_HTML.gif , we get an https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq80_HTML.gif column vector
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ12_HTML.gif
(12)

where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq81_HTML.gif is the energy normalization factor which guarantees the average transmitted energy to be https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq82_HTML.gif for one binary symbol.

https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq83_HTML.gif is fed into a parallel-to-serial converter to get https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq84_HTML.gif column vectors https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq85_HTML.gif of size https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq86_HTML.gif for https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq87_HTML.gif . The https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq88_HTML.gif transmit symbol matrix https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq89_HTML.gif is constructed by padding https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq90_HTML.gif zero guard vectors at the front of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq91_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq92_HTML.gif zero guard vectors at the end of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq93_HTML.gif (the size of all zero guard vectors is https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq94_HTML.gif ); that is, https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq95_HTML.gif . The https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq96_HTML.gif th entry of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq89_HTML.gif is denoted by https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq98_HTML.gif , which is the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq99_HTML.gif th transmit symbol of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq100_HTML.gif th data stream. The TR signal radiated by the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq101_HTML.gif th antenna at transmitter in a block duration https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq102_HTML.gif for https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq103_HTML.gif is given by
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ13_HTML.gif
(13)

where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq104_HTML.gif is the estimation of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq105_HTML.gif which stands for the impulse response of the multipath channel between the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq106_HTML.gif th antenna at transmitter and the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq107_HTML.gif th antenna at receiver. In Section 4, a channel estimation algorithm is proposed to obtain https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq108_HTML.gif . It is worthwhile to note that all https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq109_HTML.gif parallel data streams are simultaneously transmitted from the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq110_HTML.gif th antenna at transmitter.

The signal received by the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq111_HTML.gif th antenna at receiver for https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq112_HTML.gif is expressed as
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ14_HTML.gif
(14)
where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq113_HTML.gif is the AWGN at the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq114_HTML.gif th receive antenna and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq115_HTML.gif is the sum of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq116_HTML.gif correlation functions which is defined as
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ15_HTML.gif
(15)
for https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq117_HTML.gif . It can be noticed in (14) that the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq118_HTML.gif th receive antenna receives all https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq119_HTML.gif parallel data streams simultaneously from https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq120_HTML.gif equivalent channels which is represented by its impulse response https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq121_HTML.gif . At the back-end of the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq122_HTML.gif th receive antenna, a simple filter which matches to https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq123_HTML.gif captures the energy as follows:
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ16_HTML.gif
(16)
where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq124_HTML.gif is the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq125_HTML.gif th decision statistic at the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq126_HTML.gif th receive antenna, https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq127_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq128_HTML.gif . Substituting (14) into (16), we have
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ17_HTML.gif
(17)
where
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ18_HTML.gif
(18)
is the sampling value of signal and
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ19_HTML.gif
(19)

is the discrete noise component.

3.2. Space-Time Precoding Matrix Design

In order to transmit https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq129_HTML.gif parallel data streams simultaneously at a very high data rate without losing performance, the MSI and ISI must be eliminated. As the CSI is already available for the implementation of TR signal preprocessing, we can use the CSI to calculate the precoding matrix https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq130_HTML.gif . In this paper, we seek the solution based on ZF criterion.

The https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq131_HTML.gif th decision statistic vector of size https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq132_HTML.gif is given by https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq133_HTML.gif , and the corresponding signal vector and noise vector are https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq134_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq135_HTML.gif , respectively. Moreover, the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq136_HTML.gif column vectors https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq137_HTML.gif are stacked in one https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq138_HTML.gif column vector https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq139_HTML.gif ; that is, https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq140_HTML.gif . Similarly, we get https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq141_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq142_HTML.gif . Notably, the desired decision statistic vector for bit vector https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq143_HTML.gif is https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq144_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq145_HTML.gif . We stack the desired decision statistic vectors in an https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq146_HTML.gif column vector https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq147_HTML.gif , which is the decision statistic for https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq148_HTML.gif . Now, we can establish the discrete input-output relationship between https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq149_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq150_HTML.gif as
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ20_HTML.gif
(20)
where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq151_HTML.gif is the space-time channel matrix (STCM). Via extending ECIR to MIMO channel, the ECIR matrix of size https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq152_HTML.gif is given by
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ21_HTML.gif
(21)
Then, the STCM https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq153_HTML.gif in (20) can be represented as an https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq154_HTML.gif block Toeplitz matrix
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ22_HTML.gif
(22)

where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq155_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq156_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq157_HTML.gif is the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq158_HTML.gif th sampling value of ECIR matrix. From (20), it can be found that the space-time MIMO relationship between the transmitted information bits and the sampling values of received signal is constructed. Therefore, the interference in time domain (ISI) and the interference in spatial domain (MSI) can be eliminated at the same time by employing ZF precoding matrix https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq159_HTML.gif to diagonalize https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq160_HTML.gif .

Since the right pseudoinverse of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq161_HTML.gif is inexistent ( https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq162_HTML.gif ), ZF-based precoding matrix https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq159_HTML.gif cannot be directly solved from (20). On the other hand, https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq164_HTML.gif can be rewritten as https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq165_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq166_HTML.gif is the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq167_HTML.gif th row of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq168_HTML.gif . The desired statistic https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq169_HTML.gif is a part of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq170_HTML.gif , which consists of the elements ranging from the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq171_HTML.gif th to the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq172_HTML.gif th within the vector https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq170_HTML.gif . In (20), https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq169_HTML.gif is related to the rows ranging from the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq175_HTML.gif th to the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq176_HTML.gif th within the matrix https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq177_HTML.gif . Therefore, the input-output relationship between https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq178_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq169_HTML.gif is given as
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ23_HTML.gif
(23)
where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq180_HTML.gif is an https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq181_HTML.gif matrix which consists of the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq182_HTML.gif th to the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq183_HTML.gif th row in the matrix https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq184_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq185_HTML.gif . According to (23), the ZF-based precoding matrix which diagonalizes https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq186_HTML.gif is given as
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ24_HTML.gif
(24)

Since https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq187_HTML.gif is a square matrix, its right pseudoinverse exists, and (24) can be calculated.

However, the actual ECIR matrix https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq188_HTML.gif and corresponding STCM https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq189_HTML.gif cannot be obtained at transmitter, we can only achieve the estimations of them. The estimated ECIR matrix at transmitter is calculated as
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ25_HTML.gif
(25)
where
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ26_HTML.gif
(26)

is the estimated ECIR between the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq190_HTML.gif th equivalent transmit antenna and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq191_HTML.gif th receive antenna. Replacing https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq192_HTML.gif with https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq193_HTML.gif in (22), the estimated STCM https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq194_HTML.gif is immediately obtained and used to calculate the precoding matrix https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq195_HTML.gif . Obviously, if the estimations are perfect, the interference can be effectively eliminated; otherwise, the imperfect estimations may result in the residual interferences.

Some remarks about the TR-MIMO-UWB system with ZF space-time precoding are essential.
  1. (i)

    From (13), all https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq196_HTML.gif parallel data streams are simultaneously transmitted from one antenna. That means the number of transmitted parallel data streams is independent on https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq197_HTML.gif , but only lies on https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq198_HTML.gif . This is not in common with ordinary MIMO systems in which https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq199_HTML.gif parallel data streams can be normally transmitted. This is because the TR MIMO system in this paper is a wideband system, where the TR processing filters or the CIR act as orthogonal codes to spread information bits (they are actually quasiorthogonal and after TR preprocessing the interferences are mitigated to a certain extent). Therefore, the data stream number is not constrained by https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq200_HTML.gif .

     
  2. (ii)

    There is no cooperation among receive antennas in the proposed scheme so that the scheme can be naturally extended to multiuser UWB system.

     
  3. (iii)

    The motivation to insert the zero guard vectors is to prevent the interference between blocks. Admittedly, this operation will result in some data rate reduction. In fact, the data rate of the proposed system is https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq201_HTML.gif bits per second (bps). Owing to that, the coherence time of the typical indoor UWB channel is rather larger than the maximum excess delay of the channel, https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq202_HTML.gif is of the same order as https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq203_HTML.gif . Therefore, the data rate is mainly dependent upon symbol duration https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq204_HTML.gif .

     
  4. (iv)

    A ZF prefiltering scheme for MSI suppression is proposed in [10], which forces received interference to zero within the whole symbol duration. Since our ZF space-time precoding only forces the received interference to zero at the sampling time within one symbol duration, the proposed precoding scheme needs less degree of freedom than ZF prefiltering. For example, when https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq205_HTML.gif , our scheme can work well, but ZF prefiltering is inapplicable, and it needs more transmit antennas.

     

4. Channel Estimation Algorithm

As indicated in last section, the operation of the canceling interferences requires knowledge of the channels. This information must be provided by channel estimation. In this section, we address the channel estimation problem for TR-MIMO-UWB system.

The reciprocity of UWB channel has been experimentally demonstrated in [12]. Consequently, the channel from transmitter to receiver can be estimated by sending training symbols from the receiver and performing channel estimation algorithm at the transmitter. This scheme shuns the implementation of feedback channel which is unfeasible in UWB system. The gist of the proposed algorithm is that the channel is sounded by sending pilot pulses. During the estimation process, the ISI is avoided by letting the pulse repetition interval be larger than https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq206_HTML.gif , and the MSI is avoided by using orthogonal training symbols. An orthogonal training symbol set is defined as https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq207_HTML.gif , where each training symbol is represented as a vector with elements https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq208_HTML.gif taking values of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq209_HTML.gif and the orthogonality of the set guarantees the relationship
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ27_HTML.gif
(27)
holds. In the initialization stage of one block, the training symbol https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq210_HTML.gif is sent by the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq211_HTML.gif th antenna at receiver. The training pulses waveform radiated by the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq212_HTML.gif th antenna at receiver is expressed as
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ28_HTML.gif
(28)

for https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq213_HTML.gif . In (28), the repetition interval of the training pulses https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq214_HTML.gif is larger than https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq215_HTML.gif to avoid interference between training pulses.

The training pulses waveform received by the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq216_HTML.gif th antenna at transmitter is written as
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ29_HTML.gif
(29)
where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq217_HTML.gif is the channel between the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq218_HTML.gif th antenna at transmitter and the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq219_HTML.gif th antenna at receiver. The transmitter correlates and samples at every https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq220_HTML.gif time instant on the received training pulses waveform to get
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ30_HTML.gif
(30)
Substituting (29) into (30), we have
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ31_HTML.gif
(31)
where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq221_HTML.gif is zero mean Gaussian noise with variance https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq222_HTML.gif . The estimated fading coefficient of the channel between the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq223_HTML.gif th antenna of transmitter and the https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq224_HTML.gif th antenna of receiver can be obtained by
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ32_HTML.gif
(32)
for https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq225_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq226_HTML.gif . Inserting (31) into (32) and using (27), we have
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Equ33_HTML.gif
(33)

where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq227_HTML.gif the estimation noise with zero mean and variance https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq228_HTML.gif . The training symbols can be repeated to send https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq229_HTML.gif times to get https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq230_HTML.gif estimations of each fading coefficient. Then, https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq231_HTML.gif estimation results are averaged to reduce the estimation noise. The result of the averaged estimated fading coefficient is https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq232_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq233_HTML.gif is the averaged estimation noise with variance https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq234_HTML.gif . The corresponding estimated CIR is https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq235_HTML.gif . Since the UWB short-range applications always occur in the indoor entironment, where the surrounding objects and UWB transceiver are nearly quiescent [17, 18], the coherent time of channel is very long. Therefore, we can increase https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq236_HTML.gif to reduce the estimation noise within the channel coherent time; however, this will result in a data throughput reduction. When https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq237_HTML.gif goes to infinity, the estimation noise goes to zero and the estimated channel tends to perfection. The impact of channel estimation on TR-MIMO-UWB system with ZF precoding is investigated by simulations in Section 5.

5. Simulation Results

In this section, simulations and comparisons are performed to validate the proposed scheme. In all cases, the MIMO-UWB channel is generated according to IEEE 802.15.3a channel model recommendation CM4 [19] and truncated to https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq238_HTML.gif ns. Although the channel model CM4 is designed for single-input single-output (SISO) scenario, the extension to a MIMO configuration is achieved by assuming that the MIMO channel parameters are independent and identically distributed realizations from the same statistical model. The used impulse shape is the second derivative of a Gaussian function https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq239_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq240_HTML.gif is the energy normalized parameter and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq241_HTML.gif ns is the pulse shaping parameter. The duration of https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq242_HTML.gif is set as https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq243_HTML.gif ns so that the minimum multipath resolution of channel is https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq244_HTML.gif ns.

TEST 1: BER Performance Comparison between the Proposed Scheme and the Spatial Multiplexed TR-MIMO-UWB System Proposed in [11]

First, we evaluate the BER performance of TR-MIMO-UWB system with ZF precoding proposed in this paper and compare it with the spatial multiplexed TR-MIMO-UWB system proposed in [11]. In this case, both the transmitter and receiver are equipped with https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq245_HTML.gif antennas and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq246_HTML.gif parallel data streams are transmitted from transmitter simultaneously. The symbol duration https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq247_HTML.gif is set as 0.5 ns and 10 ns, respectively, which are much smaller than https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq248_HTML.gif ns. https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq249_HTML.gif is set as 200. In this test case, we assume the CSI is perfect. The BER versus https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq250_HTML.gif curves are plotted in Figure 2. It is observed that the BER performance is improved by the proposed space-time precoding scheme. When ISI is strong ( https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq251_HTML.gif ns), the BER curve of the spatial multiplexed TR-MIMO-UWB system [11] suffers a floor at high https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq252_HTML.gif , while the proposed scheme can obtain a remarkable gain. When https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq253_HTML.gif ns, https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq254_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq255_HTML.gif . We can compute the bit rate https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq256_HTML.gif Gbps.
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Fig2_HTML.jpg
Figure 2

BER performance comparison between the proposed TR-MIMO-UWB system with space-time precoding and the TR-MIMO-UWB system. https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq257_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq258_HTML.gif .

TEST 2: BER Performance Comparison between the Proposed Scheme and ZF Prefiltering Scheme [10]

Then, the comparison between the proposed scheme and ZF prefiltering scheme [10] is given. In order to meet the needs of degree of freedom for ZF prefiltering, we set the parameters https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq259_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq260_HTML.gif , and the length of prefiltering 400 chips. The CSI is perfect for both schemes. From Figure 3, the proposed scheme outperforms ZF prefiltering in terms of BER when both schemes choose the same deployment of antenna ( https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq261_HTML.gif ). The proposed precoding scheme focuses energy on the sampling time to eliminate interferences and ignores other time; therefore, it has higher energy efficiency than ZF prefiltering. Since ZF prefiltering does not consider ISI, the BER curve suffers a floor at high https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq262_HTML.gif when ISI is severe. In order to show that the proposed scheme demands less degree of freedom than ZF prefiltering, the BER performances of the proposed scheme when https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq263_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq264_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq265_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq266_HTML.gif are also evaluated. It can be shown the proposed scheme outperforms ZF prefiltering even though less transmit antennas are used. When more transmit antennas are employed, the proposed scheme obtains a considerable gain due to a higher energy efficiency provided by more degree of freedom. It is worthwhile to point out that when https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq267_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq268_HTML.gif , the proposed scheme can transmit https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq269_HTML.gif parallel data streams normally, this is not in common with ordinary MIMO systems. It is shown in Figure 3 that the performance of the proposed scheme with https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq270_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq271_HTML.gif and that with https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq272_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq273_HTML.gif are uniform. This is because the same number of transmit antennas offers the same degree of freedom to eliminate interference and results in the same performance. However, the data rate with https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq274_HTML.gif is twice as high as that with https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq275_HTML.gif .
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Fig3_HTML.jpg
Figure 3

BER performance comparison between the proposed ZF-based space-time precoding for TR-MIMO-UWB system and ZF-based prefiltering scheme.

TEST 3: The Impact of Channel Estimation on the Proposed Scheme

We have so far assumed the CSI is perfect. In this case, the impact of imperfect channel estimation on the proposed scheme is investigated. Both the transmitter and receiver are equipped with https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq276_HTML.gif antennas, and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq277_HTML.gif parallel data streams are transmitted from transmitter simultaneously. The data symbol duration https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq278_HTML.gif is set as 10 ns. The channel estimation algorithm proposed in Section 4 is employed in the initialization stage of one block. Orthogonal training symbol set https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq279_HTML.gif is used. The repetition interval of the training pulse is set as https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq280_HTML.gif ns to avoid interference between training pulses. The repetition time of training symbols is set as https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq281_HTML.gif , and 20, respectively. Increasing https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq282_HTML.gif will improve the accuracy of channel estimation. The simulation results are shown in Figure 4. The BER performance which corresponds to the perfect channel estimation is also plotted. As https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq283_HTML.gif increases, the BER performance gets better at the price of data throughput reduction. Therefore, there is a tradeoff between performance and data throughput. The imperfect estimation brings out the residual interferences, and the BER curve suffers a floor at high https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq284_HTML.gif . That is because the residual interferences become the principal factor to cause error at high https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq285_HTML.gif . When https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq286_HTML.gif , the estimation noise is small, and the corresponding BER is close to that of perfect channel estimation.
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Fig4_HTML.jpg
Figure 4

The impact of channel estimation on the proposed scheme. https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq287_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq288_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq289_HTML.gif ns.

TEST 4: BER Performance Comparison between the Proposed Scheme and Other Schemes When Imperfect CSI Presents

Finally, the dependence of three schemes (the proposed scheme, the spatial multiplexed TR-MIMO-UWB system [11] and ZF prefiltering scheme [10]) on channel estimation is investigated. The system parameters are set as follows: https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq290_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq291_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq292_HTML.gif ns. The orthogonal training symbol set used to execute channel estimation algorithm is the same as TEST 3 and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq293_HTML.gif ns. The repetition time of training symbols is set as https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq294_HTML.gif , respectively. Figure 5 presents the simulation results. When the transmitter can only use imperfect CSI to implement preprocessing (this comes nearer to practical situation), the improvement of BER performance obtained by the proposed scheme is remarkable. From Figure 5, when imperfect CSI presents, the performance of the proposed scheme is also solid and outperforms other schemes. Notably, the performance of the proposed scheme with https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq295_HTML.gif still outperforms the two other schemes with https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq296_HTML.gif . That is because the CSI is more effectively used to cancel the interferences by the proposed scheme, and the residual interferences are least. The spatial multiplexed TR-MIMO-UWB system [11] can suppress the ISI and MSI to a certain extend, and it shows some robustness to imperfect CSI. Since ZF prefiltering scheme leaves ISI out of consideration [10], its performance becomes worst at high https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq297_HTML.gif , where the ISI and the residual MSI are strong.
https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_Fig5_HTML.jpg
Figure 5

BER performance comparison between the proposed scheme and other schemes when imperfect CSI presents. https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq298_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq299_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2F2011%2F959478/MediaObjects/13638_2010_Article_2164_IEq300_HTML.gif ns.

6. Conclusion

An ultra-high data rate TR-MIMO-UWB system with space-time precoding is proposed in this paper. After the system model of TR-MIMO-UWB is investigated, the computation of the ZF criterion-based space-time precoding matrix is originally derived. With less demand for degree of freedom than other schemes, the proposed space-time precoding scheme can effectively eliminate both ISI and MSI. As a result, the TR-MIMO-UWB system achieves ultra-high data rate of the order of Gbps and keeps BER performance well. The performance of the proposed scheme is evaluated through computer simulations. It is shown that the proposed scheme outperforms the spatial multiplexed TR-MIMO-UWB system and ZF prefiltering scheme. A simple but effective channel estimation algorithm is proposed to provide the estimated CSI for preprocessing. The impact of channel estimation on the proposed scheme is also investigated by simulations. The results confirm that the CSI is more effectively used to remove the interferences by the proposed scheme.

Declarations

Acknowledgment

This work is financially supported by the National Natural Science Foundation of China (NSFC) (Grant no. 60972075).

Authors’ Affiliations

(1)
School of Information and Communication Engineering, Beijing University of Posts and Telecommunications (BUPT)

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Copyright

© T. Wang and T. Lv. 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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