
Research Article


Wideband Channel Estimation for Full Rate Full Diversity Antenna Selection Wireless Systems 

S.A. Alkhawaldeh



ABSTRACT

In this study, we proposed a wideband channel estimator for full rate full diversity antenna selection wireless system with more than two transmit antennas in conjunction with the Orthogonal Frequency Division Multiplexing (OFDM) technology. This approach is based on the pilotsymbolaided channel estimation where pilot symbols are inserted periodically through the OFDM frame at the transmitter. At the receiver, estimation of the channel at pilot locations are obtained, then, interpolating filter is used to get the estimated values of the channel at every location of the OFDM frame. Simulation results for different types of wideband channels with different Doppler frequencies are demonstrated.





Received: March 12, 2012;
Accepted: May 23, 2012;
Published: July 27, 2012


INTRODUCTION
Future mobile communications aim to satisfy high capacity and high quality
of service (Gesbert et al., 2003; Foschini
and Gans, 1998; Telatar, 1999). This can be achieved
by using multiple transmit and receive antennas (Liejun,
2011; Wang et al., 2010; Cao
et al., 2011). Spacetime block coding systems for flat fading channels
(Alamouti, 1998; Tarokh et al.,
1999) have taken a great deal of research interest as codes that achieve
high data rate and high performance with low decoding complexity. In the case
of wideband channels, these codes were presented in conjunction with OFDM technology
(Mudulodu and Paulraj, 2000; Lee
and Williams, 2000; Alkhawaldeh and Shayan, 2003)
which transforms the wideband channel into parallel multi flat fading channels.
Accurate channel estimation is required and necessary for the decoding of the
OFDM systems (Li et al., 1999). Channel estimators
that use one and two dimensional interpolating filters (Aghamohammadi
et al., 1991; Tufvesson and Maseng, 1997;
Hoeher et al., 1997; Li,
2000) have been proposed. These estimators apply pilot symbols at the transmitter
and get the estimates of the channel at pilot locations at the receiver, then
use interpolating filter to get the channel estimates at every location of OFDM
frame. In recent years, channel estimators for OFDM systems have been presented
(Alnuaimy et al., 2009; Desta
et al., 2011; Liu et al., 2006). These
estimators were designed for Single Input Single Output (SISO) OFDM systems.
For MIMO OFDM systems, several channel estimators have been presented for spacetime
block coded OFDM systems (Delestre and Sun, 2009, 2010;
Chen et al., 2010). However, these estimators
were presented for two transmit antennas with full rate. Therefore, in this
study, we propose a wideband channel estimator for the full rate full diversity
antenna selection wireless system with more than two transmit antennas (Celebi
et al., 2007) combined with the OFDM technology. The proposed scheme
is based on the pilotsymbolaided channel estimation. The channel estimation
is achieved for a system with three transmit and one receive antennas where
OFDMSTBC antenna selection system is used. Simulation results under different
channel environments are presented to show the efficiency of the proposed scheme.
WIRELESS WIDEBAND CHANNEL MODEL
The complex base band representation of the impulse response of the mobile
wireless channel between transmit antenna i and receive antenna can be described
by Li (2002) and Cavers (1991):
where, τ^{i}_{m}, γ^{i}_{m}(t) are the time delay and complex amplitude of the m^{th} multipath of the channel between transmit antenna i and receive antenna, respectively, p(τ) is a unit energy pulse that satisfies: Under the assumption that the wideband channel is slow or constant over two consecutive OFDM frame periods and γ^{i}_{m}(t)’s are described by WideSense Stationary (WSS) and narrowband complex Gaussian processes, then t is dropped and Eq. 1 can be written as: The Fourier transform of the impulse response of the channel presented in Eq. 3 is:
With proper cyclic extension and tolerable leakage, the channel frequency response
of OFDM system can be expressed as (Van de Beek et al.,
1995; Li et al., 1998):
where, W_{K} = exp(j2π/K), h_{i}(l) = h(kT_{S}/K), Δf and T_{S} are the tone spacing and symbol period, respectively. In Eq. 6, L is the number of resolvable paths of the wideband wireless channel.
FULL RATE FULL DIVERSITY ANTENNA SELECTION FOR WIDEBAND WIRELESS SYSTEMS
Figure 1 shows the block diagram of the full rate full diversity
antenna selection wireless system (Celebi et al.,
2007) combined with the OFDM technology. OFDM technology is applied to eliminate
the intersymbolinterference in the frequency selective fading channels (Arioua
et al., 2012; Ramesh and Vaidehi, 2006;
Salari et al., 2008). In this scheme, at transmit
antenna i, each OFDM frame x_{i} has K symbols and the process of encoding
is achieved frame by frame. It is assumed that the wideband channel is constant
across two consecutive OFDM frame periods.
At the output of the Discrete Fourier Transform (DFT), the received signal over two consecutive OFDM frame periods at tone k can be written as:
where, a is a vector whose elements are ±1.

Fig. 1: 
OFDM full rate full diversity antenna selection wireless system 
These values are chosen based on the relative information of the channel at
the transmitter as follows: If Re(H_{2}[k]H*_{3}[k]) is positive,
the value a[k] = 1, otherwise, it is 1. This maximizes and increases the gain
of this scheme compared to other conventional scheme (Lee
and Williams, 2000). η_{1}[k] and η_{2}[k] denote
the additive complex Gaussian noise at the receive antenna over the OFDM periods
1 and 2, respectively.
PROPOSED WIRELESS WIDEBAND CHANNEL ESTIMATOR
Here, we propose a wideband channel estimator for the system presented earlier
as shown in Fig. 1. The proposed channel estimator is based
on the pilotsymbolaided channel estimation for wideband channels. Robust channel
estimation is very important for the decoding of the OFDM systems (Li
et al., 1999). As the accuracy of the channel estimation increases
the bit error rate of the system decreases which leads to significantly improved
performance.
In our approach, at the transmitter, the pilot symbols are inserted periodically during the OFDM frame as shown in Fig. 2 where the letter p represents the pilot symbol, blank square represents the information symbol and 0 represents the zero value. In Fig. 2, the matrix A is a KxK diagonal matrix whose diagonal elements are the elements of vector a. The received pilot symbols at tone k’ are given as:

Fig. 2: 
Pilot symbols arrangement during OFDM frame 
Since, these symbols are known to the receiver, the estimates of the channel at pilot locations are obtained as: where, N = K/(No. of pilot locations in OFDM frame). After substitution y_{1} and y_{2} the estimated values of the three channels can be written as: Where: To get the estimated values of the frequency response of the three channels at all locations, the interpolating filter is used.
After the estimated values of the frequency response of the three channels
at pilot locations are obtained, zeros are inserted at other locations to form
upsampled signals .
Note that the number of estimated values at pilot locations of the channel
are twice those of the channels
and .
Thus, signal
is transmitted to low pass filter with transfer function given by:
whereas, the signals
and
are transmitted to low pass filter with transfer function given by:
The outputs of these filters ,
and
are sent to the diversity gain processor for maximum likelihood decoding.
NUMERICAL RESULTS
Here, full rate full diversity antenna selection wireless system (Celebi
et al., 2007) combined with the OFDM technology is used. The proposed
scheme is equipped with 3 transmit and one receive antennas using one bit feedback.
The mean square error of the proposed channel estimator for this system is presented.
For this approach, equal gain channel (Alkhawaldeh et
al., 2005) and ITU channel with both 50 Hz and 250 Hz Doppler frequencies
are considered. The entire bandwidth of 0.8 MHz is divided into 128 sub carrier
tones for OFDM modulation. This provides an OFDM period of 160 μsec. We
use four tones at the beginning of the OFDM frame and four at the end as guard
tones.

Fig. 3: 
Mean square error of the proposed channel estimator for equal
gain channel with f_{d} = 50 Hz and f_{d} = 250 Hz 

Fig. 4: 
Mean square error of the proposed channel estimator for ITU
channel with f_{d} = 50 Hz and f_{d} = 250 Hz 
To avoid the intersymbol interference, a guard interval of 40 μsec is
added. This yields a subchannel separation of 5 kHz. In all simulations, BPSK
modulation and the grid shown in Fig. 2 are used.
In Fig. 3, for equal gain wideband channel with two Doppler frequencies of 50 Hz and 250 Hz, the Mean Square Error (MSE) of the proposed channel estimator is presented. As expected, the MSE is the same in both cases which shows that the proposed scheme is very robust to the time variation of the wideband equal gain channel.
Figure 4 shows the MSE performance comparison when the ITU
channel is used.

Fig. 5: 
Probability of bit error with real and estimated values of
wideband equal gain channel with f_{d} = 50 Hz 
With the same parameters above, it is also shown that no difference in the
MSE in both cases which presents how much the proposed channel estimator is
robust and efficient to the time variation of the wideband ITU channel.
In Fig. 5, we present the probability of bit error as a function
of signal to noise ratio of the full rate full diversity antenna selection wireless
system (Celebi et al., 2007) combined with the
OFDM technology with the real and estimated values of the equal gain wideband
channel with Doppler frequency of 50 Hz. As can be seen, performance gain of
approximately 3.5 dB is achieved in the case of real values of the channel compared
to the case of estimated values of the channel which is very acceptable. This
shows that the estimated values of the channel using the proposed channel estimator
provides very good probability of bit error performance.
CONCLUSION
In this study, we have proposed a wideband channel estimator for the full rate
full diversity antenna selection wireless system (Celebi
et al., 2007) combined with the OFDM technology. The combination
of the coding scheme and OFDM technology maximizes the diversity order of the
wideband wireless systems. Using the perfect knowledge of the channel at the
transmitter requires large number of feedback bits which is not practical. Instead
of this, the presented coding scheme uses one feedback bit at the transmitter.
In the proposed channel estimator, it was shown that for equal gain or ITU wideband
channels with f_{d} = 50 Hz and f_{d} = 250 Hz, the MSE has
the same values. This shows the robustness of the proposed scheme to the time
variation of the wideband channels. Also, it was noted that the performance
gain of only 3.5 dB is achieved in the case of real values of the channel compared
to the case of estimated values of the channel. This presents the validity and
efficiency of the proposed channel estimator.

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