A Pilot Based RLS Channel Estimation for LTE SC-FDMA in High Doppler Spread

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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 6, September 2010

A Pilot Based RLS Channel Estimation for LTE
SC-FDMA in High Doppler Spread
M. M. Rana
Department of Electronics and Communication Engineering
Khulna University of Engineering and Technology
Khunla, Bangladesh
Email: mrana928@yahoo.com

Abstract—Main challenges for a terminal implementation are [6-8]. Pilot symbols can be placed either at the beginning of
efficient realization of the inner receiver, especially for channel each burst as a preamble or regularly through the burst. Pilot
estimation (CE) and equalization. In this paper, pilot based sequences are transmitted at certain positions of the SC-
recursive least square (RLS) channel estimator technique is FDMA frequency time pattern, in its place of data.
investigate for a long term evolution (LTE) single carrier-
Adaptive CE has been, and still is, an area of active research
frequency division multiple access (SC-FDMA) system in high
Doppler spread environment. This CE scheme uses adaptive RLS topics, playing imperative roles in an ever growing number of
estimator which is able to update parameters of the estimator applications such as wireless communications where the
continuously, so that knowledge of channel and noise statistics channel is rapidly time-varying. Signal processing techniques
are not required. Simulation results show that the RLS CE that use recursively estimated, time varying models are
scheme with 500 Hz Doppler frequency has 3 dB better normally called adaptive. Different adaptive CE algorithms
performances compared with 1.5 kHz Doppler frequency. have been proposed over the years for the purpose of updating
the channel coefficient. The least mean square (LMS) method,
Keywords— Channel estimation, LTE, RLS, SC-FDMA. its normalized version (NLMS), the affine projection
algorithm (APA), as well as the recursive least square (RLS)
method are well known examples of such CE algorithms. The
I. INTRODUCTION well known LMS/NLMS CE algorithms are attractive from a
computational complexity point of view but their convergence
The 3rd generation partnership project (3GPP) members behavior for highly correlated input signals is poor. The RLS
started a feasibility study on the enhancement of the universal CE method resolves this trouble, but at the expense of
terrestrial radio access (UTRA), to improve the mobile phone increased complexity. A very large number of fast RLS CE
standard to cope with future requirements. This project was methods have been developed over the years, but regrettably,
called long term evolution (LTE) [1], [2]. LTE uses it seems that the better a fast RLS CE method is in terms of
orthogonal frequency division multiple access (OFDMA) for computational efficiency and numerical stability. In addition,
downlink and single carrier-frequency division multiple the RLS algorithm has the recursive inversion of an estimate
access (SC-FDMA) for uplink transmission [1]. A highly of the autocorrelation matrix of the input signal as its
efficient way to cope with the frequency selectivity of cornerstone, problems arise, if the autocorrelation matrix is
wideband channel is OFDMA. OFDMA is an effective rank deficient.
technique for combating multipath fading and for high bit rate In this paper, we investigate the adaptive RLS CE method
transmission over mobile wireless channels. Channel in the LTE SC-FDMA systems in high Doppler spread
estimation (CE) has been successfully used to improve the environment. This CE method uses adaptive estimator which
system performance. It can be employed for the purpose of is able to update parameters of the estimator continuously so
detecting received signal, improve signal-to-noise ratio that knowledge of channel and noise statistics are not
(SNR), channel equalization, cochannel interference (CCI) required. Simulation results show that the RLS CE scheme
rejection, and improved the system performance [3-5]. with 500 Hz Doppler frequency has 3 dB better performances
In general, CE techniques can be divided into three compared with 1500 Hz Doppler frequency.
categories such as pilot CE, blind CE, and semi-blind CE [10], We use the following notations throughout this paper: bold
[11]. Pilot CE techniques offer low computational complexity face lower letter is used to represent vector. Superscripts x*
and good performance [12]. The blind CE techniques exploit and xT denote the conjugate and conjugate transpose of the
the statistical behavior of the received signals and require a complex vector x respectively.
large amount of data [13]. Semi-blind CE methods are used a The remainder of the paper is organized as follows: section
combination of data aided and blind methods [11]. The pilot II describes wireless communication systems and LTE SC-
CE algorithm requires probe sequences; the receiver can use FDMA systems model is describes in section III. The RLS CE
this probe sequence to reconstruct the transmitted waveform scheme is presented in section IV, and its performance is

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analyzed in section V. Finally, some concluding remarks are III. LTE SC-FDMA SYSTEMS DESCRIPTION
given in section VI.
In this section, we briefly explain LTE SC-FDMA system
II. WIRELESS COMMUNICATION SYSTEMS model, fading channel statistics, and received signal model.

Nowadays, cellular mobile phones have become an A. Baseband system model
important tool and part of daily life. In the last decade, cellular
systems have experienced fast development and there are A baseband block diagram for the communications system
currently about two billion users over the world. The idea of under investigation is shown in Fig. 2.
cellular mobile communications is to divide large zones into
small cells, and it can provide radio coverage over a wider
area than the area of one cell. This concept was developed by
researchers at AT & T Bell laboratories during the 1950s and
1960s. The initial cellular system was created by nippon
telephone & telegraph (NTT) in Japan, 1979. From then on,
the cellular mobile communication has evolved.
The mobile communication systems are frequently
classified as different generations depending of the service
offered. The first generation (1G) comprises the analog
communication techniques, and it was mainly built on
frequency modulation (FM) and frequency division multiple
accesses (FDMA). Digital communication techniques
appeared in the second generation (2G) systems, and main
access schemes are time division multiple access (TDMA) and
code division multiple access (CDMA). The two most
commonly accepted 2G systems are global system for mobile
(GSM) and interim standard-95 (IS-95). These systems mostly
offer speech communication, but also data communication
limited to rather low transmission rates. The concept of the
third generation (3G) system started operations on October, Fig. 2. Block diagram of a LTE SC-FDMA system.
2002 in Japan. The 3GPP members started a feasibility study
on the enhancement of the universal terrestrial radio access At the transmitter, a baseband multiple phase shift keying
(UTRA) in December 2004, to improve the mobile phone modulator takes binary sequence and produces the signaling
standard to cope with future requirements. This project was waveforms
called LTE. LTE uses SC-FDMA for uplink transmission and
OFDMA for downlink transmission. Fig. 1 summarizes the 2E
mi (t) = cos(ωt + αi ), 0 < t < T
evolution path of cellular mobile communications systems. T
2E
= [cos(αi ) cos(ωt) - sin(αi ) sin(ωt)]
T
= a i b(t) + ci d(t), (1)
where T is the symbol duration, E is the energy of mi (t),
ω = 2πf, f is the carrier frquency, phase anagle
2π i
α= , M is the alphabate size, α i = E cos α i
M
2
inphasse basis , b(t) = cos(ωt), ci = E sinαi , and
T
2
quadrature basis, d(t) = - cos(ωt). CE is often achieved
T
by multiplexing known symbols, so called, pilot symbols into
data sequences [1]. These modulated symbols and pilots
perform N-point discrete Fourier transform (DFT) to produce
Fig. 1. Evolution path in mobile communication systems. a frequency domain representation:

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1 N-1 -j2π mt Since, the channel coefficient is usually unknown to the
si (t) = ∑
N t=0
mi (t) e N , (2) receiver, it needs to be efficiently estimated. The impulse
response of multipath fading channel can be represented by a
where j is the imaginary unit. It then maps each of the N-point tap-delayed line filter with time varying coefficients and
DFT outputs to one of the orthogonal sub-carriers mapping that symbol-rate spaced coefficients.
can be transmitted. There are two principal sub-carrier mapping
modes: localized mode, and distribution mode. In distributed
sub-carrier mode, the outputs are allocated equally spaced sub-
carrier, with zeros occupying the unused sub-carrier in
between. While in localized sub-carrier mode, the outputs are
confined to a continuous spectrum of sub-carrier. Interleaved
sub-carrier mapping mode of FDMA (IFDMA) is another
special sub-carrier mapping mode [13], [14]. The difference
between DFDMA and IFDMA is that the outputs of IFDMA
are allocated over the entire bandwidth, whereas the DFDMAs Fig. 3. L-tapped delay line filter of a fading channel.
outputs are allocated every several subcarriers [15], [16].
Finally, the inverse DFT (IDFT) module output is followed At the receiver, the opposite set of the operation is
by a cyclic prefix (CP) insertion that completes the digital stage performed. After synchronization, CP samples are discarded
of the signal flow. The CP is used to eliminate ISI and preserve and the remaining samples are processed by the DFT to
the orthogonality of the tones. Assume that the channel length retrieve the complex constellation symbols transmitted over
of CP is larger than the channel delay spread [17]. the orthogonal sub-channels. The received signals are de-
mapped and equalizer is used to compensate for the radio
B. Channel model channel frequency selectivity. After IDFT operation, these
received signals are demodulated and soft or hard values of
Channel model is a mathematical representation of the the corresponding bits are passed to the decoder. The decoder
transfer characteristics of the physical medium. These models analyzes the structure of received bit pattern and tries to
are formulated by observing the characteristics of the received reconstruct the original signal.
signal. According to the documents from 3GPP, a radio wave
propagation can be described by multipaths which arise from IV. RLS ADAPTIVE CE METHOD
reflection and scattering [17]. The received signal at the mobile
terminal is a superposition of all paths. If there are L distinct An adaptive CE technique is a process that changes its
paths from transmitter to the receiver, the impulse response of parameters as it gain more information of its possibly
the multipath fading channel can be represented as [17]: changing environment. Among many iterative techniques that
L
exist in the open literature, the well-liked classes of
∑
ω(m,τ) = ωj (m) δ[m - τj (m)],
j =1
(3) approaches which are achieve from the minimization of the
mean square error (MSE) between the output of the adaptive
where ω j (m) and τ j (m) are attenuations and delays for each filter and desired signal to perform CE as shown in Fig. 4.
path at time instant m, and δ(.) is the Dirac delta function. The
fading process for the mobile radio channel is given by
ω(v) = ω j 1- (v/f d ) , (4)
where Doppler frquency f d = s/λ, s is the speed of the mobile,
and λ is the wavelength of the transmitted carrier. In order to
do simulations as close to the reality as possible, it is essential
to have a good channel model. This model is used to describe
the fast variations of the received signal strength due to
changes in phases when a mobile terminal moves. In case of
wideband modeling, each path of the impulse response can be
modeled as Rayleigh distributed with uniform phase except line
of sight (LOS) component cases [17].
Fig. 4. Scheme for adaptive CE.
C. Received signal model The signal s(m) is transmitted via a time-varying channel
w(m), and corrupted by an additive noise estimated by using
The transmitted symbols propagating through the radio any kind of CE method. The main aim of most channel
channel can be modeled as a circular convolution between the estimation algorithms is to minimize the MSE i.e., between
CIR and the transmitted data block i.e., [s(m)*ω (m,τ )] . the received signal and its estimate, while utilizing as little

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computational resources as possible in the estimation process. δc(m) n
In the Fig. 4, we have unknown multipath fading channel, that
has to be estimated with an adaptive filter whose weight are δw (m)
= 0 = -2 ∑λ
m =1
n-m
s(m)e H (m) + 2δλ n w (m)
updated based on some criterion so that coefficients of n
adaptive filter should be as close as possible to the unknown = -2 ∑ λ n-m s(m)[h(m) - w H (m)s(m)]H + 2δλ n w (m)
channel. The RLS CE requires all the past samples of the m=1
input and the desired output is available at each iteration. The n n
objective function of a RLS CE algorithm is defined as an w (m)[ ∑ λ n-ms(m)s H (m) + δλ n I ] = ∑λ n-m
s(m)h H (m)
exponential weighted sum of errors squares: m=1 m =1
n
R s (m)w (m) = R sh (m)
c(m) = ∑λ e (m)e(m) + δλ n w H (m)w (m),
n-m H
(5)
m=1 w (m) = R −1 (m) R sh (m)
s (8)
where δ is a positive real number called regularization
parameter, e(m) is the prior estimation error, and λ is the
exponential forgetting factor with 0 < λ < 1. The λ is used to where R s (m) is the transmitted auto-correlation matrix
ensure that data in the distant past are paid less concentration n

in order to provide the filter with estimating facility when it R s (m) = ∑λ
m=1
n-m
s(m)s H (m) + δλ n I = λR s (m-1) + s(m)s H (m)
operates in a time varying environment. When λ = 1, the
algorithm has growing memory because the values of the filter and R sh (m) is the cross correlation matrix
coefficients are a function of all the precedent input. In this i.e.,
case, all the values of the error signal, from the time the filter n
starts its process to the present, have the same influence on the R sh (m) = ∑ λ n-ms(m)h H (m) = λR sh (m-1) + s(m)h H (m) .
cost function. Consequently, the adaptive filter losses its m=1
estimating ability, which is not important if the filter is used in
a stationary environment. In contrast, when 0 < λ < 1, the
According to the Woodbury identity , the above R sh (m) can
algorithm has exponentially decaying memory as the recent be written as
values of the observations have greater influence on the -1 -1
λ -2 R sh (m-1)s(m)s H (m)R sh (m-1)
formation of the filter coefficients and tends to forget the old
-1 -1
R sh (m) = λ -1R sh (m-1) - (9)
ones as shown in Fig. 5.
-1
1+ λ -1s H (m)R sh (m-1)s(m)

For convenience of computing, let D(m) = Rsh(m) and
λ -1D(m-1)s(m)
α0 K (m) = (10)
1+λ -1s H (m)D(m-1)s(m)

The K(m) is referred as a gain matrix. We may rewrite (9)
α1 as:
D(m) = λ -1D(m-1) - λ -1K (m)s H (m)D(m-1) (11)
αm
( m − m) (m − 1) (m − 0) (m + 1) So simply (10) to
-1
K (m) = D(m)s(m) = R sh (m)s(m) (12)
Fig. 5. Exponential weighting of observations at different time index.
Substituting (11), (12) into (8), we obtain the following RLS
The prior estimation error is the difference between the CE formula
desired response and estimation signal: w (m) = w (m-1) + K (m)[h(m) - w H (m-1)s(m)]H
e(m) = h(m) - w H (m) s(m) (7) = w (m-1) + K (m)ε H (m), (13)
The objective function is minimized by taking the partial
derivatives with respect to w(n) and setting the results equal to where ε(m) is a prior estimation error as
zero. ε(m) = h(m) - w H (m-1)s(m) (14)
Therefore equation (13) is the recursive RLS CE algorithm to
update channel coefficient.

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V. PERFORMANCE ANALYSIS versus SNR for the RLS CE method with different Doppler
frequencies 500Hz and 1.5kHz. One can observed that the
A. Complexity Analysis RLS CE method with 500 Hz Doppler frequency has 3 dB
better performances compared with 1.5kHz Doppler
The complexity of CE algorithm is of vital importance frequency as desired. This CE scheme uses adaptive RLS
especially for time varying wireless communication channels, estimator which is able to update parameters of the estimator
where it has to be performed periodically or even continuously, so that knowledge of channel and noise
continuously. Table I summarizes the computational statistics are not required. The similar behavior can be
complexity of the RLS CE technique, where L is the channel observed for BER performance in Fig. 7.
length, and real number indicates scalar operation. Here we
0
assume that each iteration requires the evaluation of the inner 10
product D(m)h(m) between two vectors of size L each. This For Doppler frequency 1500Hz
calculation requires L multiplications and L-1 additions. Also For Doppler frequency 500Hz
assumed that the evaluation of the scalar addition or
subtraction needs one real addition and multiplying the scalar -1
10
by the vector requires L multiplications.

TABLE I
COMPLEXITY PER ITERATION
-2

MSE
Operation Complexity 10
Division 1
Multiplication L2 + 5L+1
Addition L2 + 3L
-3
10

B. Experimental results

The error performance of the aforementioned iterative -4
10
estimation algorithm is explored by performing extensive 0 5 10 15 20 25 30
computer simulations. All simulation parameters of the LTE SNR [dB]
SC-FDMA system in Doppler spread environments are
Fig. 6. MSE performance comparisons of the LMS CE method.
summarized in Table II.

Table II 0
THE SYSTEMS PARAMETERS FOR SIMULATION 10
For Doppler frequency 1500Hz
Systems parameters Assumptions For Doppler frequency 500Hz
System bandwidth 5 MHz
Sampling frequency 7.68 MHz -1
10
Sub-carrier spacing 9.765 kHz
Modulation data type BPSK
FFT size 16
Sub-carrier mapping scheme IFDMA -2
BER

IFFT size 512 10
Data block size 32
Cyclic prefix 4µs
Channel Rayleigh fading
-3
Forgetting factor 0.99 10
Equalization ZF
Doppler frequency 100, and 1.5 kHz

-4
In practice, the perfect channel coefficient is unavailable, 10
so estimated channel coefficient must be used instead. The 0 5 10 15 20 25 30
more correct estimated channel coefficient is, the better MSE SNR [dB]
performance of the CE will achieve. Fig. 6 shows the MSE Fig.7. BER performance comparisons of the LMS CE method.

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VI. CONCLUSION

In this paper, we explore the performance of RLS CE
method for LTE SC-FDAM wireless communication systems
with different Doppler frequencies. The complexities, MSE
and BER performance of the RLS CE method, are analyzed
and compared with the different Doppler frequencies. We can
come to the conclusion that the RLS CE method with 500 Hz
Doppler frequency has 3 dB superior performances compared
with 1.5 kHz Doppler frequency.

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