Channel Estimation Algorithms, Complexities and LTE Implementation Challenges

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

Channel Estimation Algorithms, Complexities
and LTE Implementation Challenges
Md. Masud Rana
Department of Electronics and Communication Engineering
Khulna University of Engineering and Technology
Khunla, Bangladesh
Email: mrana928@yahoo.com

Abstract—The main purposes of the long term evolution Many CE techniques have already been proposed for
(LTE) are substantially improved enduser throughputs, the LTE OFDMA systems. The simple least square (LS)
low latency, reduced user equipment (UE) complexity, algorithm, which is independent of the channel model,
high data rate, and significantly improved user experience is commonly used in CE [10-14]. But the radio channel
with full mobility. LTE uses single carrier-frequency
is time-variant; hence a method has to be found in order
division multiple access (SC-FDMA) for uplink
transmission and orthogonal frequency division multiple to perform estimation in a time-varying channel. The
access (OFDMA) for downlink transmission. The major minimum mean-squared error (MMSE) estimate has
challenges for LTE terminal implementation are efficient been shown to be better than the LS estimate for CE in
channel estimation (CE) method as well as equalization. wireless communication systems [15]. The important
This paper discusses the basic CE techniques and future problem of the MMSE estimate is its high
direction for research in CE fields. Simulation results computational complexity, which grows exponentially
demonstraters that the linear mean square error (LMMSE) with inspection samples [16]. In [17], a low rank
CE method outperforms the least square (LS) CE method approximation is applied to a linear MMSE (LMMSE)
in term of mean square error (MSE) by more than around
estimator that employs the correlations of the channel.
3dB. Hence, based on a given LTE systems resources and
specifications, a appropriate method among the presented To further improve the system performance, Wiener
methods can be applied for OFDMA systems. estimation has been investigated [18]. Although it
exhibits the best performance among the existing linear
Keywords— LS, LMMSE, LTE, OFDMA. algorithms, it requires accurate knowledge of second
order channel statistics, which is not always feasible at a
mobile receiver. Also, this scheme requires higher
I. INTRODUCTION complexity.
This paper outlines the developments of the LTE
OFDMA systems, and highlights some upcoming
The wireless evolution has been stimulated by an challenges, where advanced signal processing could
explosive growing demand for a wide variety of high play a important role in resolving them. Specifically, we
quality of services in voice, video, and data. This investigates various types of CE techniques such as LS,
rigorous demand has made an impact on current and and LMMSE CE methods and find out which is the
future wireless applications, such as digital audio/video more efficient one. The performance is measured in
broadcasting, wireless local area networks (WLANs), terms computational complexity, and mean square error
worldwide interoperability for microwave access (MSE). Simulation results shows that the LMMSE CE
(WiMAX), wireless fidelity (WiFi), cognitive radio, and algorithm outperforms the existing LS CE in term of
3rd generation partnership project (3GPP) long term MSE by more than around 3dB. Hence, based on a
evolution (LTE) [1], [2]. LTE uses single carrier- given LTE systems resources and specifications, a
frequency division multiple access (SC-FDMA) for appropriate method among the presented methods can
uplink transmission and orthogonal frequency division be applied.
multiple access (OFDMA) for downlink transmission The rest of the paper is organized as follows. We give
[3], [4]. SC-FDMA utilizes single carrier modulation a brief overview of the wireless communication systems
and frequency domain equalization, and has similar in section II. The classification of CE is described in
performance and essentially the same overall section III. The LS and LMMSE CE methods are
complexity as those of OFDMA system. These describes in section IV and its performance are analyzed
advanced applications in which the transmitted signal in section V. In section VI, we highlight the challenges
disperses over the time and the frequency domains, for LTE terminal implementation. Finally, some
show the need for highlydeveloped signal processing conclusions are made in section VII.
algorithms. In particular, one of the main challenges in The following notations are used in this paper: bold
the mobile communication is a wireless channel that face lower and upper case letters are used to represent
suffers from numerous physical impairments due to
multipath propagation, interference from other users or vectors and matrices respectively. Superscripts XT
layers, and the time selectivity of a channel [5-9].

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Vol. 8, No. 8, November 2010

X+ denote the transpose and congugate transpose of the The 3GPP members started a feasibility study on the
enhancement of the universal terrestrial radio access
X , and I is the identity matrix.
(UTRA) in December 2004, to improve the mobile
phone standard to cope with future requirements. This
project was called LTE [5], [8]. 3GPP LTE uses SC-
II. COMMUNICATION SYSTEMS
FDMA for uplink transmission and OFDMA for
Nowadays, cellular mobile phones have become an downlink transmission [9]. Fig. 2 summarizes the
cellular mobile communication systems and its access
important tool and part of daily life. In the last decade,
cellular systems have experienced fast development and schemes [10].
there are currently about two billion users over the
world [6]. Mobile penetration is based on population,
pay TV and broadband is households.

60
Mobile
Total pay TV
50 Broadband
P e n e t ra t io n p e rc e n t a g e

10
Fig.2 (a): Evolution path in mobile communication
systems.
0
2004 2005 2006 2007 2008 2009 2010 2011
User

Fig. 1 Mobile is the key growth platform.

The idea of 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 Fig. 2 (b) Multiple access schemes.
division multiple accesses (FDMA). Digital
communication techniques appeared in the second From the beginning wireless communications there is
generation (2G) systems, and main access schemes are a high demand for realistic mobile fading channels. The
time division multiple access (TDMA) and code motive for this significance is that efficient channel
division multiple access (CDMA). The two most models are necessary for the investigation, design, and
commonly accepted 2G systems are global system for deployment of wireless communication system for
mobile (GSM) and interim standard-95 (IS-95). These reliable transfer of information between two parties.
systems mostly offer speech communication, but also Correct channel models are also important for testing,
data communication limited to rather low transmission parameter optimization, and performance evolution of
rates [7]. The concept of the third generation (3G) wireless communication systems. The performance and
system started operations on October, 2002 in Japan. complexity of signal processing algorithms, transceiver

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Vol. 8, No. 8, November 2010

designs, and smart antennas, employed in future transmitted at certain positions of the OFDMA
wireless communication systems, are highly dependent frequency time pattern, in its place of data as shown in
on design methods used to model mobile fading Fig. 4. An amount of training sequences is raise the
channels. The effect of the channel on the transmitted accuracy of CE, but it is reduces the system efficiency,
information must be estimated in order to recover the because there isn’t any new information in the training
transmitted information correctly [11]. symbols.

III. CLASSIFICATION OF CE

Channel can be described everything from the
source to the destination of a radio signal. This
includes the physical medium between the transmitter
and the receiver through which the radio signal
propagates. On the other hand, CE is the process of
characterizing the effect of the physical channel on the
input sequence. It can be employed for the purpose of
detecting received signal, improve signal to noise ratio
(SNR), channel equalization, reduced ISI, mobile
localization, and improved system performance [8], [9].
Fig. 4 Positions of data and pilot symbols.
In general, both iterative and noniterative CE
techniques can be divided into three categories such as
the training CE, blind CE, and semi-blind CE [10],
B. Blind CE
[21].
A blind CE method requires no training sequences
[13]. They exploit certain underlying mathematical
information regarding the type of data being transmitted.
These CE methods might be bandwidth efficient but
still have their own downfalls. These methods are
enormously computationally intensive and convergence
is slow [21]. A popular category of blind CE method is
decision directed algorithms. These methods rely upon
the demodulated and detected signal at the receiver to
reform the transmitted signal. The drawback of these
CE algorithm is that a bit error at the receiver is cause
the construction of an erroneous transmitted sequence.
Fig. 3 Outline of the CE.
C. Semi-blind CE

A. Taining CE Semi-blind CE methods are used a combination of
data aided and blind methods [11]. Since, there are a
The training CE algorithm requires probe sequences; large number of channel coefficients, a large number of
the receiver can use this probe sequence to reconstruct pilot symbols may be required. It would result in a
the transmitted waveform [10]. It has the advantage of decrease of data throughput. To avoid it, the semi-blind
being used in any radio communications system quite CE methods with fewer pilot symbols can be used. As a
easily. Even if this is the most popular CE method, it result, improve system performance in compared with
still has its drawbacks. The drawback of training using equal pilots in LS method. Moreover, there is a
sequence methods is that the probe sequence occupies trend to use superimposition of pilot and data symbols.
valuable bandwidth, reducing the throughput of the In fact, these methods by superimposing pilot and data
communication system. This scheme also suffers due to symbols in the same time economize the system
the fact that most communication systems send bandwidth. But in superimposed training sequence
information lumped frames. It is only after the receipt of scheme, there is disadvantage due to the interference of
the entire frame that the channel estimate can be information data. So, an accurate CE has been one of
reconstructed from the embedded probe sequence. Since, the most important issues for reliable mobile
the coherence time of the channel might be smaller than communication systems. So, CE can be performed by
the frame time, for rapid fading channels this CE might many ways inserting pilot tones into each OFDMA
not be sufficient. Training symbols can be placed either symbol with a specific period or blind CE.
at the beginning of each burst as a preamble or regularly
through the burst [21]. Training sequences are

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IV. LS and LMMSE CE ALGORITHMS w LS = (ρ I + SS ) -1S + r , (4)
Pilot estimators are often achieved by multiplexing where ρ is regularization parameter and has to be
training sequence into the data sequence. These pilot chosen such that the resulting eigenvalues are all
-1
symbols allow the receiver to extract channel defined and the matrix (ρI + SS ) is least perturbed.
attenuations and phase rotation estimates for each Here the channel is considered as a deterministic
received symbol, facilitating the compensation of parameter and no knowledge on its noise statistics is
channel fading envelope and phase. A general CE needed. The LS estimator is computationally simple but
procedure for communication system is shown in Fig. 5. problem is that the inversion of the square matrix turns
out to be ill-conditioned (sometime). So, it will need to
regularize the eigenvalues of the matrix to be inverted
by adding a small constant term to the diagonal [14].

MMSE CE method proposes at the minimization of
the MSE between the actual and estimated channel
impulse response (CIR). The most important problem of
the MMSE estimate is its high computational
complexity, which grows exponentially with inspection
samples [15], [16]. In [17], a low rank approximation is
applied to a linear MMSE (LMMSE) estimator that
Fig. 5 General CE procedure.
employs the correlations of the channel. The general
expression of LMMSE is described as
The signal S is transmitted via a unknown time-
varying channel w, and corrupted by an additive white
Gaussian noise (AWGN) z, before being detected in a w est = R ww (R ww + ΓI /SNR) -1w LS , (5)
receiver. The channel coefficient w est , is estimated where R ww is the auto-covariance matrix of w, w LS is
using any kind of CE method. In the channel estimator, the channel response in LS estimation, and is a constant
transmitted signal S is convolved with an estimate of depending on the modulation constellation
the channel w est . The error between the received
2 2
signal and its estimate is Γ = E[ S k ] E[ 1/S k ]. (6)
For QPSK modulation, is 1[17]. Here, w LS is not
e = r - rest (1)
very important issue in the matrix computation, the
The aim of most CE algorithms is to minimize the MSE,
while utilizing as little computational resources as inversion of R ww does not require to be estimated every
possible in the estimation process. time the transmitted sybmols in w LS varies. Also, if
The idea behind LS CE method is to fit a model to signal to noise ratio (SNR) and R ww are identified
measurements in such a way that weighted errors earlier or are set to fixed nominal values, the matrix
between the estimation and the true model are
minimized [14]. The received signal can be written as
(R ww + ΓI /SNR)-1 needs to be computed at once.
vector notation as Under these situation, the estimation requires L
multiplications per tone.
r = Sw + z , (2)
In order to calculate computational complexity, we
T
where r = [r1 , r2 ......rL ] is the received signal, assume that the evaluation of the scalar addition or
subtraction needs L addition and multiplying the scalar
S = diag[s1 , s 2 ......s L ] is the transmitted signal,
by the vector requires L multiplications, and multiplying
w = [w1 , w2 ......wL ]T is the unknown channel two matrix need 4L multiplications and 4L-1 additions.
T Table I summarizes the computational complexity of the
coefficients, and z = [z1 , z2 ......z L ] is additive white different CE methods.
Gaussian noise (AWGN). The LS estimate of such a
system is obtained by minimizing square distance Table I Complexity of the CE methods
between the received signal and its estimate as [14] Operation LS CE LMMSE CE
Matrix inversion 1 2
j = (r - Sw ) (r - Sw )† . (3) Multiplication 11L 17L
Now differentiate this with respect to w and set the Addition 11L - 3 17L - 5
results equal to zero to produce [14]:

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We calculate the number of complex addition and on some preferred requirements such as cell-edge
multiplications which are needed to implement the spectral efficiency in the uplink transmission [19]. LTE
algorithm. It shows that the LS CE algorithm has lower implementation poses the following signal processing
complexity than LMMSE method. For this LMMSE challenges in terms of performance, cost and power
estimator, the main contribution to the complexity consumption:
comes from the term R ww (R ww + ΓI /SNR) .
-1 • Regrettably, the development of data rates is not
matched by advanced in semiconductor structures,
terminal power consumption improvements.
Therefore, advanced signal processing architectures
V. ANALYTICAL RESULT as well as algorithms are needed to cope with these
data rates [19].
In this simulations, we consider a system operating
• High performance multiple input multiput output
with a bandwidth of 1.25MHz, with a total symbol
(MIMO) receivers such as sphere decoders,
period of 520µs, of which 10 µs is a cyclic prefix. The
maximum likelihood receivers offer substantial
entire channel bandwidth is divided into 128 sub-
system performance gains but enforce an
carriers, implemented by 128-point IDFT. Sampling is
implementation challenge, especially when the high
performed with a 1.92MHz. The data symbol is based
peak data rates are targeted [19].
on BPSK. In practice, the ideal channel coefficient is
• LTE utilizes precoding, which requires accurate CE.
unavailable, so estimated channel coefficient must be
used instead. The more accurate estimated channel Advanced methods like iterative decision directed
CE and pilot based CE offer system performance
coefficient is, the better MSE performance of the CE
improvements, but pose again a computational
will achieve. The performance is measured using MSE
complexity challenge [19].
between the actual and the estimated channel response.
Fig. 6 shows the MSE versus SNR for the different • LTE has a large ”toolkit” of MIMO methods and
channel estimators. We can see that LMMSE CE can adaptive methods. The choice and combination of
always achieve better performance than LS CE. The the accurate technique in a cell with heterogeneous
main reason is, LMMSE CE method uses channel devices, channel conditions and bursty data
correlation as well as SNR but the LS CE method does services is a challenge [19].
not uses channel correlation. Finally, it concludes that • It is very difficult to implement many antennas in a
the LMMSE CE method has higher computational small hand portable unit. In near future, we need to
complexity and around 3dB better performance use wearable antenna on head.
compared with the LS CE method. • LTE roll-out will be gradual in most cases-
interworking with other standards such as GSM or
0
10
HSPA is required for a long time. This imposes not
only a cost and computational complexity issue.
One of the reasons many early 3G terminals had
LMMSE CE poor power consumption was the need for second
-1
10 LS CE generation (2G) cell search and handover in
addition to normal 3G operation. Reduced talk-time
for dual-mode devices is not suitable [19]. Fig. 7
-2 shows the estimated complexity based on the
10
baseline receiver. Note that the complexity of the
LTE receiver grows linearly with respect to system
MSE

bandwidth and the corresponding maximum
-3
10 nominal throughput. Interestingly, MIMO mode
requires less than double the SIMO mode
complexity.
-4
10

-5
10
0 5 10 15 20 25 30 35
SNR [dB]

Fig. 6 MSE of the LS and LMMSE CE methods.

VI. IMPLEMENTATION CHALLENGES

LTE meets the important obligations of next
generation mobile communications, but still falls short

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