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

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].

                                                                                                ISSN 1947-5500
                                                                                                    (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                    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.

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




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

                                                 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

                                                                                                                                                 ISSN 1947-5500
                                                 (IJCSIS) International Journal of Computer Science and Information Security,
                                                 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.


    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
                                                                    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

                                                                                               ISSN 1947-5500
                                                   (IJCSIS) International Journal of Computer Science and Information Security,
                                                   Vol. 8, No. 8, November 2010

        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
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
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]:

                                                                                                    ISSN 1947-5500
                                                        (IJCSIS) International Journal of Computer Science and Information Security,
                                                        Vol. 8, No. 8, November 2010

  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
                                                                           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
        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
                                                                           baseline receiver. Note that the complexity of the
                                                                           LTE receiver grows linearly with respect to system

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

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

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


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

                                                                                                   ISSN 1947-5500
                                                                                             (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                             Vol. 8, No. 8, November 2010

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