Performance Analysis of Pilot Aided ChannelEstimation Methods for LTE System in

Time-Selective Channels

K.Rajeswari1, T.Sangeetha1, A.P Natchammai1, M.Nandhini1, and S.J.Thiruvengadam1,2

1Department of Electronics and Communication Engineering,2TIFAC CORE in Wireless Technologies

Thiagarajar College of Engineering,Madurai, India

{rajeswari, stalesa, natchammai, nandhinivijay, sjtece}@tce.edu

Abstract—This paper deals with the performance analysis ofchannel estimation methods for LTE downlink system over timevarying mobile environments. The analysis of channel estimationin the presence of interference is also done. Least squarefrequency domain (LS_Freq), least square time domain(LS_Time), maximum likelihood (ML) and minimum meansquare error estimation (MMSE) techniques are focused fordifferent bandwidth by varying the number of resource blocksused in OFDM structure of LTE system. As number of pilotsincreases with increasing bandwidth, performance of theestimator increases. Computer simulations are used in thecomparisons. Linear Interpolation is performed to get thechannel estimation of data symbols. Theoretical results arederived for LS_Time and ML techniques. MMSE performs wellat low SNR. LS_Time and ML performs well at high SNR asthey use the knowledge of number of channel taps.

We achieve interference mitigation using channel estimationusing repeated interference features obtained from the two typesof pilot symbols used with different pilot density. This techniquenot only makes the channel estimation robust to the time-selectivity of the channel but also reduces the number of pilotsubcarriers needed to estimate the channel.

Keywords- Channel estimation, LS, ML, MMSE, LinearInterpolation, Interference mitigation, pilot density, time-selectivechannel.

I. INTRODUCTION

Long Term Evolution (LTE) is a project within the ThirdGeneration Partnership Project (3GPP) in order to improve theUMTS (Universal Mobile Telecommunications System)mobile phone standard such that future requirements can bemet. The good aspect of 3GPP is the centralization of thestandards, since a single organization for these technologiesensures global interoperability. LTE uses OrthogonalFrequency Division Multiplexing (OFDM) which hasachieved much popularity in wireless communication systemsdue to its high data rate capability and robustness to multi-pathdelay [1].

For LTE downlink channel estimation, recursive wienerfiltering is used and it is deduced that the performance can be

increased by repetitive iterations and the channel is consideredstatic over duration of one OFDM symbol [2]. LS estimationand its computationally complexity of inversing the matrix forvehicular A channel is discussed in [3]. Though two solutions,regularization and down-sampling of the channel impulseresponse, for overcoming the problem are provided, theproposed methods provide better results only for less numberof subcarriers. MMSE based estimation techniques areapplied considering that the channel is stationary in [4].Further no time domain interpolations are involved. Theimpact of Wiener filter length and pilot spacing on theperformance of an LTE system are dealt in [5]. It assumesperfect knowledge of the actual channel statistics andestimation is done for a frequency selective channel. [6] dealswith estimation of LTE downlink channel for LS, MMSE,and Modified MMSE.

For the DFT-based estimator, the observed AdjacentChannel Interference (ACI) can be duplicated in the timedomain, and this repetition of the ACI is determined by thedistance between pilot subcarriers, i.e., pilot density in thefrequency domain [7]. In [8], a new channel estimationtechnique with interference mitigation using this repetitionproperty is used for cellular OFDM downlink systems.

In this paper, the mean square error performance comparisonof ML, MMSE and LS Frequency domain and LS timedomain estimators for LTE downlink channel, ExtendedVehicular A channel is done. The channel is time varyingfrom symbol to symbol. Additionally, mitigating the effects ofinterference during estimation is also dealt.

The rest of the paper is organized as follows: Section IIreviews the LTE OFDM downlink frame structure. In SectionIII, the signal model is introduced and the time correlation ofthe channel is derived. In Section IV, different channelestimation techniques are presented. In addition, system modelwith interference is introduced and the interference mitigationmethod is explained in this section. The simulation resultsgiven in Section V evaluates the performance of thetechniques described and analyzes the system behavior in thepresence of interference in time-varying channel. The

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performance comparisons are done for different bandwidth.Finally, conclusions are drawn in Section VI.

II. OFDM STRUCTURE IN LTE DOWNLINKSYSTEM

In LTE downlink structure, one radio frame consists of 20subframes, where each sub frame is divided into two time slots[1]. Each slot has 6 or 7 OFDM symbols. The number ofsubcarriers in each OFDM symbol depends on the number ofresource blocks used.

A physical resource block is defined as DLsymN consecutive

OFDM symbols in the time domain and RBscN consecutive sub

carriers of frequency 15 kHz each, in the frequency domain.As per configuration DL

symN =6 when extended cyclic prefix is

used and RBscN =12. A physical resource block thus consists of

DLsymN * RB

scN resource elements, corresponding to one slotin the time domain and 180 kHz in the frequency domain.Physical resource blocks are numbered from 0 to DL

RBN -1 inthe frequency domain.

The reference signal sequence for channelestimation mr

snl , shall be mapped to complex-valued

modulation symbols )(),(

plka used as reference symbols for

antenna port p in slot ns according to)(

),(p

lka ', mrsnl (1)

where 6mod6 shiftmk

3,21

1,03,0

pifpifN

lDLsymb

12.............1,0 DLsymbNm

DLRB

DLsymb NNmm max,'

The variables v and vshift define the position in the frequencydomain for the different reference signals where v is given by

32mod3322mod3

000013003000

pifnpifn

landpiflandpiflandpiflandpif

s

s

The cell-specific frequency shift is given byvshift = 6modcell

IDNwhere cell

IDN is the physical layer cell identity .

Resource elements (k,l) used for reference signaltransmission on any of the antenna ports in a slot shall not beused for any transmission on any other antenna port in thesame slot and set to zero.

The figure 1 shows one sub frame with 12 subcarriers ineach symbol. The shaded region is the position of subcarrierused for reference signal. The symbols with reference signalcalled as pilot data, are called as pilot symbols and thesymbols consisting of only data subcarriers are called as datasymbols.

Fig.1 .A subframe with 12 subcarriers in LTE OFDM downlink structure

III. SIGNAL MODEL

Consider a LTE downlink OFDM system. It is assumedthat the Mobile station (MS) is connected to a Base Station(BS), called the serving BS, and the serving BS transmits datato the desired MS. When the MS is synchronized to the BS,the MS received signal is given by,

),()()()( nVnXnHnY qqqq 10 Nn10 Sq (2)

where )(nX q and )(nYq are the transmitted signal and thereceived signal at the nth subcarrier and qth symbol,respectively, and )(nVq is the Additive White Gaussian

Noise(AWGN) with zero mean and variance 2V at the

receiver. N represents the number of subcarriers in one OFDMsymbol and S represents number of OFDM symbols. Inaddition, it is assumed that BS is coordinated indownlink/uplink phases, so there is no disturbance betweentwo phases.

)(nHq , the channel frequency response (CFR) of the qthOFDM symbol at the nth subcarrier, is given by,

,)(][)(1

0, khGnH q

L

kknq

10 Nn (3)

where )(khq is the complex amplitude of the kth channel pathfor the qth OFDM symbol. L denotes the maximum length ofthe channel. The length of cyclic prefix (CP) is sufficientlylonger than L to avoid inter-symbol interference. G is a matrixwith entries,

,][ /2,

Nnkjkn eG 10 Nn

10 Lk (4)

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Due to the mobility of MS, the channel is time-selective,and the channel taps )(khq are wide-sense stationary (WSS)narrowband complex Gaussian processes, which areindependent for different paths. Further, )(khq has the same

normalized correlation function ][ qhkr for all k. Hence,

)()( * khkhEqr qqqhk

qhhk r 2 (5)

where 2hk is the average power of the kth path. The

correlation function of the frequency response between Δqseparated OFDM symbols is

1

0

22L

lhkH

where 2H is the

total average power of the CIR. For an OFDM system withsymbol length Ts, the correlation function for n OFDMsymbols apart can be written as sdh TnfJnr 20 from

Jakes’ model where xJ 0 the zeroth-order Bessel function ofthe first kind and fd is the Doppler frequency with respect tothe vehicle speed and the carrier frequency.

The received signal at the pilot location is given as,

10,)( Pmqmqmqmq NmiViXiHiY (6)where im is the subcarrier at which reference signal, also calledas pilot , is inserted and NP is the number of pilot subcarriersin one OFDM pilot symbol.

IV. CHANNEL ESTIMATION TECHNIQUES

In all the techniques discussed here, channel at pilotsymbols are estimated first. Linear Interpolation is used todetermine the channel at data symbols.

A. LS Estimation-Frequency DomainThe frequency domain least square (LS) estimated Channel

Frequency Response (CFR) at pilot locations at the MS isexpressed as[9],

mqmqmLSFq iYiXiH *_

(7)It can also be expressed as,

mqmqmLSFq iWiHiH

_ (8)

where )( mq iW is the AWGN with variance 22VW . The

total CFR for the pilot symbol is obtained by linearinterpolation.

B. LS Estimation-Time Domain

The LS time domain estimated channel LSTq _

h is the first L

taps of Th which is given by[8],

zBh HT (9)

where B is a NP X L matrix with entries,

)10(10

10,/2,

LpNme P

Npijpm

mB

and z is LS frequency domain estimated channel LSFq _

H atpilot locations. The time domain LS estimation uses theknowledge of number of channel taps. CFR of the qth pilot

symbol LSTq _

H is DFT of LSTq _

h .The average Mean Square Error for the pilot symbol in LS

time domain estimation is derived as ,

2

__, )( nHnHE LSTqLSTqLSTP, 10 Nn (11)

NLPLSTP /, (12)where P is the distance between pilot subcarriers in the pilotsymbol. The average MSE for the data symbol is expressed as[9],

2, )/( WQQLSTD NLP (13)

Where

C. Maximum Likelihood Channel EstimationThe ML estimate also uses the knowledge of number of

channel taps. The Channel Impulse Response got through MLestimation is given by[10],

zBDh Hq

1^

(15)where, D is a square matrix of size L X L,

BBD H (16)In ML estimation technique, the MSE values for the pilotsymbol is derived as [7],

1

0

1

0

/2,

12,

L

k

L

p

NkpnjpkWMLP eD (17)

After linear interpolation, DFT is taken to get CFR for datasymbols. The MSE for data symbol in ML estimation isderived as,

54321, /)(2 QnMLD (18)

where, ,/2/ 221 qQqQw

qQqQrh /0 22 , QqqQrh /2

3 ,

qQqrh 4 , qQrq h 5

and

1

0

* ,,)(pN

mmnpmlemnpmlen

where

1

0,

/2,

1/2),(L

pk

Nipjpk

Nknj meemnpmle D (19)

and Q is distance between two pilot symbols.

QQ

Q 312

)14(,1

41011

1

Q

qHHQHQQ qr

QqQ

QQrr

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D. MMSE EstimationThe MMSE estimation for the frequency response

estimation of the qth pilot symbol at pilot locations isexpressed [11], omitting the index for pilot subcarrierlocations for simplicity as,

LSFqHHqHHqMMSEq HRRHLSLSLS

_1___

112__

qqWHHqHHq XXRR LSFqH _

(20)

where HqqHHq HHER _ , H

LSFqqHHq HHERLS __

HLSqLSqHHq HHER

LSLS ___

E.Interference mitigation through Channel EstimationIn the proceeding sections, the system affected only by the

multipath channel is considered. Now, let us assume that theMS receives a signal from another surrounding BS, called asinterfering station. The received signal model becomes[8],

),()()()()( nVnInXnHnY qqqqq 10 Nn10 Qq (21)

Where )(nIq is the amount of interference from theinterfering BSs at the nth subcarrier.

To facilitate interference mitigation, channel estimation andinterpolation are performed for every block, and this block iscalled as unit transmission block (UTB). For example, a blockcould be a set of symbols consisting of two pilot symbols andtwo data symbols as shown in Fig 2.

(a) E-UTB structure (b) U-UTB structureFig. 2. Example of equal and unequal pilot density UTB structures.

Fig. 2 shows two kinds of UTB structures with respect topilot symbol density. A UTB consists of Q + 1 OFDMsymbols, two pilot symbols at the borders and Q - 1 datasymbols inside the block. The first UTB, called as “E-UTB”,is composed of pilot symbols with equal pilot density (Fig.2(a)). On the other hand, the second UTB, called as “U-UTB”,is formed from two types of pilot symbols with different pilotdensities. We define these two symbols as multi-cell pilotsymbols (MCPS) with relatively high density and single-cell

pilot symbols (SCPS) with relatively low density, respectively(Fig. 2(b)).

In the MCPS, a lower amount of interference can beobserved for CIR estimation as the number of pilot subcarriersare more compared to SCPS. In U-UTB, the MCPS is utilizedto observe the response of the ACI as well as the CIR of theserving BS. This ACI response is saved in a buffer to mitigateinterference for the SCPS. In the SCPS relatively greateramount of interference is shown in the CIR estimationcompared to the interference in the MCPS, since NS < NM,where NM denotes the number of pilot subcarriers in MCPSand NS denotes the number of pilot subcarriers in SCPS.However, this increased interference can be mitigated byinterference cancellation using the ACI observed in theMCPS.

Fig. 3 depicts the block diagram of the estimator based onU-UTB. Linear Interpolation is used for CIR interpolation.

Fig. 3. Channel estimator using interference mitigation technique

This method is applied to the LTE OFDM Downlink structureto achieve better MSE performance with less pilot overhead.

V. SIMULATION RESULTSA cellular OFDM downlink system over multipath Rayleigh

fading environments is considered to compare theperformance of the estimators. The simulation parameterstaken for analysis are listed in table I. We evaluate theperformance of the estimators in 18MHZ and 9MHzbandwidth. With the subcarrier spacing of 15 kHz, 18 MHzbandwidth corresponds to N=1200 (100 Resource Blocks) and9MHz corresponds to N=600 (50 Resource Blocks). Theresults are taken for the channel length of 78, the same as thethat of ITU-R Extended Vehicular A channel. To show theperformance difference of the estimators for reduced channellength, the comparison is performed with the same channelwith the most significant taps only i.e. L=54.

TABLE I - LTE SIMULATION PRARAMETERS FOR COMPARISONOF CHANNEL ESTIMATION METHODS

Slot duration 0.5 msSampling Frequency 30.72MHzCarrier Frequency 2.3GHzSubcarrier spacing 15kHzDistance between Pilot symbols,Q (for extendedcyclic prefix, one antenna port)

3

Distance between pilot subcarriers in one OFDMsymbol

6

Total number of OFDM symbols 19

Fig.4 and 5 shows the comparison of LS_Freq , LS_Time,ML and MMSE estimation techniques for different channellengths. At low SNR, MMSE outperforms all the methods. Athigh SNR, as MLE and LS_Time methods have the

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knowledge of channel length, their performance overwhelmsthat of MMSE. Performance of LS_Freq is inferior to all thetechniques. MMSE is more complex and it requires theknowledge of channel statistics.

Fig.4 MSE vs SNR for various estimation techniques. L=78, fd=100Hzapproximately 40 km/hr

Fig.5 MSE vs SNR for various estimation techniques. L=54, fd=100Hzapproximately 40 km/hr

The simulation parameters taken for interference mitigationare tabulated in table II.

TABLE II - FRAME PRARAMETERS FOR E-UTB AND U-UTB FORANALYSIS WITH INTERFERENCE

Frame Identifier FE-UTB FU-UTB

Basic UTB structure E-UTB U-UTBTotal OFDM symbols 19 19

Total pilot symbols 3 4 (MCPS: 2, SCPS: 2)Pilot symbol distance 9 6

Pilot subcarrier distance 6 MCPS: 6, SCPS: 12Overall

pilotoverhead

N=1200 1/38 1/38N=600 1/19 1/19

Fig. 6 shows MSE versus SNR curve for MMSE and MLestimation for the bandwidth of 18 MHz and 9 MHz,corresponding to N=1200 and N=600. Better MSE values areobtained for increased bandwidth in both the estimationmethods.

Fig.6 Comparison of MSE vs SNR for N=1200 and N=600, L=54, fd=100Hzapproximately 40 km/hr

Fig. 7 depicts the simulation values of MSE versusreceived SIR of the MS when SNR = 30dB, and fd = 400Hz.Since the mismatch resulting from the time-selectivity of thechannel far outweighs the interference from the adjacent BSsat high SIR, the MSE of the estimator for FU−UTB outperformsthat of FE−UTB for high SIR. Increasing the bandwidthincreases the performance by more than 2db. The simulationvalues are approximately the same as the MSE from thenumerical results.

Fig. 7 Average MSE vs received SIR, for the FE-UTB and FU-UTB structures andthe proposed estimator using IC with fd=400 Hz approximately 180 km/hr,SNR = 30dB.

The fig.8 clearly shows that the MSE of the estimator forFE−UTB is the best when the MS is stationary, since much of

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the ACI is eliminated by allocating many pilot subcarriers inthe frequency domain. However, the MSE for the FE−UTBworsens rapidly as the MS speed increases. Interferencemitigation no longer works for high mobility.

Fig.8 MSE vs Doppler frequency fd for the FE-UTB and FU-UTB structures. SIR =10dB, SNR = 30dB, L=54.

The bound of Q or fdTs for which InterferenceCancellation(IC) process works safely can be derived fromthe condition MSEE-UTB(Q) ≥ MSEU-UTB,IC(Q).

.

Fig. 9 Average MSE vs UTB size to obtain the maximum required UTB sizeFE-UTB and FU-UTB structures. εreq = 2.8 x10-2 , SIR = 10dB, SNR =30dB,L=54 N=1200.

From Fig. 9, we can decide the UTB size, QE and QUrequired to meet the required MSE in FEUTB and FUUTB at aparticular Doppler frequency, where QE is the UTB size ofFE−UTB structure and QU is for FU−UTB structure. Since thereare additional noise and interference terms in the FU−UTBestimator, it needs to have a smaller block size than the FE-UTBin order to satisfy the required MSE.

The MSEs of both estimators are more dominated byinterpolation errors than the interference and noise terms, asthe UTB size increases. Hence, as the required MSE increases,QE and QU has similar values.

VI. CONCLUSION

The LS_Freq, LS_Time, ML and MMSE Channelestimation techniques for LTE Downlink OFDM structurehave been thoroughly investigated in time varying mobileenvironment. In addition, performance of LS_Time channelestimation technique is analyzed in the presence ofinterference. MMSE estimator using the channel statistics forestimation performs well. ML channel estimation methodrequires the knowledge of channel length for estimation.Because of this knowledge, it outperforms MMSE at highSNR when the channel length is decreased. LS_Freq givespoor performance. LS_Time technique mitigates interferencewhile estimating the channel by forming an unequal pilotdensity structure. Better channel Estimation withinterference mitigation is achieved for all the bandwidth. Theperformance analysis in MIMO-OFDM LTE system is focus ofnext stage of work.

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