Reference Signals and Channel Estimation - · PDF fileReference Signals and Channel Estimation Leumaleu Djikeussi Cedric Anthony ... Code rate r =1/2, GSM Typical Urban (TU) channel

Seminar

Ausgewählte Kapitel der Nachrichtentechnik, WS 2009/2010

LTE:

Der Mobilfunk der Zukunft

Reference Signals and Channel Estimation

Leumaleu Djikeussi Cedric Anthony

25. November 2009

Abstract � The Reference Signals (RS) are a very important point in the domain of

the Mobile communication. This topic shows how the RS for Uplink and Downlink

case in Long Term Evolution (LTE) are generated in di�erent ways to enable the

Channel Estimation. The topic also presents the di�erent requirements and the

key-features of both types of RS. A major problem is always to resolve interference

between signals. This work answers how to prevent the Reference Signals from

interference to enable a exact channel estimation. And �nally, it is explained how

to estimate the channel in frequency domain, where estimation is considered to be

applied in frequency, time or spatial direction.

1 Introduction

A Reference Signal (RS) is a pre-de�ned signal, pre-known to both transmitter and receiver.So we distinct in LTE RSs of the two directions: Uplink RSs (Signals in the direction fromMobile Station (MS) to Base Station (BS)), and Downlink RSs (Signals in the direction fromBase Station to Mobile Station). Since Signals are transmitted through a wireless channel, weare going to use them to estimate our channel. When Reference Signals are sent, they takemany directions (multipath fading), and are re�ected on building, cars or obstructed by trees(Shadowing). And those e�ects lead to self-interference and �nally bit errors by the receiver.The question now is what thus have to look like the Reference Signals, so that we can get abetter receiving, and how to estimate the channel to enable signal equalizations.

2 Leumaleu Djikeussi Cedric Anthony

2 Uplink RSs

The Uplink transmission uses the SC-FDMA feature with 15 KHz subcarrier spacing, to enablethe MS to transmit signals with low PAPR (Peak-to-Average-Power-Ratio). This allows theUE (User Equipment) or the MS, consuming less energy. It is used QPSK, 16-QAM and 64-QAM for modulation, and �nally a bandwidth for 1.4 to 20 MHz. The �gure1 represents thetransmitter and receiver structure of a SC-FDMA transmission. The RSs are inserted by thesubcarrier mapping in frequency domain. For further details about SC-FDMA please refer tocorresponding seminar topic "`SC-FDMA and LTE Uplink Physical Layer Design"'.

Figure 1: Transmitter and receiver structure of a SC-FDMA. [1]

2.1 Criteria for Reference Signal design

For a good transmission in the Uplink direction, the RSs have to ful�ll certain conditions. Theymust have a constant amplitude in the frequency domain, for equal excitation of all the allocatedsubcarriers for unbiased channel estimates. A Low Cubic Metric (CM) in time domain. This CMhas the same properties as Peak-to-Average-Power-Ratio (PAPR), and it allows the amplitudeof our signal not to be longer as necessities. We also need a good autocorrelation properties foraccurate channel estimation. And �nally good cross-correlation property between di�erent RSsto reduce interference from RSs transmitted on the same resources. For that reason, we have togenerate our RSs by signal sequences. Each cell is associated with a Base sequence. And divideall available Base sequences into groups (Sequence-Grouping), to put the RSs orthogonal eachother Via Cyclic Time-Shifts of a Base sequence, and �nally to reduce the interference betweencell by using hopping method (Sequence-Group Hopping and Planning, Cyclic Shift hopping).And to close this �rst part, we are going to present the di�erent types of Uplink RSs.

2.2 Sequence Generation of RSs

The generation of RSs is based on the Zado�-Chu sequence. A Zado�-Chu sequence is acomplex-valued mathematical sequence which, when applied to radio signals, gives rise to an

Reference Signals and Channel Estimation 3

electromagnetic signal of constant amplitude. The formula of a Zado�-Chu Sequence in fre-quency domain is de�ned as follows:

aq(n) = exp

[−j2πqn(n+ 1)/2

NZC

]The exponent depends on the position index n= 0,. . . ,NZC − 1, and the sequence index q=1,. . . ,NZC − 1. When n or q increase, the exponential function has a constant Amplitude butthe phase rotations become faster. Note that is the largest prime number smaller or equal than(RS sequence length).

2.2.1 Base RS Sequences and Sequence-Grouping

There are 30 Base sequences. For MRSsc ≥ 3NRB

sc , where NRBsc is the Number of Subcarriers

per Resource Block and MRSsc = mNRB

sc is the length of the RS with 1 ≤ m ≤ Nmax,ULRB .

The allocation of a Zado�-Chu Base sequence to a Base RS sequence is de�ned as follows.ru,v(n) = aq(n mod NZC). The argument n mod NZC means that when we want to usemany subcarriers, we have to repeat the sequence as long as n is less than NZC − 1. Here q isa function of u and v as follows.

q = [q + 1/2] + v · (−1)2q (1)

q = NRSZC · (u+ 1)/31 (2)

where u∈ 0, 1, ..., 29 is the sequence-group number, and v ∈ 0, 1 the base sequence index. ForMRS

sc < 3NRBsc we have QPSK RS, which is de�ned as

ru,v(n) = ejϕ(n)π/4

with ϕ(n) = f(u, v). Note that the QPSK RS Base sequence is not a Zado�-Chu sequence.That leads to non-zero correlation between signals, because the properties of Zado�-Chu arenot present any more. One Base sequence corresponds to one sequence group. Sequences of aSequence-group are derived from the Base-sequence by means of di�erent Cyclic Time Shifts.One of these sequence groups is used to support Uplink transmission of one cell.

2.2.2 Orthogonal RS via Cyclic Time-Shifts (CTS) of a Base Sequence

By using a Cyclic Time-Shifts (CTS) on a Base Sequence as it is shown in Fig. 2, we see thatfor one CTS, we copy the last element at the beginning of the symbol and we push the wholeof a jump towards the right side. And for another CTS, we do the same scenario. . . etc.

There are 12 Cyclic Time-Shifts in LTE which correspond to a multiple of the elementary timedelay of τmax = 5.55µs. A Cyclic Time-Shift corresponds to a phase ramp in the frequencydomain. So we can express our Base sequence according to it as follows.

r(α)u,v (n) = ejαnru,v(n)


Figure 2: Cyclic shifts of a sequence. [2]

with phase α given by α = 2πnt/p where is the CTS index for the transmitter t and p is thenumber of CTS (in LTE P = 12). Finally the CTS avoid collision between RSs because of zerocross-correlation. This allows the Channel Impulse Responses to be estimated separately, andreduce interference between cells.

2.3 Sequence-Group hopping and Planning, Cyclic Shift hopping

Whereas CTS allow a good separation between cells because each cell has its own sequencegroup, there are many complex interference problems between cells. The neighboring cells towhich RSs are assigned can have di�erent bandwidths, which partially overlap in frequencydomain. Therefore hopping are applied methods to resolve that problem. The Sequence-Grouphopping has a group-hopping pattern fgh(ns), which is the same for PUSCH (Physical UplinkShare Channel) and PUCCH (Physical Uplink Control Channel) transmissions given by:

fgh(ns) =

0 If the group-hopping is disabled,(7∑i=0

c(8ns + i)2i)

mod 30 If the group-hopping is enabled,

where c (.) is the Gold sequence, ns the slot index. fgh(ns) is used to reduce interference. ASequence-Group Planning enables neighbouring cells to be assigned to sequence groups withlow cross-correlation to reduce RS interference at the cell borders. Finally, the Cyclic shifthopping is used to avoid Inter-Cell-Interference for PUCCH and PUSCH transmissions.

2.3.1 Types of Uplink RS

There are two types of RS in LTE Uplink. We have Demodulation RSs (DM RS) and SoundingRSs (SRS). The DM RS are used for channel estimation for a coherent demodulation, and SRSare used to estimate the channel quality to enable frequency-selective scheduling on the uplink.Concerning the DM RS, they are either concentrated in one position in a slot, or divided intotwo equal parts at di�erent positions. For the �rst case the DM RS is denoted as Long BlockReference Signal(LB RS)(See the �gure3). For the second case of two di�erent positions, theDM RS is denoted as Short Block Reference Signal(SB RS)(See the �gure4).


Figure 3: Long Blok RS.[3]

Figure 4: Short Blok RS.[3]

Now we focus on the question why we have to divide the RS into two blocks. The following�gure shows the demodulation performance for Long Block RS in terms of Block Error Rateversus Es/No and Short Block RS. We remark that for a given speed of 30km/h there is nodi�erence between both.

Figure 5: Demodulation performance comparaison for Long Block and Short Block RS struc-ture. Code rate r =1/2, GSM Typical Urban (TU) channel model, 30 km/h, 2 GHz carrierfrequency.[3]

In the �gure 6, the more the speed increases compared to the �gure 5 the more the demodulationperformance using LB RS becomes worse and the one using SB RS better. The latter case canbe explained by the fact that time diversity can be exploited, because of a good enough channelestimation with a SB RS. But the time diversity could not be used by LB RS because by higherspeed, the channel estimation is too worse. Thus SB RS supports higher speed than LB RS.

However the LB RS has the advantage of providing longer sequences for a given bandwidth,which leads to a larger number of di�erent Reference sequences with desirable characteristics,and better frequency resolution for channel estimation.


Figure 6: Demodulation performance comparaison for Long Block and Short Block RS struc-ture. Code rate r =1/2, GSM Typical Urban (TU) channel model, 250 km/h, 2 GHz carrierfrequency.[3]

The SRS are transmitted at the end of every second slot, as shown in the �gure 7. They aretransmitted on request of the BS. It means that the SRS may be sent not permanently.

Figure 7: Sounding RS.[4]


3 Downlink RS

The Downlink transmission uses the OFDMA feature with 15 KHz subcarrier spacing (7.5 KHzfor MBSFN RS), It also uses QPSK, 16-QAM and 64-QAM for modulation, and �nally hasa bandwidth of 1.4 to 20 MHz. There are three types of Downlink RSs, all having the sameformula, given by

rl,ns(m) =1√2

[1− 2c(2m)] + j1√2

[1− 2c(2m+ 1)]

Notice that ns is the Slot number, l the Symbol number, and C (.) the Gold sequence. Wedistinct thus Cell-speci�c reference signals, MBSFN (Multimedia Broadcast Single FrequencyNetwork) reference signals, and UE-speci�c reference signals.

3.1 Cell-speci�c reference signals

Cell-speci�c reference signals are the normal case of transmissions in LTE. That means signalscontaining normal calls, SMS, Email�etc, which are transmitted from the BS to just one receiver(Unicasting). In this case the signals are transmitted with 1, 2 or 4 antennas. Cell speci�c RSare transmitted every �rst and �fth OFDM symbol of a slot. The following �gure illustratesthe subcarrier mapping of OFDMA, for the case of a transmission with one antenna.

Figure 8: 1 antenna port.[5]

For the case of a transmission with two antennas, a RS is sent on the �rst OFDM symbol ofthe �rst antenna, then the �rst OFDM symbol of the second antenna is not use, and vice versa.The same scenario occurs for the �fth OFDM symbol of the two antennas, see �gure 9

The case of four antennas presents a particularity. We see that the two last antennas containjust four pilots. (See �gure 10)

That can be explained through the fact that when the channel is good enough to transmit viafour antennas, then four pilots are su�cient for antennas 2 and 3.


Figure 9: 2 antenna ports modus.[5]

3GPP

3GPP TS 36.211 V8.5.0 (2008-12)66Release 8

The cell-specific frequency shift is given by 6modcellIDshift Nv = .

Resource elements ( )lk, used for reference signal transmission on any of the antenna ports in a slot shall not be used for any transmission on any other antenna port in the same slot and set to zero.

Figures 6.10.1.2-1 and 6.10.1.2-2 illustrate the resource elements used for reference signal transmission according to the above definition. The notation pR is used to denote a resource element used for reference signal transmission on antenna port p .

0=l0R

0R

0R

0R

6=l 0=l0R

0R

0R

0R

6=l

One

ant

enna

por

tTw

o an

tenn

a po

rts

Resource element (k,l)

Not used for transmission on this antenna port

Reference symbols on this antenna port

0=l0R

0R

0R

0R

6=l 0=l0R

0R

0R

0R

6=l 0=l

1R

1R

1R

1R

6=l 0=l

1R

1R

1R

1R

6=l

0=l0R

0R

0R

0R

6=l 0=l0R

0R

0R

0R

6=l 0=l

1R

1R

1R

1R

6=l 0=l

1R

1R

1R

1R

6=l

Four

ant

enna

por

ts

0=l 6=l 0=l

2R

6=l 0=l 6=l 0=l 6=l2R

2R

2R

3R

3R

3R

3R

even-numbered slots odd-numbered slots

Antenna port 0


Antenna port 1


Antenna port 2


Antenna port 3

Figure 6.10.1.2-1. Mapping of downlink reference signals (normal cyclic prefix).

3GPP

3GPP TS 36.211 V8.5.0 (2008-12)66Release 8

The cell-specific frequency shift is given by 6modcellIDshift Nv = .

Resource elements ( )lk, used for reference signal transmission on any of the antenna ports in a slot shall not be used for any transmission on any other antenna port in the same slot and set to zero.

Figures 6.10.1.2-1 and 6.10.1.2-2 illustrate the resource elements used for reference signal transmission according to the above definition. The notation pR is used to denote a resource element used for reference signal transmission on antenna port p .

0=l0R

0R

0R

0R

6=l 0=l0R

0R

0R

0R

6=l

One

ant

enna

por

tTw

o an

tenn

a po

rts

Resource element (k,l)

Not used for transmission on this antenna port

Reference symbols on this antenna port

0=l0R

0R

0R

0R

6=l 0=l0R

0R

0R

0R

6=l 0=l

1R

1R

1R

1R

6=l 0=l

1R

1R

1R

1R

6=l

0=l0R

0R

0R

0R

6=l 0=l0R

0R

0R

0R

6=l 0=l

1R

1R

1R

1R

6=l 0=l

1R

1R

1R

1R

6=l

Four

ant

enna

por

ts

0=l 6=l 0=l

2R

6=l 0=l 6=l 0=l 6=l2R

2R

2R

3R

3R

3R

3R


Antenna port 0


Antenna port 1


Antenna port 2


Antenna port 3

Figure 6.10.1.2-1. Mapping of downlink reference signals (normal cyclic prefix). Figure 10: 4 antenna ports modus.[5]


3.2 MBSFN (Multimedia Broadcast Single Frequency Network) ref-

erence signals

MBSFN is a broadcast modus (BS to many UE). It means that the transmitted signals of theBS are received by many UEs. These can be for example the climate information, the calendarinformation, or the time information. MBSFN reference signals are transmitted on antennaport 4.

Figure 11: Mapping of MBSFN reference signal.[5]

3.3 UE-speci�c reference signals

UE-speci�c transmission allows beamforming. That means the UE-speci�c information aretransmitted in one unique direction from the BS to a particular receiver. Here the Refer-ence signals are transmitted on antenna port 5 (see the �gur ??). Note that because of thatbeamforming we have more pilots as by Cell Speci�c RS.

4 Channel Estimation

Now that we know how appears our Reference Signals according to both directions. We canhenceforth cross in the channel estimation. We are going to estimate the channel in the fre-quency direction, in the time direction, and in the spatial direction. Whereas, we cannotestimate the channel without knowing its properties.


Figure 12: Mapping of UE-speci�c reference signals (normal cyclic pre�x).[5]

4.1 Channel properties

The �gure 13 shows the channel transfer function (CTF) over frequency f and moving distancex. We can see that the channel properties change in function of place and the time. For that

Figure 13: Channel transfer function over frequency f and moving distance x.[6]

reason, we distinct two types of channel properties: Slow-Fading channel, and Fast -Fadingchannel.

Slow-Fading channel (Signal variations when moving long distance) The movement ofthe receiver following a long distance leads to a slow phenomen of decrease because of multipleobstructions as trees, mountains, walls, which weaken the signal, or to a slow change of thechannel.

Fast -Fading channel (Fluctuations due to moving Short distance) Here it is about themovement of the receiver following a short distance. The channel varies very fast because of themultipath e�ect. That means the transmitted signal arrives at the receiver, where dependent


on the phase di�erences of the path signals, the summation yields a constructive or destructivesuperposition.

4.2 Channel Estimation in Frequency-Direction

The CTF can be estimated using a Maximum Likelihood approach in frequency domain at pilotpositions. A channel estimate vector is given by

Hp = Hp +Np = Fph+Np

with P the number of available reference symbols, Np the P x 1 Noise vector, h the L x 1 channelImpulse Response (CIR), the P x L matrix obtained by selecting the rows corresponding to thereference symbol positions and the �rst L columns of the N x N DFT matrix, and FL the N x Lmatrix obtained by taking the �rst L columns of the DFT matrix. This channel estimate vectorshall be used in each case of estimation in frequency direction for all subcarriers estimations.

4.2.1 Channel estimation by interpolation

Here two estimators are considered: the linear interpolation Estimator, and the Inverse FastFourier Transform (IFFT) Estimator. The linear interpolator uses a �lter matrix A so that theCTF estimate can be written as

Hi = AHp. (3)

The IFFT interpolator uses a �lter AIFFT given by

AIFFT =1

PFLF

HP

That means the channel estimate vector is through FHP inverse Fourier transformed (in time

domain) and through FL Re-transformed in frequency domain.

4.2.2 Linear Channel Estimation

For this estimation we are going to use a general matrix given by

Agen = B(GHG + R)−1GH

Notice that B, G, R are matrices that vary according to each estimator as expressed in thefollowing subsections. Leacsh square (LS) Estimator (B= FL , G= FP , R=0), Regularized LSEstimator: the choice of LTE system parameters does not allow LS Estimator to be applieddirectly. That is why we use the Regularized LS Estimator to counter that problem. Forthat reason we replace the regularized matrix R by αIL. B and G stay the same as for


LS. The Minimum Mean Square Error (MMSE) Estimator belongs to the class of statisticalestimators. It is a complex estimator, but optimum. R= σ2

NpCh−1 with Ch the channel

covariance matrix. A Mismatched MMSE can beused to avoid estimation of the needes second-order channel statistics by setting (R=

σ2Np

σ2h. IL) The curve below shows the frequency-domain

channel estimation performance.

Figure 14: Frequency-domain channel estimation performance.[8]

We can remark that the MMSE Estimator is the best compared to the others. Because itconsiders the channel properties by its estimation, but the IFFT or the linear interpolator donot. Note that Regularized LS performance is equal to Mismatched MMSE performance forthe joice of α = σ2

Np.

4.3 Channel Estimation in Time-Direction

The vector h given by h(M)l,n =

[hl,n, · · · , hl,n−M+1

]T, is �ltered by wl, the Mx1 vector of the

�nite Impulse Response (FIR) �lter coe�cients. So we get a smoothed CIR (Channel ImpulseResponse) given by

ˆhl,n = wHl h

(M)l,n

Notice that the MMSE corrction is applied to derive wl=(Rh + σ2nI)−1rh., l is the tap position,

n the time instant, M the length of the vector h(M)l,n , Rh the l channel tap M x M correlation

matrix, σ2n the additive noise variance, rh the M x 1 correlation vector between the tap of the

current channel realization and M past and future realizations including the current one.


4.4 Channel estimation in Spatial-Direction

In the case of many receive antennas, one may estimate the corresponding channels jointly,because they are assumed to be correlated. The estimation occurs by �ltering the receivevector r with the �lter matrix Q as follows:

h = Qr (4)

where Q = 1√NTx

ChGH(

1NTx

GChGH + σ2

nIN.NRx

)−1

, NTx is the number of transmitting Anten-nas, NRx the number of receiving antennas, G the receive signal matrix. N is the DFT length.The �gure below shows that we gain by estimating the channel in spatial direction, comparedto the maximum likelihood approach.

Figure 15: Spatial-domain channel estimation performance.cir NMSE VERSUS SNR.[8]

5 Summary

The Uplink and Downlink reference signals in LTE are important, because they facilitate thechannel estimation which is essential for coherent demodulation. Application of Cyclic timeshifts on Zado�-Chu sequence allows obtaining Orthogonal RS sequences for a good separationof the channel. It is also important to note that by SB RS the time diversity is used, but notby LB RS. However the LB RS provide RS with desirable properties. Concerning the Chan-nel estimation in frequency direction, we declare that Arithmetic interpolation is worse thanestimation methods. If more than one receive antennas are available, the channel estimationcan gain additionally, from the correlation in spatial direction. And in the case the channelestimation in time direction, the path correlation in time direction is exploited.


References

[1] Hyung G. Myung, Junsung Lim, and David J. Goodman, "Single Carrier FDMA forUplink Wireless Transmission", IEEE Vehicular Technology Magazine, vol. 1, no. 3,Sep. 2006, pp. 30-38

[2] K.Fazel and G. P. Fettweis, Multi-Carrier Spread-Spectrum. Kluwer Academic

[3] Motorola, R1-073756: Bene�t of Non-Persistent UL Sounding for frequency HoppingPUSCH www.3GPP.org 3 GPP TSG RAN WG1,meeting 52, Sorrento,Italy, February2008

[4] 3GPP Technical Speci�cation 36.211, Physical Channels and Modulationwww.3GPP.org, 26 November 2008

[5] Overview of the 3GPP Long Term Evolution Physical Layer , 07/2007,k Dr. WesMcCoy, Technical Editor

[6] Grundlagen, der Mobilkommunikation, Vorlesungskript Prof. Dr -Ing W.Koch,WS2009

[7] H.Bölcskei,D. Gebert and C.Papadias, space-time wireless Systems: From Array Pro-cessing to MIMO Communications. Cambrige University Press2006

[8] LTE The UMTS Long Term Evolution, From the Theory to Practice, Edited by:Stefania Sesia.Issam Tou�k. Matthew Baker

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Reference Signals and Channel Estimation - · PDF fileReference Signals and Channel Estimation Leumaleu Djikeussi Cedric Anthony ... Code rate r =1/2, GSM Typical Urban (TU) channel