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 dierent ways to enable the Channel Estimation. The topic also presents the dierent 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.
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Introduction
A Reference Signal (RS) is a pre-dened signal, pre-known to both transmitter and receiver. So we distinct in LTE RSs of the two directions: Uplink RSs (Signals in the direction from Mobile Station (MS) to Base Station (BS)), and Downlink RSs (Signals in the direction from Base Station to Mobile Station). Since Signals are transmitted through a wireless channel, we are going to use them to estimate our channel. When Reference Signals are sent, they take many directions (multipath fading), and are reected on building, cars or obstructed by trees (Shadowing). And those eects 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 a better receiving, and how to estimate the channel to enable signal equalizations.
Leumaleu Djikeussi Cedric Anthony
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Uplink RSs
The Uplink transmission uses the SC-FDMA feature with 15 KHz subcarrier spacing, to enable the MS to transmit signals with low PAPR (Peak-to-Average-Power-Ratio). This allows the UE (User Equipment) or the MS, consuming less energy. It is used QPSK, 16-QAM and 64QAM for modulation, and nally a bandwidth for 1.4 to 20 MHz. The gure1 represents the transmitter and receiver structure of a SC-FDMA transmission. The RSs are inserted by the subcarrier mapping in frequency domain. For further details about SC-FDMA please refer to corresponding 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 fulll certain conditions. They must have a constant amplitude in the frequency domain, for equal excitation of all the allocated subcarriers for unbiased channel estimates. A Low Cubic Metric (CM) in time domain. This CM has the same properties as Peak-to-Average-Power-Ratio (PAPR), and it allows the amplitude of our signal not to be longer as necessities. We also need a good autocorrelation properties for accurate channel estimation. And nally good cross-correlation property between dierent RSs to reduce interference from RSs transmitted on the same resources. For that reason, we have to generate our RSs by signal sequences. Each cell is associated with a Base sequence. And divide all available Base sequences into groups (Sequence-Grouping), to put the RSs orthogonal each other Via Cyclic Time-Shifts of a Base sequence, and nally to reduce the interference between cell by using hopping method (Sequence-Group Hopping and Planning, Cyclic Shift hopping). And to close this rst part, we are going to present the dierent 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 a complex-valued mathematical sequence which, when applied to radio signals, gives rise to an
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electromagnetic signal of constant amplitude. The formula of a Zado-Chu Sequence in frequency domain is dened as follows:
n(n + 1)/2 aq (n) = exp −j2πq NZC
The exponent depends on the position index n= 0,...,N − 1, and the sequence index q= 1,...,N − 1. When n or q increase, the exponential function has a constant Amplitude but the phase rotations become faster. Note that is the largest prime number smaller or equal than (RS sequence length). ZC
ZC
2.2.1 Base RS Sequences and Sequence-Grouping
There are 30 Base sequences. For M ≥ 3N , where N is the Number of Subcarriers per Resource Block and M = mN is the length of the RS with 1 ≤ m ≤ N . The allocation of a Zado-Chu Base sequence to a Base RS sequence is dened as follows. r¯ (n) = a (n mod N ). The argument n mod N means that when we want to use many subcarriers, we have to repeat the sequence as long as n is less than N − 1. Here q is a function of u and v as follows. q = [¯ q + 1/2] + v · (−1) (1) q¯ = N · (u + 1)/31 (2) where u∈ 0, 1, ..., 29 is the sequence-group number, and v ∈ 0, 1 the base sequence index. For we have QPSK RS, which is dened as M < 3N RS sc
u,v
q
RB sc
RB sc
RS sc RB sc
max,U L RB
ZC
ZC
ZC
2¯ q
RS ZC
RS sc
RB sc
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 are not present any more. One Base sequence corresponds to one sequence group. Sequences of a Sequence-group are derived from the Base-sequence by means of dierent 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 that for one CTS, we copy the last element at the beginning of the symbol and we push the whole of 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 time delay of τ = 5.55µs. A Cyclic Time-Shift corresponds to a phase ramp in the frequency domain. So we can express our Base sequence according to it as follows. max
(α) ru,v (n) = ejαn r¯u,v (n)
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Figure 2: Cyclic shifts of a sequence. [2] with phase α given by α = 2πn /p where is the CTS index for the transmitter t and p is the number of CTS (in LTE P = 12). Finally the CTS avoid collision between RSs because of zero cross-correlation. This allows the Channel Impulse Responses to be estimated separately, and reduce interference between cells. t
2.3 Sequence-Group hopping and Planning, Cyclic Shift hopping
Whereas CTS allow a good separation between cells because each cell has its own sequence group, there are many complex interference problems between cells. The neighboring cells to which RSs are assigned can have dierent bandwidths, which partially overlap in frequency domain. Therefore hopping are applied methods to resolve that problem. The Sequence-Group hopping has a group-hopping pattern f (n ), which is the same for PUSCH (Physical Uplink Share Channel) and PUCCH (Physical Uplink Control Channel) transmissions given by: If the group-hopping is disabled, 0 P f (n ) = c(8n + i)2 mod 30 If the group-hopping is enabled, where c (.) is the Gold sequence, n the slot index. f (n ) is used to reduce interference. A Sequence-Group Planning enables neighbouring cells to be assigned to sequence groups with low cross-correlation to reduce RS interference at the cell borders. Finally, the Cyclic shift hopping is used to avoid Inter-Cell-Interference for PUCCH and PUSCH transmissions. gh
gh
s
7
s
s
i
i=0
s
gh
s
2.3.1 Types of Uplink RS
There are two types of RS in LTE Uplink. We have Demodulation RSs (DM RS) and Sounding RSs (SRS). The DM RS are used for channel estimation for a coherent demodulation, and SRS are 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 into two equal parts at dierent positions. For the rst case the DM RS is denoted as Long Block Reference Signal(LB RS)(See the gure3). For the second case of two dierent positions, the DM RS is denoted as Short Block Reference Signal(SB RS)(See the gure4).
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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 Rate versus Es/No and Short Block RS. We remark that for a given speed of 30km/h there is no dierence between both.
Figure 5: Demodulation performance comparaison for Long Block and Short Block RS structure. Code rate r =1/2, GSM Typical Urban (TU) channel model, 30 km/h, 2 GHz carrier frequency.[3] In the gure 6, the more the speed increases compared to the gure 5 the more the demodulation performance using LB RS becomes worse and the one using SB RS better. The latter case can be explained by the fact that time diversity can be exploited, because of a good enough channel estimation with a SB RS. But the time diversity could not be used by LB RS because by higher speed, 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 dierent Reference sequences with desirable characteristics, and better frequency resolution for channel estimation.
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Leumaleu Djikeussi Cedric Anthony
Figure 6: Demodulation performance comparaison for Long Block and Short Block RS structure. Code rate r =1/2, GSM Typical Urban (TU) channel model, 250 km/h, 2 GHz carrier frequency.[3] The SRS are transmitted at the end of every second slot, as shown in the gure 7. They are transmitted on request of the BS. It means that the SRS may be sent not permanently. Figure 7: Sounding RS.[4]
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Downlink RS
The Downlink transmission uses the OFDMA feature with 15 KHz subcarrier spacing (7.5 KHz for MBSFN RS), It also uses QPSK, 16-QAM and 64-QAM for modulation, and nally has a bandwidth of 1.4 to 20 MHz. There are three types of Downlink RSs, all having the same formula, given by 1 1 rl,ns (m) = √ [1 − 2c(2m)] + j √ [1 − 2c(2m + 1)] 2 2
Notice that n is the Slot number, l the Symbol number, and C (.) the Gold sequence. We distinct thus Cell-specic reference signals, MBSFN (Multimedia Broadcast Single Frequency Network) reference signals, and UE-specic reference signals. s
3.1 Cell-specic reference signals
Cell-specic reference signals are the normal case of transmissions in LTE. That means signals containing 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 specic RS are transmitted every rst and fth OFDM symbol of a slot. The following gure illustrates the 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 of the 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 contain just four pilots. (See gure 10) That can be explained through the fact that when the channel is good enough to transmit via four antennas, then four pilots are sucient for antennas 2 and 3.
Resource elements (k, l ) used for reference signal transmission on any of the antenna ports i 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 tr denote aDjikeussi resource Cedric elementAnthony used for reference si above definition. The notation R p is used to Leumaleu
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antenna port p . 66
3GPP TS 36.211 V8.5.0 (2008-12)
One antenna port
cell given by vshift = N ID mod 6 .
R0
R0
R0
R0
eference signal transmission on any of the antenna ports in a slot shall not be used ntenna port in the same slot and set toR zero. R 0
0
lustrate the resource elements used for reference signal transmission according to the R R l=0 l =6 l =0 l =6 is used to denote a resource element used for reference signal transmission on 0
0
Resource element (k,l)
Two antenna ports
R0
R0
Figure 9: 2 antenna ports modus.[5]
Four antenna ports
R1
R1
R1
R1
R1 l =6 l =0
R1
R0
R0 Resource element (k,l)
R0
R0
l=0
R2
R1
R1
R1
odd-numbered slots
R2
R1
R2
R1 l =6
l =6
R1
R0
even-numbered slots
R1 l =6 l =0
R1
R0 R0 Not used for transmission on this antenna port
Not used for transmission on this antenna port
Reference symbols on this antenna port
R1 l =6
R1
R1
R0 l =6 l =0
R0 R0 Reference symbols on this antenna port l=0 l =6 l =0
R1
=0
R1
R0
R0
R1
R1
R0
l=0
R1
R1
R0
l=0
R1 l =6 l =0
even-numbered slots
R2 l =6
odd-numbered slots
l =0
l=6 l=0
even-numbered slots
l=6
odd-numbered slots
l =6
Antenna port 0
Antenna port 1
Antenna port 2
Figure 6.10.1.2-1. Mapping of downlink reference signals (normal c
R1
R1
R1
R1
R1
R3
R2
R1 l =6 l =0
even-numbered slots
R3
R2 l =6
odd-numbered slots
Antenna port 1
R3
R2
R1
R1
=0
R2
l =0
R3 l=6 l=0
even-numbered slots
l=6
odd-numbered slots
Antenna port 2
l=0
l =6 l =0
even-numbered slots
odd-numbered slots
Antenna port 3
Figure 10: 4 antenna ports modus.[5]
Mapping of downlink reference signals (normal cyclic prefix).
l =6
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3.2 MBSFN (Multimedia Broadcast Single Frequency Network) reference signals
MBSFN is a broadcast modus (BS to many UE). It means that the transmitted signals of the BS are received by many UEs. These can be for example the climate information, the calendar information, or the time information. MBSFN reference signals are transmitted on antenna port 4.
Figure 11: Mapping of MBSFN reference signal.[5] 3.3 UE-specic reference signals
UE-specic transmission allows beamforming. That means the UE-specic information are transmitted in one unique direction from the BS to a particular receiver. Here the Reference signals are transmitted on antenna port 5 (see the gur ??). Note that because of that beamforming we have more pilots as by Cell Specic RS. 4
Channel Estimation
Now that we know how appears our Reference Signals according to both directions. We can henceforth cross in the channel estimation. We are going to estimate the channel in the frequency direction, in the time direction, and in the spatial direction. Whereas, we cannot estimate the channel without knowing its properties.
Leumaleu Djikeussi Cedric Anthony
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Figure 12: Mapping of UE-specic reference signals (normal cyclic prex).[5] 4.1 Channel properties
The gure 13 shows the channel transfer function (CTF) over frequency f and moving distance x. 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 -Fading channel. Slow-Fading channel (Signal variations when moving long distance) The movement of the receiver following a long distance leads to a slow phenomen of decrease because of multiple obstructions as trees, mountains, walls, which weaken the signal, or to a slow change of the channel. Fast -Fading channel (Fluctuations due to moving Short distance) Here it is about the movement of the receiver following a short distance. The channel varies very fast because of the multipath eect. That means the transmitted signal arrives at the receiver, where dependent
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on the phase dierences of the path signals, the summation yields a constructive or destructive superposition. 4.2 Channel Estimation in Frequency-Direction
The CTF can be estimated using a Maximum Likelihood approach in frequency domain at pilot positions. A channel estimate vector is given by ˆ p = Hp + Np = Fp h + Np H
with P the number of available reference symbols, N the P x 1 Noise vector, h the L x 1 channel Impulse Response (CIR), the P x L matrix obtained by selecting the rows corresponding to the reference symbol positions and the rst L columns of the N x N DFT matrix, and F the N x L matrix obtained by taking the rst L columns of the DFT matrix. This channel estimate vector shall be used in each case of estimation in frequency direction for all subcarriers estimations. p
L
4.2.1 Channel estimation by interpolation
Here two estimators are considered: the linear interpolation Estimator, and the Inverse Fast Fourier Transform (IFFT) Estimator. The linear interpolator uses a lter matrix A so that the CTF estimate can be written as ˆ = AH ˆ . H (3) The IFFT interpolator uses a lter A given by i
p
IF F T
AIF F T =
1 FL FPH P
That means the channel estimate vector is through F inverse Fourier transformed (in time domain) and through F Re-transformed in frequency domain. H P
L
4.2.2 Linear Channel Estimation
For this estimation we are going to use a general matrix given by Agen = B(GH G + R)−1 GH
Notice that B, G, R are matrices that vary according to each estimator as expressed in the following subsections. Leacsh square (LS) Estimator (B= F , G= F , R=0), Regularized LS Estimator: the choice of LTE system parameters does not allow LS Estimator to be applied directly. That is why we use the Regularized LS Estimator to counter that problem. For that reason we replace the regularized matrix R by αI . B and G stay the same as for L
L
P
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LS. The Minimum Mean Square Error (MMSE) Estimator belongs to the class of statistical estimators. It is a complex estimator, but optimum. R= σ C with C the channel covariance matrix. A Mismatched MMSE can beused to avoid estimation of the needes secondorder channel statistics by setting (R= . I ) The curve below shows the frequency-domain channel estimation performance. 2 Np
2 σN p 2 σh
h
−1
h
L
Figure 14: Frequency-domain channel estimation performance.[8] We can remark that the MMSE Estimator is the best compared to the others. Because it considers the channel properties by its estimation, but the IFFT or the linear interpolator do not. Note that Regularized LS performance is equal to Mismatched MMSE performance for the joice of α = σ . 2 Np
4.3 Channel Estimation in Time-Direction
The vector h given by is ltered by w , the Mx1 vector of the nite Impulse Response (FIR) lter coecients. So we get a smoothed CIR (Channel Impulse Response) given by h iT ˆh(M ) = h ˆ ,··· ,h ˆ , l,n l,n−M +1 l,n
l
ˆˆ H ˆ (M ) h l,n = wl hl,n
Notice that the MMSE corrction is applied to derive w =(R + σ I) r ., l is the tap position, n the time instant, M the length of the vector hˆ , R the l channel tap M x M correlation matrix, σ the additive noise variance, r the M x 1 correlation vector between the tap of the current channel realization and M past and future realizations including the current one. l
(M ) l,n
2 n
h
h
h
2 n
−1
h
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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 receive vector r with the lter matrix Q as follows: ˆ = Qr h (4) where Q = C G GC G + σ I , N is the number of transmitting Antennas, N 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, compared to the maximum likelihood approach. √1 NT x
h
H
1 NT x
h
H
2 n N.NRx
−1
Tx
Rx
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 the channel estimation which is essential for coherent demodulation. Application of Cyclic time shifts on Zado-Chu sequence allows obtaining Orthogonal RS sequences for a good separation of the channel. It is also important to note that by SB RS the time diversity is used, but not by LB RS. However the LB RS provide RS with desirable properties. Concerning the Channel estimation in frequency direction, we declare that Arithmetic interpolation is worse than estimation methods. If more than one receive antennas are available, the channel estimation can gain additionally, from the correlation in spatial direction. And in the case the channel estimation in time direction, the path correlation in time direction is exploited.
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References
[1] [2] [3] [4] [5] [6] [7] [8]
Hyung G. Myung, Junsung Lim, and David J. Goodman, "Single Carrier FDMA for Uplink Wireless Transmission", IEEE Vehicular Technology Magazine, vol. 1, no. 3, Sep. 2006, pp. 30-38 K.Fazel and G. P. Fettweis, Multi-Carrier Spread-Spectrum. Kluwer Academic Motorola, R1-073756: Benet of Non-Persistent UL Sounding for frequency Hopping PUSCH www.3GPP.org 3 GPP TSG RAN WG1,meeting 52, Sorrento,Italy, February 2008 3GPP Technical Specication 36.211, Physical Channels and Modulation www.3GPP.org, 26 November 2008 Overview of the 3GPP Long Term Evolution Physical Layer , 07/2007,k Dr. Wes McCoy, Technical Editor Grundlagen, der Mobilkommunikation, Vorlesungskript Prof. Dr -Ing W.Koch,WS 2009 H.Bölcskei,D. Gebert and C.Papadias, space-time wireless Systems: From Array Processing to MIMO Communications. Cambrige University Press2006 LTE The UMTS Long Term Evolution, From the Theory to Practice, Edited by: Stefania Sesia.Issam Touk. Matthew Baker