Combating Timing Asynchronism in Relay Transmission for 3GPP LTE ...

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.

Combating Timing Asynchronism in Relay Transmission for 3GPP LTE Uplink Animesh Yadav, Markku Juntti and Juha Karjalainen Centre for Wireless Communication P.O.Box 4500 FI-90014 University of Oulu, Finland Email: {animesh.yadav, markku.juntti, juha.karjalainen}@ee.oulu.fi Abstract—Relays are used between the source and the destination to improve network coverage and reliability in cooperative relay system. Imperfect time delay synchronization at the receiver arises because of time difference in propagation of the signals from the source and the relay to the receiver. The performance degrades due to interference from the previous block and the defective channel matrix. In this paper, we study the effect of time delay asynchronism and propose to use interblock interference cancelation and cyclic prefix reconstruction techniques on amplify and forward relay based distributed space-time block coding for single carrier-frequency domain equalization system, which removes the unwanted interference part and reconstructs the defective channel matrix to circulant one. The proposed method significantly reduces the effect of time delay asychronism at the receiver without disturbing the 3rd generation partnership project-long term evolution (3GPP LTE) uplink frame structure, data rate and increasing the complexity over frequency selective channels.

I. I NTRODUCTION Use of single carrier (SC) transmission scheme has been standardized in 3rd generation partnership project-long term evolution (3GPP LTE) uplink [1]. Recently, the SC with frequency domain equalization (FDE) has gain a lot of attention as an alternative to the orthogonal frequency division multiplexing (OFDM), especially in the uplink communications. The SCFDE is also well suited at the mobile side because of its simple structure and low peak-to-average power ratio (PAPR) [2]. Space-time block coding (STBC) [3] is an effective technique to exploit spatial diversity not only in multiple-input multiple-output (MIMO) communications but also in cooperative communications [4]. Most of the existing studies on co-operative transmission assume perfect synchronization between the users and the co-operative relay, which means that the user and relay timings, carrier frequency, and propagation delay are identical [5], [6], [7]. However, such perfect synchronization between the user and the relay is difficult because of their different locations with their own local oscillators which do not share a timing reference. Poor synchronization in time will introduce intersymbol interference (ISI). If the transmission uses STBC, ISI destroys the orthogonal structure of STBC, and the conventional efficient decoding fails. Recently, co-operative diversity without This research has been supported by Tekes, the Finnish Funding Agency for Technology and Innovation, Elektrobit Group, Nokia, Nokia Siemens Networks, and Texas Instruments.

the requirement of synchronization has been discussed in some studies. Mei et al. [8] proposed to use either timereversed space-time codes (TR-STC) or space-time orthogonal frequency division multiplexing (ST-OFDM) codes to combat synchronization errors among relays. Their proposed schemes achieve diversity gain at the expense of data rate by adding cyclic prefix (CP) to OFDM symbols or by inserting guard intervals between blocks of symbols in TR-STC technique. Other proposals include delay-tolerant space-time codes with minimum delay length [9], delay-tolerant distributed threaded algebraic space-time (TAST) codes for co-operative diversity [10], and delay-tolerant distributed linear convolutive spacetime codes (DLC-STC) [11]. These codes are insensitive to the timing errors, i.e., they achieve the full spatial diversity under any delay profile. STBC with co-operative transmission, OFDM, and limited asynchronism in timing and in carrier frequency has been considered in [12],[13],[14]. OFDM has been shown to tolerate small timing/delay asynchronism in [15]. As the delay plus multipath delay spread exceeds CP length, the symbol error rate (SER) of co-operative transmission increases faster than that of non-cooperative schemes. Space-frequency block coding (SFBC) co-operative transmission with OFDM to combat the timing errors and to achieve higher data rate and simplified implementation aslo has been considered in [16]. Different from the earlier ones, Yan et al. [17] has proposed a scheme for a SC system, where the distributed space-time block code (D-STBC) encoded transmission was analyzed in frequency selective channel. However, this scheme was based on the assumption that multipath delay spread plus relative propagation delay between the relays is less then the CP length. If the multipath delay spread plus the relative propagation delay exceeds the CP length, the performance degrades because inter block interference (IBI) is introduced and the channel matrix becomes non-circulant. In this paper we propose an equalization scheme for DSTBC under the condition that multipath delay spread plus the relative propagation delay is larger than the CP length, without disturbing the frame structure of the 3GPP LTE, decreasing the data rate or increasing receiver complexity . This scheme is based on interblock interference cancelation (IBIC) and cyclic prefix reconstruction (CPR) [18] and has been extended to a relay based system. Amplify and forward

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(AF) relaying protocol which is the simplest class of cooperative communication protocol [19] is used at the relay terminal. It is shown through simulation that if the relative propagation delay and channel impulse response at the receiver is known, then through IBI cancelation and CPR, the effect of time delay is reduced significantly. Notations: (·)∗ , (·)T and (·)H denote conjugate, transpose, and Hermitian transpose operations, respectively. [·]k,l denotes the (k, l)th entry of a matrix, [·]k denotes the (k)th entry of a vector. 0M ×M denotes all-zero matrix of size M × M, diag(v) stands for a diagonal matrix with vector v on its diagonal, and FN represents the N × N fast fourier transform (FFT) √ matrix whose (l,k) elements is given by FN (l,k) = (1/ N) exp (−j2πlk/N ) where 0 ≤ l, k ≤ N − 1. We define a set of N × N permutation matrices {P} and {Rτ } that performs a reversed cyclic shift and a cyclic shift respectively, i.e., for a vector a = [a0 · · · aN −1 ]T , [Pa]n = H a(−n mod N ) and [Rτ a]s = a(s−τ √ ) mod N . Rτ = FM Dτ FM , where Rτ = diag([FM ]0:M −1,τ M ). Bold upper-case letters denote matrices and bold lower-case letters denote vectors. R

R

hrd

hsr

S

D

S

Listening Phase

Fig. 1.

hsd

D

Cooperative Phase

Illustration of the D-STBC SC-FDE protocol.

II. S YSTEM M ODEL A. 3GPP-LTE Co-operative Uplink Consider a AF relay based D-STBC transmission scheme for SC-FDE 3GPP LTE uplink. In Fig. 1, a co-operative system is shown with one source (S) terminal, one fixed relay (R) terminal and one destination (D) terminal. All terminals are equipped with a single transmit and receiver antenna. Adopted the user co-operation protocol III proposed by Nabar et al. [20],[21]: Each transmission has two signaling phases, the first called the listening phase in which the source terminal communicate with the relay terminal. There is no direct transmission from the source to the destination terminal during this period. The second phase called co-operation phase, in which both the relay and the source terminals communicate with the destination terminal. In co-operation phase, the problem of time asynchronisation arises at the destination terminal because of time difference in propagation of the signal from the source terminal and from the relay terminal to the destination terminal. For the link between the relay and the destination, AF relaying is used, in which the relay terminal amplifies and retransmits the signal received from the source terminal in listening phase. Any linear modulation techniques such as

quadrature phase shift keying (QPSK), quadrature amplitude modulation (QAM) can be used. One radio frame One slot #1

#2

#3

#4

#19

#20

One subframe = TTI

11 00 00 11 00 11 00 11 0 1 0 1 11 00 0 1 CP

LB

1 0 0 1 0 1 0 1

SB

11 00 00 11 00 11 00 11

LB

Fig. 2.

11 00 00 11 00 11 00 11

LB

11 00 00 11 00 11 00 11

LB

11 00 00 11 00 11 00 11

LB

1 0 0 1 0 1 0 1

SB

11 00 00 LB 11 00 11 00 11

3GPP-LTE frame structure.

The 3GPP LTE uplink frame structure is shown in Fig. 2 Each uplink radio frame is of 10 ms duration and consists of 20 slots each of 0.5 ms duration. And each slot is made up of 6 long blocks (LB) and 2 short blocks (SB). Two slots form one subframe which is also called as transmission time interval (TTI). Each TTI has 12 LBs and 4 SBs and all are cyclic prefix with length Lcp to remove IBI and to make channel matrices circulant. The multipath delay spread plus propagation delay is assumed to be larger than CP length. Therefore, IBI takes place between LBs and SBs within the TTI and the circulant structure of the channel matrix gets destroyed and leads to performance degradation. B. Signal Model Assume that all underlying links experience frequency selective fading. The channel impulse response (CIR) for the j th transmission is given by hab = [hjab (0), hjab (1), · · · , hjab (Lab )], where Lab is the channel memory length corresponding to link a→ b and subscript (ab) can be source-to-relay (sr), relay-to-destination (rd) or source-to-destination (sd). The CIRs for all links vary independently for every link and are assumed to be constant over two transmissions. T T Two consecutive TTIs, sj1 = [xj1 (0), . . . , xj1 (15)]T ∈ CN T T and sj2 = [xj2 (0), . . . , xj2 (15)]T ∈ CN , where N = 12(M + Lcp ) + 4(K + Lcp ) is the length of a TTI, M is the length of a LB, K is the length of a SB, xj1 (n) and xj2 (n) ∈ CM orK are LBs or SBs from uplink frame depending upon there position in the TTI as shown in the Fig. 2 are sent in every j th transmission. Each LB contains data symbols and SB contains reference signal for channel and delay estimation. The received signal vector rjR ∈ CN at the relay during the listening phase is given by rjR = Hjsr sj1 + njR

(1)

where Hjsr ∈ CN ×N channel convolution matrix for channel from the source to the relay, and njR ∈ CN is the additive white Gaussian noise (AWGN) vector at the relay with each entry having zero-mean and variance N0 /2 per dimension.


As mentioned before, because of the timing errors, the signal from the source terminal arrives at the destination terminal τ samples later than the signal from the relay terminal in the second transmission time interval. The timing errors will cause τ samples shift between the signals from the source and the relay terminals. Assume that the amplifying factor at the relay terminal is unity. Therefore, the received vector rjD ∈ CN at the destination terminal, in the co-operative phase is given by, rjD = Hjrd rjR + Rτ Hjsd sj2 + njD Hjrd ,

(2)

III. R ECEIVER FOR P ROPOSED D-STBC SC-FDE S CHEME The receiver for the proposed D-STBC SC-FDE system is illustrated in Fig. 3. At the receiver, decoding is performed LB by LB. Therefore, the received vector can be rewritten by using (3) and (6) in terms of the LBs. After removing the CP, we obtain ˜ sr xj (n) + R ˜ rd H ˜ τ Hsd xj (n) + HIBI xj (n − 1) + wj , ˜rjD = H 1 2 2 D (8) and ˜rj+1 D

N ×N

Hjsd

where ∈ C channel convolution matrices for channel from the relay to the destination and from the source to the destination respectively, and njD ∈ CN is an AWGN vector at the destination. Finally, combining (1) and (2), we obtain, ¯jD rjD = Hjrd Hjsr sj1 (n) + Rτ Hjsd sj2 (n) + n

(3)

¯jD ∈ CN at the where we define the effective noise term n destination as ¯jD = Hjrd njR + njD n

(4) T

= [−Px∗j In the (j + 1)th transmission interval, ¯sj+1 2 (0), 2 T ∗j T . . . , −Px2 (15)] is transmitted from the source to the relay T ∗j T T terminal and ¯sj+1 = [Px∗j 1 1 (0), . . . , Px1 (15)] is transmitted from source to the destination terminals. This transmission has time reversed (TR) LBs which helps in STBC decoding as can be seen later. The channel is assumed to be quasi-static, i.e., channel matrix Hjab remains constant over the j th and (j + 1)th transmission but random and independent from TTI ∈ CN at the relay to TTI. Thus, the received vector rj+1 R during listening phase is = Hjsr¯sj+1 + nj+1 rj+1 2 R R

(5)

∈ CN at the destination terminal and the received vector rj+1 D during co-operative phase is ¯j+1 = Hjrd Hjsr¯sj+1 + Rτ Hjsd¯sj+1 +n rj+1 2 1 D D where we define the effective noise term

¯j+1 n D

∈C

N

wjD

CP Removal

IBIC

STBC Decoder

Freq. Domain Equalizer

CPR

Fig. 3.

The proposed receiver.

Demapper

x ˆ

(9) ˜rj+1 D

where J = (M −Lsd +δ) and δ = (Lsd +τ )−Lcp , the number of last samples from the previous LB which are interfering Note that the decoding is done only for the LBs and not for SBs. At the receiver, STBC decoding to estimate xj1 (n) and xj2 (n) from ˜rjD and ˜rj+1 D , will turn out to be efficient if we exploit the following properties of circulant matrices. • P1). Circulant matrices can be diagonalized by FFT operation ˜ ab H ˜H H ab

=

FH M Dab FM

(11)

=

∗ FH M Dab FM

(12)

˜ ab (ej0 ), · · · , H ˜ ab (ej2π(M −1)/M )). ˜ ab = diag(H where the D •

Delay/Channel Estimation

˜rjD ,

wj+1 D

, ∈ CM are AWGN vectors, ∈ CM where ˜ rd , H ˜ sr ∈ CM ×M are circulant channel are received vectors, H matrices for the channel from the relay to the destination and ˜ τ ∈ CM ×M is a from the source to the relay respectively, R cyclic shift matrix and Hsd ∈ CM ×M is a defective channel ˜ sd − HIBI , where H ˜ sd ∈ CM ×M matrix given by Hsd = H circulant channel matrix for channel from the source to the destination and HIBI ∈ CM ×M is a inter block interference matrix, can be written as ⎤ ⎡ hsd (Lsd ) · · · hsd (δ + 1) .. ⎥ ⎢ .. ⎥ ⎢ . 0 . ⎥ ⎢ ⎥ ⎢ .. . . ⎢ . . hsd (Lsd ) ⎥ ⎥ (10) HIBI = ⎢ 0 ⎥ ⎢ M ×J .. ⎥ ⎢ . 0 ⎥ ⎢ ⎥ ⎢ . .. ⎦ ⎣ 0 0 ··· 0

as (7)

˜ sr Px∗j (n) + R ˜ rd H ˜ τ Hsd Px∗j (n) −H 2 1 + HIBI Pxj1 (n − 1) + wj+1 D

(6)

¯j+1 n = Hjrd nj+1 + nj+1 D R D

=

˜ ab by P yields H ˜ Tab P2). Pre and Post-multiplying H ˜ ab P PH ˜ ∗ab P PH

= =

˜ Tab H ˜H H ab

(13) (14)

The first step towards equalization called IBI cancelation, which remove the unwanted IBI in the received vector from the previous LB within the TTIs. To do so, subtract the last δ samples of the previously estimated LB from the first δ samples of the current LB. Note that in the protocol for


D-STBC, each link between the source, the relay and the destination is used for only one of the two signaling phases, i.e., when the link between source and relay is busy, the other links are idle in listening phase and vice versa in co-operation phase. Therefore, the very first LB of every received TTI will have no IBI. Now the received signals after IBI cancelation is given by ¯rjD ¯rj+1 D

˜ sr xj (n) + R ˜ rd H ˜ τ Hsd xj (n) + wj H 1 2 D ˜ sr Px∗j (n) + R ˜ rd H ˜ τ Hsd Px∗j (n) = −H 2 1 =

+ wj+1 D

(15) (16)

Left multiplying (16) by P, conjugating, and then using P2, we obtain P¯r∗j+1 D

=

˜ rd xj (n) + HH ˜ j ˜ sr H −H sd Rτ x1 (n) 2 H

H

+ Pw∗j+1 D

H

squared of the ith DFT coefficient of the first and second CIR’s. The filtered noise vector has a diagonal auto-correlation ˜ Δ). ˜ Therefore, the MMSE-FDE is matrix equal to diag(Δ, represented by M × M diagonal matrix whose (i, i) element is given by Δ∗ (i, i) (22) W(i, i) = |Δ(i, i)|2 + SN1 R 2 2 where signal to noise ratio (SNR) def = σx /σn . The output of the MMSE-FDE denoted by r = W˜y, is transformed back to time domain followed by the estimate of xj1 (n) and xj2 (n). The second step towards equalization called CPR, which equalizes the channel matrix in (15) and (16). Since Hsd was not a circulant matrix, use the estimate of xj1 (n) and xj2 (n) to ˜ sd , in this way make Hsd approximately equal to H

ˇrjD

(17)

Hsd is not a circulant matrix, and, therefore, it is not possible to use minimum mean square error (MMSE) frequency domain equalizer, but to keep receiver complexity minimal and to ˜ sd instead of Hsd in (15) perform MMSE-FDE proceed with H and (17). Concatenating (15) and (17), we obtain

˜ sr ˜τH ˜ sd ˜ rd H R H ¯rjD xj1 (n) = ˜ H −H ˜H ˜H P¯r∗j+1 xj2 (n) HH D sd Rτ sr Hrd wjD + (18) Pw∗j+1 ) D Based on P1, and taking FFT of (18) we obtain

˜ sr ˜τD ˜ sd ˜ rd D D D F¯rjD Fxj1 (n) = ˜H ˜ H −D ˜H ˜H FP¯r∗j+1 Fxj2 (n) D D sd Dτ sr Drd FwjD (19) + FPw∗j+1 ) D Writing (19) more compact notation, F¯rjD Δ1 Δ2 Fxj1 (n) ydef = = Δ∗2 −Δ∗1 FP¯r∗j+1 Fxj2 (n) D

Δ FwjD (20) + FPw∗j+1 ) D ˜ sr , Δ2 = D ˜ rd D ˜ τ Dsd . where Δ1 = D Since Δ is an orthogonal matrix, we can (without loss of optimality) multiply both sides of (20) by Δ∗ to decouple the two signals xj1 (n) and xj2 (n) resulting in j ˜ 0 x1 (n) Δ ∗ def ˜ y=Δ y = ˜ 0 Δ xj2 (n) FwjD ∗ +Δ (21) FPw∗j+1 ) D ˜ def |Δ1 |2 + |Δ2 |2 where the resulting noise is still white, Δ = is an M × M diagonal matrix with (i, i) elements equal to |Δ1 (i, i)|2 + |Δ2 (i, i)|2 which also equals to the sum of the

˜ sr xj (n) + R ˜ rd H ˜ τ Hsd xj (n) H 1 2 ˜ τ Csd ˆxj (n) + w ¯j +R

=

2

ˇrj+1 D

D

˜ sr xj (n) + R ˜ sd xj (n) + w ˜ rd H ˜τH ¯ jD H 1 2 ˜ sr Px∗j (n) + R ˜ rd H ˜ τ Hsd Px∗j (n) −H

= =

2

1

2

1

˜ τ Csd Pˆx∗j (n) + w ¯ j+1 +R 1 D ˜ sr Px∗j (n) + R ˜ sd Px∗j (n) ˜ rd H ˜τH −H

=

¯ j+1 +w D M ×M

where Csd ∈ C be written as ⎡

Csd

(23)

⎢ ⎢ ⎢ ⎢ ⎢ =⎢ ⎢ 0M ×R ⎢ ⎢ ⎢ ⎣

(24)

˜ sd = Hsd + Csd , which can such that H

hsd (Lsd ) 0 .. . .. . .. . 0

··· .. . .. .

hsd (Lsd ) 0

···

⎤

hsd (δ + 1) .. .

0 0

0M ×δ

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(25) where R = (M − Lsd ). Eqs. (23) and (24) are similar to (15) and (16), so perform the same processing as it was done for (15) and (16) to get the better estimate of xj1 (n) and xj2 (n). IV. S IMULATION R ESULTS The simulation parameters consider uncoded systems with LB size of M = 256, QPSK constellation, 5MHz bandwidth and 7.36 MHz sampling frequency. All the underlying links experience frequency selective fading channels and are modeled as pedestrian B channel with 6 taps Rician fading with exponential power delay profile. Assume link S→D has maximum delay spread of 3.7 μs (28 samples) and S→R and R→D has maximum delay spread of 1.8 μs (14 samples) each. Assume maximum relative propagation delay can occur is 3.0 μs (22 samples) (the case when source and destination are 1 km apart and relay is 0.25 km from destination), and CP is 4.0 μs (30 samples). Fig. 4 shows the performance of D-STBC SC-FDE system. Under perfect synchronization, relay based system has 5dB


−1

10

Single−input singlr−output (no relay) Perfectly Synchronized (relay) Asynchronize with τ = 18 samples (2.5 μs) τ = 18 with IBIC τ = 18 with IBIC & CPR (1 iteration) τ = 18 with IBIC & CPR (2 iteration)

−2

Bit Error Rate

10

−3

−4

10

CP=30 smaples (4.0 μs) Max Delay Spread: S→ D = 28 samples (3.7 μs) S→ R = 14 samples (1.8 μs) R→ D = 14 samples (1.8 μs) 10

15

20

25

Bit Error Rate

without any technique with IBIC technique with IBIC & CPR (2 iteration) with IBIC & CPR (1 iteration)

−2

10

−4

10

−6

10

4

4.5

5

5.5

6

τ = 12 samples

6.5

7

7.5

8 −6

x 10

τ = 22 samples

SNR at 20 dB

0

10

without any technique with IBIC technique with IBIC & CPR (1 iteration) with IBIC & CPR (2 iteration)

−2

10

−4

10

−6

10

4 τ=2

4.5

5

5.5 6 6.5 7 Relative delay + Max. delay spread (3.7 μs) τ = 14 samples

7.5

8

τ = CP

−6

x 10 τ = 27 samples

Fig. 5. BER vs relative propagation delay comparison for relay based proposed techniques.

show that the proposed technique of interblock interference cancelation and CP reconstruction, gracefully combat time asynchronization in D-STBC SC-FDE transmission scheme. In future, we will extended this technique over multiple relays, MIMO communications, with channel coding. R EFERENCES

10

5

SNR at 15 dB

0

10

Bit Error Rate

performance gain at bit error rate (BER) = 10−3 over the SISO case, because of co-operative diversity associated with the relay based system. System performance degrades significantly when there is time asynchronism in the system. Here the relative propagation delay of 18 samples plus the maximum delay spread of 28 greater than CP duration of 30 samples. Under the assumption that delay is unknown to receiver, BER degrades because of IBI effect and defective channel matrix structure. The case where the channel and the delay are known to the receiver, system performance improves significantly after IBI cancelation. BER further improves by 2 dB when cyclic prefix is reconstructed which helps in making the channel matrix to circulant matrix. There is further improvement on performance with one more iteration over CPR loop. Since, the proposed techniques can’t remove the errors completely, therefore there is an error floor in the curves at high SNR region. Fig. 5 compares the BER versus relative propagation delay with and without proposed techniques. The propagation delay is varied from 2 samples delay up to the 30 samples delay (CP length). At SNR = 20 dB and BER = 10−3 , it can be observe that the combined IBIC and CPR technique has longer delay tolerance of 27 samples (3.8 μs) than to the technique having only IBIC or none. At SNR = 15 dB, the proposed techniques have inferior performance to the SNR = 20 dB.

30

SNR [dB]

Fig. 4. BER vs SNR for uncoded system for SISO (no relay) and for relay based proposed techniques with and without relative propagation delay of 2.5 µs (18 samples) under pedestrian B channel.

V. C ONCLUSION This paper discussed the effect of time asynchronism in a relay based system for SC-FDE system. Proposed technique to combat the problem, has been constructed on top of the 3GPP LTE uplink standard. Under the condition that relative propagation delay plus multipath delay spread is larger than CP length, there is degradation in the performance is caused by unwanted interference and defective channel matrix. Simulation results

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