6SDWLDO7HPSRUDO 3URFHVVLQJLQ7'6&'0$ Chengke Sheng Ed Martinez WHITE PAPER TPTDSCDMAWP Rev. 0, 9/2004 Spatial Temporal Processing in TD-SCDMA Table of Contents 1. INTRODUCTION.............................................................................................................. 5 2. TYPES OF CHANNEL IMPULSE RESPONSE ...............................................................12 2.1. 2.2. NON-DIRECTIONAL CHANNEL IMPULSE RESPONSE. ...........................................................12 DIRECTIONAL CHANNEL IMPULSE RESPONSE ....................................................................12 3. ESTIMATION OF NON-DIRECTIONAL CHANNEL IMPULSE RESPONSE....................14 4. ESTIMATION OF DIRECTIONAL CHANNEL IMPULSE RESPONSE.............................17 5. ESTIMATION OF TRANSMITTED DATA .......................................................................18 6. SUMMARY .....................................................................................................................21 Error! Reference source not found. 2 Spatial Temporal Processing in TD-SCDMA Table of Figures FIGURE 2-1 ANTENNA ARRAY MODEL .............................................................................................13 FIGURE 5-1 STRUCTURE OF THE SPREADING SIGNATURE CODE MATRIX .............................................18 FIGURE 5-2 STRUCTURE OF VECTOR CD ........................................................................................19 FIGURE 5-3 THE STRUCTURE OF MATRIX HDA(K,KD) .............................................................................19 Error! Reference source not found. 3 Spatial Temporal Processing in TD-SCDMA Terms and Acronyms Term CDMA JD TD-SCDMA UMTS Mcps Error! Reference source not found. Definition Code Division Multiple Access Joint Detection Time Division Synchronous CDMA Universal Mobile Telecommunications System Mega Chip Per Second 4 Spatial Temporal Processing in TD-SCDMA 1. Introduction 1.1. Scope and Audience This paper presents details of the spatial-temporal processing of a received TDSCDMA signal and its channel impulse response. This document is targeted at systems engineers who are designing TD-SCDMA systems who are interested in deploying the Motorola MRC6011 in their designs. It is also targeted to applications engineers and marketing professions who want to learn more about the broad range of applications of the Motorola RCF technology. 1.2. Executive Summary CDMA based systems suffer from Multiple Access Interference (MAI) and it affects all users equally. FDD based systems attempt to deal with the problem by using detection schemes such as the rake receiver, however these schemes are sub-optimal because they only consider one user's signal information and do not take into account the interference from all other users in the system. Joint Detection algorithms on the other hand are designed to process all users in parallel by including the interference information from the other users. In general Joint Detection schemes are complex and computationally intensive (complexity grows exponentially as the number of users increases) because most of the operations are matrix and vector based operations, as the number of the users increase, the sizes of the matrices and vectors increases and therefore the computation power that is required to separate the users. TD-SCDMA however, solves this problem by limiting the number of users in a given time slot to 16, this creates a very manageable number of users that need to be processed in parallel, furthermore these users are also synchronized. 1.3. Background In the year 1998 the Chinese Wireless Telecommunications Standards (CWTS, http://www.cwts.org) put forth a proposal to the International Communications Union (ITU) based on TDD and Synchronous CDMA technology (TD-SCDMA) for TDD. This proposal was accepted and approved by the ITU and became part of 3GPP in March of 2001. TD-SCDMA was incorporated as part of the TDD mode of operation in addition to the existing TDD-CDMA mode of operation. To accommodate both modes, 3GPP now includes a "low chip rate" mode of 1.28 Mcps that corresponds to the TD-SCDMA specifications. Because of this TD-SCDMA is sometimes referred to as the low-chip rate mode of UTRA TDD. Table 1-1 shows where TD-SCDMA fits in relationship to other 3GPP standards Error! Reference source not found. 5 Spatial Temporal Processing in TD-SCDMA 3GPP Name Access Mode Chip Rate WCDMA FDD 3.84 Mcps TDD-CDMA TDD 3.84 Mcps TD-SCDMA TDD 1.28 Mcps Table 1-1 TD-SCDMA in relationship to other 3G standards Error! Reference source not found. 6 Spatial Temporal Processing in TD-SCDMA 2. Signal Model 2.1. TDD/TDMA Internet based applications, media (audio and video) enabled applications and file transfers have very different bandwidth requirements for uplink and downlink traffic. TD-SCDMA does not dictate a fixed utilization of the frequency band; rather uplink and downlink resources are assigned according to traffic needs. UL DL Symmetric Traffic UL DL Asymmetric Traffic Figure 2-1 Symmetric and Asymmetric traffic support in TD-SCDMA The variable allocation of the time slots for uplink or downlink traffic is what allows TD-SCDMA to efficiently support asymmetric traffic requirements and a variety of users. Figure 2-1 illustrates this principle where for symmetric traffic, the time slots are equally split and for asymmetric traffic the DL can use more time slots. 2.2. TD-SCDMA Frame Hierarchy TD-SCDMA uses both unique codes and time signatures to separate the users in a given cell. The standard defines a very specific frame structure as shown in Figure 2-2. There are three different layers: the radio frame, the sub-frame and the individual time slots. Depending on the resource allocation, the configuration of the radio frames becomes different. The radio frame is 10ms; the sub-frame is 5 ms in length and is divided into 7 slots. The standard also specifies various ratios for the number of slots between these two groups in order to meet specific traffic requirements. All physical channels require a guard symbol in every time slot. Error! Reference source not found. 7 Spatial Temporal Processing in TD-SCDMA Radio Frame (10 ms) Frame #i Frame i+1 Subframe (5 ms) Subframe #1 TS0 Subframe 2 TS1 TS2 TS3 TS4 TS5 TS6 Time Slot (0.675 ms) Data Midamble Data G Time Slot (0.675 ms) Figure 2-2 TD-SCDMA Frame Structure 2.3. TD-SCDMA Slot Structure A TD-SCDMA time slot has been designed to fit into exactly one burst. The time slot (Figure 2-3) consists of four parts, a midamble with 144 chips duration, and two identical data fields with 352 chips duration at each side of the midamble and followed by a 16 chips guard period. The midamble is used by the receiver to carry out channel estimation tasks. Data symbol s 352chips Midamble 144 chips Data symbol s 352 chips GP 16 CP 675 s Figure 2-3 The TD-SCDMA Slot Structure Error! Reference source not found. 8 Spatial Temporal Processing in TD-SCDMA 3. System Model 3.1. Channel Model In a TD-SCDMA system, we have K users who access the channel simultaneously. On the same frequency and in the same time slot. Figure 3-1 shows a general model of a TD-SCDMA System. (1) C (1) d (k ) d b C (k) (K ) d n h(1) b C(K) b (1) d (1) e Data Esti mation h(k) (k ) h(K) (k ) d (K ) d (K ) Figure 3-1 Discrete base band model of a TD-SCDMA system. In the system of Figure 3-1 we assume that there are Ka antennas for the receiver . th The k user transmits a data symbol sequence block with N symbols: ( (k ) [ (1) d (k ) = d1 , d 2 (k ) d ) (k ) T d ( k ) = d 1 , d1 , ( 2) d (k ) 1 (1) k = 1,2,.....,K N (1) ( 2) , d2 , d2 , d , , d (k ) 2 (1) N , dN ( 2) , d ] (k) T N (2) Where N is the number of symbols in each data block. ( c ( k ) = c1 c 2 (k ) (k ) d ) (k ) T k = 1, 2 ... K Q (3) c (k ) is the kth user signature, N is the number of symbols in each data block and Q is the spreading factor. All users are assumed to be at the same spreading factor. Each of the K channels in the system is characterized by its impulse response [ h ( k ) = h1 h2 (k ) (k ) h ] (k ) T W k = 1,2 ... K (4) Where W is the number of taps in the channel. Error! Reference source not found. 9 Spatial Temporal Processing in TD-SCDMA Similarly, we have the noise vector for antenna ka [ n ( ka ) = n1 ( ka ) n2 ( ka ) n ( ka ) NQ +W -1 ] T (5) and [ N = n (1) n ( 2 ) n ] ( Ka ) T (6) n = vec [N] The transmission of the block on N symbols can be modeled by a system of linear equations that relates the spreading codes, the channel's input response and the impact of noise in the signal. 3.2. Received Signal Model th The received sequence received at chip rate from the ka antenna is: (ka) e (ka) = (e1 (ka) , e2 (ka) T , . . . , eNQ+W-1 ) (7) where Q again is the spreading factor of the data symbol and W is the number of taps in channel. e ] [ E = e (1) , e ( 2) . ( Ka ) T e = vec[E] (8) = c(k ) * h ( k ,ka ) (9) From Figure 3-1 we can see that ( b ( k ,ka ) = b1 ( k , ka ) , b2 ( k ,ka ) , b ) ( k , ka ) T Q +W -1 Is the convolution of the channel input response with the corresponding spreading code. ( k ,ka ) (h is the channel impulse response between the user k and antenna ka, c(k) is the spreading code of the user k.) Then the we can see that the signal arriving at the receiver can be described by a linear system of equations that relate the user's signal and the receiver input: E = A (I ( Ka ) d) + N Where, 8 is the Kronecker product . (10) Or e = Ad + n (11) The matrix A is called channel matrix and is defined as [ A = A (1) A ( 2) A ] Error! Reference source not found. ( Ka ) T (12) 10 Spatial Temporal Processing in TD-SCDMA K K b (ka) b(ka) A (ka) NQ+W = b (ka) = b (1,kaa)) (2,ka) b b (K,ka) Q+W b(ka) Figure 3-2 The Channel Matrix A Error! Reference source not found. 11 Spatial Temporal Processing in TD-SCDMA 4. Types of Channel Impulse Response When dealing with spatial-temporal signal processing in the TD-SCDMA, we need to identify two types of channel impulse responses - non-directional channel impulse response and directional channel impulse response. 4.1. Non-Directional Channel Impulse Response. Let's first discuss the non-directional channel impulse response. The impulse response is defined between each individual user and its antenna. A nondirectional channel response between user k and antenna ka can be modeled as a FIR filter with W taps: h (k,ka) (k,kd) , (k,kd) , h2 = [h1 ... , hW (k,kd) T ] (13) We can stack all of the channel impulse responses of the k users together to form the non-directional channel impulse response matrix: H (k ) h 1 ( k ,1) ( k ,1) h = 2 ( k ,1) h W ( k ,2) h1 ( k , 2) h2 hW ( k , Ka ) h1 ( k , Ka ) h2 ( k , Ka ) hW ( k ,2) (14) Then we stack all users' matrixes together to form the system non-directional channel impulse response matrix: H = [ H(1)T, H(2)T,......, H(K)T ] 4.2. Directional Channel Impulse Response The second type of channel impulse response is the directional channel impulse response. The directional channel impulse response is directly related to each signal path with a DoA and it is defined to be the channel impulse response between user k and a reference point: (k,kd) hd (k,kd) , = [hd1 (k,kd), hd2 ... , hdW (k,kd) T ] Similarly as with the non-directional channel impulse response matrix, we have: Hd (k) h d1 ( k ,1) ( k ,1) h = d2 ( k ,1) h dW ( k ,2) h d1 ( k , 2) h d2 h dW ( k ,2) ( k , Kd ( k )) h d1 ( k , Kd ( k )) h d2 ( k , Kd ( k )) h dW (15) Where Kd(k) is the number of DoA paths of the kth user. Error! Reference source not found. 12 Spatial Temporal Processing in TD-SCDMA Hd = [ Hd (1), Hd (2),......, Hd (K)] (16) (Note that there is no transpose operation) There is a close link between the non-directional channel impulse response and the directional channel impulse response. The non-directional channel impulse response for a given user k and given antenna ka is the summation of all directional channel impulse responses of the user k on the antenna ka: h (k, ka) = Kd ( k ) e j ( k , ka , kd ) hd ( k , kd ) (17) kd =1 where (k,ka,kd) = {2L(ka)cos((k,kd) - (ka) )}/ (k) 1...Kd ; k=1...K ka = 1...Ka and kd = Interference ki Antenna ka (ki) (ka) (k,kd) L(ka) Reference point Signal k, DoA kd Figure 4-1 Antenna array model For a given user k and DoA kd , e j(k,ka,kd) ( ka = 1....Ka) forms its steering vector. Thus we define: A(k) = [ a(k,1), a(k,2),....., a(k,Kd(k))] k=1...,K (18) th as the user k user's steering matrix. Then the relation between the directional channel impulse response and non-directional channel impulse response is given by H (k ) = Kd ( k ) hd ( k ,kd ) a ( k , kd )T = H d (k ) A ( k )T (19) kd =1 Error! Reference source not found. 13 Spatial Temporal Processing in TD-SCDMA 5. Non-directional channel impulse response We will estimate the non-directional channel impulse response first. The estimated response can be used to estimate the DoA for each user and each path. Then based on the estimated DoA and non-directional channel impulse response, the directional channel impulse response can be derived. The estimation will be based on the midamble training sequence with length of W+L., where W is the maximum number of channel delay taps. Suppose we have x = Ad + n, where n is a Nx1 Gaussian noise vector (it is not necessary to be white), A is an Nxp known matrix, d is px1 signal vector and x is Nx1 observed signal, then a ML estimator of d can be derived as -1 -1 d = (A H R n A) A H R n x (20) is an efficient MVU (Minimum Variance Unbiased estimator reaching Actually, the estimator d the Cramer-Rao Lower Bound) if the vector n is a complex Gaussian noise vector. (ka) for ka=1...Ka. em(ka is the received signal Now, we define Ka Lx1 column vectors: em for the antenna ka based on the last L midamble training sequence. Stack Ka vectors together to form the received L x Ka matrix ) Em = [em(1) , em(2) ,..., em(Ka) ] Similarly, we define received noise vectors and LxKa matrix Nm = [nm(1) , nm(2) ,..., nm(Ka) ] Then we have Em= GH + Nm where the matrix G is an L x KW observing matrix. Moreover we have (Ka) em= vec{ Em }= vec{ GH } + vec{Nm} = vec{ GHI } + nm (Ka) G)vec{H}+ nm = (I(Ka) G)h+ nm (Ka) is a Ka-by-Ka identity matrix, and is the Kronecker product operator. = (I where I (21) Thus, from (8), we have -1 -1 h = {( I ( ka ) G ) H R m (I ( ka ) G )}-1 (I ( ka ) G ) H R m e m (22) Now we have to work out the matrix G and the noise covariance matrix Rm before the nondirectional channel impulse response vector h can be obtained. We define the matrix G to be G = [G(1), G(2),..., G(K)] (23) (k) where G k=1...K is the LxW Toeplitz matrix of the midamble training sequence for the kth user. It is clear that the matrix G is pre-defined since it is composed from the given midamble training code for all K users. For the noise covariance matrix Rm, we have Error! Reference source not found. 14 Spatial Temporal Processing in TD-SCDMA R m (1,1) ( 2,1) R Rm = m ( Ka ,1) R m Rm Rm (1, 2 ) ( 2,2 ) ( Ka , 2 ) (1, Ka ) ( 2 , Ka ) Rm Rm ( Ka , Ka ) Rm Rm (24) In (24), we have Rm(i,j) = E{ nm(i)nm(j)H } Ki = E{ e j ( ki ,i ) nd ( ki ) ki =1 Ki e - j ( kj , j ) nd ( kj ) H } kj =1 Ki = E{ e j [ ( ki ,i )- ( ki , j )] nd ( ki ) nd ( ki ) H } ki =1 Ki ~ ( ki ) = e j [ ( ki ,i )- ( ki , j )] Rm ( ki ) 2 ki =1 ~ where R m ( ki ) = E{n d ( ki ) nd ( ki ) H ~ ( ki ) } / ( ki ) 2 . Notice that R m is the same for all Ki, Then let Ki ~ ~ ( ki ) * R m = R m for all ki=1....Ki and ri , j = ri , j = ( ( ki ) 2 )e j[ ( ki ,i )- ( ki , j )] ki =1 we have Rm (i , j ) ~ = ri , j Rm for i,j = 1.....Ka and ~ Rm = Rd Rm (25) where [Rd ]i,j = ri,j ~ The matrix R m is a temporal covariance matrix and Rd is spatial covariance matrix. From (10) -1 -1 h = {( I ( ka ) G ) H R m (I ( ka ) G )}-1 (I ( ka ) G ) H R m e m since (ka) (I ~ -1 -1 H G ) (Rd Rm ) -1 H ~ -1 = Rd G Rm G ) Rm = (I H -1 (ka) Error! Reference source not found. 15 Spatial Temporal Processing in TD-SCDMA -1 -1 H ~ -1 -1 H ~ -1 h = { Rd G Rm G } (Rd G Rm )em -1 H ~ -1 -1 H ~ -1 = { Rd ( G Rm G ) }(Rd G Rm )em (ka) H ~ -1 -1 H ~ -1 = {I ( G Rm G ) G Rm }em (ka) Mm}em = {I Where ~ ~ -1 M m = (G H R m G ) -1 G H R m ~ ( If R m = 1 then M m = G G H ) -1 -1 GH Error! Reference source not found. 16 Spatial Temporal Processing in TD-SCDMA 6. Directional channel impulse response The directional channel impulse response is based on each directional signal path. It is the impulse response between a given directional signal path and reference point. Based on (7) H (k ) = Kd ( k ) hd ( k ,kd ) a ( k , kd )T = H d (k ) A ( k )T kd =1 (k) (k)T if H and A (k) can be obtained or estimated, then Hd can be derived. From em = vec{G H } + nm = Gdhd + nm we have the ML estimator of hd ~ ~ H H h d = (G d (R d R m ) -1 G d ) -1 G d (R d R m ) -1 e m ~ -1 ~ -1 H H -1 -1 where X m = (G d ( R d R m ) G d ) is the decorrelator filter and G d ( Rd @ Rm ) is the spatial-temporal whitening matched filter and ( ) ( ) (A ) ( ) ( ~ -1 A (1) H G (1) H R d -1 R m H -1 G d (R d R m ) = ~ -1 A ( K ) H G ( K ) H R d -1 R m ( = ) ~ -1 -1 R d G (1) H R m ~ -1 -1 A (1) H R d G (1) H R m (1) H ) Then we have ~ Vec{G~(1)HRm-1 Em (Rd -1)*A(1)* } ~ Vec{G(2)HRm-1 Em (Rd -1)*A(2)* } GdH(Rd Rm) -1 vec{Em}= ~ Vec{G(K)HRm-1 Em (Rd -1)*A(K)* } Where G(k)HRm-1 is the temporal whitening matched filter and (Rd -1)*A(k)* is the spatial whitening matched filter of the user k. We define the spatial whitening matched filter W (k) =(Rd-1)*A(k)* = [ w(k,1), w(k,2),....., w(k,Kd(k))], thus w(k,kd) is beanformed for the kd's DoA. Error! Reference source not found. 17 Spatial Temporal Processing in TD-SCDMA 7. Estimation of transmitted data Based on the directional channel impulse response, we will estimate the transmitted data. As we will see, beam-forming will be generated for each DoA path and all the DoA paths of the same user will be coherently combined to enhance the system's performance. We define vector d as the transmitted data column vector of length KN for all K users; d = [d(1)T, d(2)T,......, d(K)T]T where d(k)T is user k's transmitted data vector of length N Define matrix E the received signal matrix with dimension (NQ+W-1) x Ka: E = [ e(1), e(2),....., e(Ka)], where e(ka) is the received signal vector of length NQ+W-1 from antenna ka. And we also define e = vec{E} and the combined noise vector n = [n(1)T, n(2)T,......, n(K)T]T of length (NQ+W-1)Ka: The data d has to been spreaded by the special signature code before it can be transmitted, thus we define the spreading signature code matrix for user k: Q (k) C (N) =I N blocks = NQ rows c = (k) N Figure 7-1 Structure of the Spreading signature code matrix (k) (k) Where c is the special signature code for user k, k=1...K. Stack all C k=1...K together to form the combined signature code matrix (1) C = blockdiag[ C (2) ,C (K) ,....., C ] The spreaded data can be written as: (1) C d = blockdiag[ C (2) ,C (K) ,....., C Error! Reference source not found. ] [d(1)T, d(2)T,......, d(K)T]T 18 Spatial Temporal Processing in TD-SCDMA k=1 NQ KNQ = k=2 k=K Figure 7-2 Structure of Vector Cd The received signal vector e is the transmitted spreaded data pass the directional channel plus the noise: e = Ad Hda C d + n Where Ad= A I (NQ+W-1) (1) Hda= blockdiag[ Hda H da (k ) , A=[A(1), A(2),......, A(K)] and (2) , Hda (K) ,....., Hda ] H da ( k ,1) ( k ,2) H da = ( k , Kd ( k )) H da hd1(k,kd) W Had(k,kd) = NQ+W = hd2(k,kd) hdW(k,kd ) All vectors are N Figure 7-3 The structure of matrix Hda(k,kd) Error! Reference source not found. 19 Spatial Temporal Processing in TD-SCDMA Then based on the ML rule, we can estimate transmitted data: ~ -1 ~ -1 H H -1 H H -1 H -1 H d = ( C Hda Ad (Rd Rn )AdHdaC) C Hda Ad (Rd Rn ) e ~ -1 H H -1 H = X C Hda Ad (Rd Rn )e ~ -1 H -1 where X = ( C Hda Ad (Rd Rn )AdHdaC) is a zero force equalizer. H ~ H -1 -1 Since Ad (Rd Rn ) =( A I H -1 H (NQ+W-1) ~ -1 ~ ) (Rd Rn )= A Rd Rn -1 H -1 -1 ~ -1 ~ -1 H -1 H -1 T H H H d = X C Hda (A Rd Rn )vec{E} = X C Hda vec{ Rn E (Rd ) A*} We define w(k,1) (k) -1 T W = (Rd ) A (k)* w(k,2) w(k,Kd(k)) = K Kd(k) As the weight matrix for the user k and -1 T (1,1) (1,Kd(1)) ,......, w(K,1),..., w(K,Kd(K))] is the combined antenna weight matrix W = (Rd ) A* = [ w , ..., w for all K users. Then the combined beam output is (1,1) Z = EW = [y , ..., y(1,Kd(1)),......, y(K,1),..., y(K,Kd(K))], where y(k,kd)= Ew(k,kd) ~ -1 ~ -1 H -1 H H H H d = X C Hda (A Rd Rn )vec{E} = X C Hda vec{ Rn E W } ~ -1 H H = X C Hda vec{ Rn Z } ~ ~ -1 -1 (Kd) Since vec{ Rn Z }= vec{ Rn Z I (Kd) } =( I ~ -1 Rn )vec{Z}, then ~ -1 H (Kd) H d = X C Hda ( I Rn )vec{Z} is the estimate of the transmitted data. H H (Kd) = X C Hda ( I ~ -1 (1,1)T (1,Kd(1))T ,......, y(K,1)T,..., y(K,Kd(K))T] Rn ) [y , ..., y Error! Reference source not found. 20 Spatial Temporal Processing in TD-SCDMA 8. Summary In this paper, the spatial-temporal processing of a received TD-SCDMA signal is presented. The directional channel impulse response is estimated based on the non-directional response. It is shown in this paper that the ML estimator of the transmitted data utilizes both the temporal and spatial information of the signal and that the estimator consists of a bean former followed by a zero-force equalizer. Error! Reference source not found. 21 Spatial Temporal Processing in TD-SCDMA References 1. http:// www.3gpp.org 2. http://www.tdscma.org. 3. Josef Johannes Blanz, Apostolos Papathanassiou, Martin Haardt, Ignasi Furio and Paul Walter Baier, "Smart Antennas for Combined DoA and Joint Channel Estimation in TimeSlotted CDMA Mobile Radio Systems with Joint Detection" IEEE Tran. On vehicular tech. Vol.49, No.2, March 2000. Error! 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