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ZF-BLE Joint Detection for
TD-SCDMA
Chengke Sheng
Ed Martinez
February 19, 2004
ZFBLEWP./D
Rev 0
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Table of Contents
1.
INTRODUCTION .......................................................................................................................... 6
1.1.
1.2.
1.3.
2.
SIGNAL MODEL........................................................................................................................... 8
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2.1.
2.2.
2.3.
3.
CHANNEL MODEL .................................................................................................................... 10
RECEIVED SIGNAL MODEL ....................................................................................................... 11
ZERO FORCE BLOCK JOINT ESTIMATOR........................................................................... 13
4.1.
4.2.
4.3.
5.
TDD/TDMA ............................................................................................................................. 8
TD-SCDMA FRAME HIERARCHY ............................................................................................... 8
TD-SCDMA SLOT STRUCTURE .................................................................................................. 9
SYSTEM MODEL........................................................................................................................ 10
3.1.
3.2.
4.
SCOPE AND AUDIENCE ............................................................................................................... 6
EXECUTIVE SUMMARY ............................................................................................................... 6
BACKGROUND ........................................................................................................................... 6
ESTIMATING THE CHANNEL MATRIX A ..................................................................................... 13
COMPUTATION OF THE WHITENING MATCHED FILTER ............................................................... 15
COMPUTATION OF THE ZERO FORCE EQUALIZER ....................................................................... 16
JOINT DETECTION RECEIVER IMPLEMENTATION ......................................................... 18
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Table of Figures
FIGURE 2-1 SYMMETRIC AND ASYMMETRIC TRAFFIC SUPPORT IN TD-SCDMA ........................................... 8
FIGURE 2-2 TD-SCDMA FRAME STRUCTURE [6]....................................................................................... 9
FIGURE 2-3 THE TD-SCDMA SLOT STRUCTURE [5]................................................................................... 9
FIGURE 3-1 DISCRETE BASE BAND MODEL OF A BLOCK TRANSMISSION CDMA SYSTEM. ............................ 10
FIGURE 3-2 THE CHANNEL MATRIX A ..................................................................................................... 12
FIGURE 4-1 ZF-BLE ESTIMATOR ............................................................................................................. 13
FIGURE 4-2 ESTIMATION OF THE SPATIAL COVARIANCE MATRIX .............................................................. 15
FIGURE 4-3 ZERO FORCE EQUALIZER MATRIX ......................................................................................... 16
FIGURE 4-4 C0 AND C1 SUBMATRICES ....................................................................................................... 17
FIGURE 5-1 JOINT DETECTION BASED RECEIVER ...................................................................................... 18
FIGURE 5-2 MRC6011 BASED TD-SCDMA RECEIVER............................................................................. 19
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Terms and Acronyms
Time Division Duplex
Frequency Division Duplex
Code Division Multiple Access
Time-Division Multiple Access
Frequency-Division Multiple Access
Base station
Multiple Access Interference
Reconfigurable Computing Fabric
Joint Detection
Zero-Forcing Block Linear Equalizer
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TDD
FDD
CDMA
TDMA
FDMA
BS
MAI
RCF
JD
ZF-BLE
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Abstract
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This paper presents the Block Linear Equalizer (ZF-BLE) Joint Detection Algorithm, which is one of the
algorithms used in the implementation of a TD-SCDMA receiver. The paper presents a very brief
introduction to TD-SCDMA and the technical aspects relevant to the discussion of the Joint Detector,
including a brief signal and system mode, followed by a detailed description of the ZF-BLE algorithm and
finally a discussion of its implementation.
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1.
Introduction
1.1.
Scope and Audience
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This documented is targeted at wireless systems engineers who are interested in obtained
detailed knowledge in the mathematical background behind the Zero Forcing Block
Linear Equalizer (ZF-BLE) Joint Detection Algorithm used in TD-SCDMA systems. The
paper presents a very brief introduction to TD-SCDMA and the technical aspects relevant
to the discussion of the Joint Detector, including a brief signal and system model, this is
followed by a detailed description of the ZF-BLE algorithm and finally a discussion of its
implementation.
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. This results in a reasonable
complexity joint detector that can be easily implemented in today’s parallel
computational architectures.
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
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3GPP
Name
Access Mode
Chip Rate
WCDMA
FDD
3.84 Mcps
TDD-CDMA
TDD
3.84 Mcps
TD-SCDMA
TDD
1.28 Mcps
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Table 1-1 TD-SCDMA in relationship to other 3G standards
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2.
Signal Model
2.1.
TDD/TDMA
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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 TDSCDMA to 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 [6].
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Radio Frame (10 ms)
Frame #i
Frame i+1
Subframe (5 ms)
Subframe #1
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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 [6]
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 symbols
352chips
Midamble
144 chips
Data symbols
352 chips
GP
16
CP
675 µs
Figure 2-3 The TD-SCDMA Slot Structure [5]
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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 TDSCDMA System.
(1)
C (1)
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d
M
(k )
d
b
C (k)
M
(K )
d
n
h(1)
b
C(K)
b
(1)
dˆ
M
(1)
e
M
Data
Estimation
h(k)
M
M
(k )
(k )
dˆ
(K )
dˆ
h(K)
(K )
Figure 3-1 Discrete base band model of a block transmission CDMA system.
In the system of Figure 3-1 we assume that there are Ka antennas for the receiver .
The kth user transmits a data symbol sequence block with N symbols:
(
(k )
[
(1)
d (k ) = d1 , d 2
(k )
Kd N
)
(k ) T
k = 1,2,…..,K
d ( k ) = d 1 , d1 , K d 1 , d 2 , d 2 , K d 2 , K, d N , d N
( 2)
(k )
(1)
( 2)
(k )
(1)
( 2)
(1)
,K d N
(k)
]
T
(2)
Where N is the number of symbols in each data block.
(
c ( k ) = c1 c 2
(k )
(k )
Kd Q
)
(k ) T
k = 1, 2 … K
(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 )
K hW
(k )
]
T
k = 1,2 … K
(4)
Where W is the number of taps in the channel.
Similarly, we have the noise vector for antenna ka
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[
n ( ka ) = n1
( ka )
n2
( ka )
K n NQ +W −1
( ka )
]
T
(5)
and
[
N = n (1) n ( 2 ) K 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.
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3.2.
Received Signal Model
The received sequence received at chip rate from the kath antenna is:
e
(ka)
= (e1
(ka)
, e2
(ka)
, . . . , eNQ+W-1
(ka) T
)
(7)
where Q again is the spreading factor of the data symbol and W is the number of taps in
channel.
[
E = e (1) , e ( 2) .K e ( Ka )
]
T
e = vec[E]
(8)
)
(9)
From Figure 3-1 we can see that
(
b ( k ,ka ) = b1
( k , ka )
, b2
( k ,ka )
,K bQ +W −1
( k , ka ) T
= c(k ) * h ( k ,ka )
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
(10)
Where, U is the Kronecker product .
Or
e = Ad + n
(11)
The matrix A is called channel matrix and is defined as
[
A = A (1) A ( 2) K A ( Ka )
]
T
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(12)
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K
K
b
(ka)
b(ka)
A
(ka)
NQ+W
=
b
(ka)
=
b
(1,kaa)) (2,ka)
b
b
(K,ka)
Q+W
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b(ka)
Figure 3-2 The Channel Matrix A
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4.
Zero Force Block Joint Estimator
We want to find the estimate of the transmitted data vector d from the received signal E.
E = A (I ( Ka ) ⊗ d) + N
(13)
If we treat the data vector d as an unknown nonrandom vector, we want to find an estimate of the N data
symbols transmitted by the kth user during the sub frame Based on the principle of Maximum Likelihood
estimation, we can obtain this estimate by
−1
−1
dˆ = ( A H R n A ) −1 A H R n e
{
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where R n = E nn
H
} is the noise covariance matrix. Since we need R
-1
H
singular. We will use the Cholesky decomposition: Rn = L L to arrive at Rn
-1
n we
-1
(14)
assume that Rn is non-
The estimation of the data block the data block dˆ can be broken to a Whitening Filter A Rn followed by a
H
-1
-1
Zero-Force Equalizer (A Rn A) (see Figure 4-1).
H
e = Ad + n
Channel
A
Whitening
Filter
L
Matched
Filter
A HLH=
(LA)H
-1
Zero-Force
equalizer
(A HRn-1A)-1
n
Figure 4-1 ZF-BLE Estimator
To estimate the data vector d, we need to know both noise covariance matrix Rn and the channel matrix A.
4.1.
Estimating the Channel Matrix A
Estimation of the channel matrix A is based on the midamble chips in each slot.
Suppose em(ka) = (e1(ka) , e2(ka) ,. . . , eL(ka))T is the received midamble chip vector from
antenna ka and the received midamble chips are not contaminated by its previous data
symbol. (Thus, we pick up the midamble chips from 17 to 144 for a total of 128 chips,
i.e. L = 128 and we assume that the multi-path dispersion is within 16 chips).
We stack all Ka such vectors together to form the received matrix.
−1
−1
dˆ = ( A H R n A ) −1 A H R n e
(1)
(2)
(ka)
Em = [em , em , … , em
]
(15)
(16)
Similarly, the received noise vector for antenna ka is
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^
d
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(ka)
nm
= (n1
(ka)
, n2
(1)
(ka)
(ka)
)T and stacked noise matrix is
, . . . , nL
(2)
(ka)
Nm = [nm , nm , … , nm
(17)
]
(18)
We define h(k,ka) as the W-tap channel impulse response between the user k and antenna
ka
(k,ka)
h
= (h 1
(k,ka)
, h2
(k,ka)
(k,ka) T
, . . . , hW
)
(19)
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Then the channel impulse response matrix for user k is stacked matrix from all Ka
antennas:
H
(k)
(k,1)
= [h
H = [H
(k,2)
,h
(1)T
,H
(2)T
(k,ka)
,…, h
]
(20)
(K)T T
,…, K
]
The key to estimate the channel matrix A is to estimate the channel’s impulse response
based on the given midamble training code sequence. Thus we build up the midamble
matrix:
(k)
G is a L x W Toeplitz matrix of the midamble training code sequence for kth user. And
(1)
(2)
(K)
G = [G , G , … , G
] stacked midamble training code matrix for all users
(21)
.Then, we have
Em = GH+ Nm
(22)
(Ka)
em = vec{Em} = vec{GH+ Nm } = vec{GH} + vec{ Nm } = ( I
(ka)
=(I
(Ka)
where I
UG )vec{H} + nm
(23)
U G )h + nm
is a Ka x Ka identity matrix.
Then the ML estimator of vector h is
−1
−1
hˆ = {I (Ka) ⊗ (G H R t G ) −1 G H R t }e m
Where
(24)
H
Rm = E{ nmnm }= RdURt
Then, we have
−1
−1
(ka)
hˆ (ka) = (G H Rt G ) −1 G H Rt e m
(25)
Since Rt is the temporal covariance, we will assume that Rt = I, Then
(ka)
(ka)
hˆ (ka) = (G H G ) −1 G H e m = Me m
where
H
–1
(26)
H
M =(G G) G
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-1
If G is a square matrix, then M = G is a square right circulant matrix, then [4]
(ka)
h
= D*Λ m D em
(ka)
= IFFT(FFT( em
4.2.
= IFFT( Λ m FFT( em
(ka)
(ka)
))
(27)
)/.Diag(Λ m ) )
(28)
Computation of the Whitening Matched Filter
From the previous analysis, it is known that the estimated data vector can be written as
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−1
−1
dˆ = ( A H Rn A) −1 A H Rn e = (AHRn-1A)-1 dMF
where Rn = RdU Rt = RdU I and
output.
H
(29)
-1
dMF = A Rn e is the whitening matched filter
The key to compute the whitening match filter output is to estimate the spatial covariance
matrix Rd
[ Rd ]i,j = Σp=1 (np
M
(i)
np(i)*)/Μ = (n(i)n(j)H )/Μ
i,j = 1,2,…., Ka; M=NQ+W-1.
(30)
We estimate the spatial covariance matrix based on the noise detected from the data field
of the slot. There are total NQ+W-1 noise samples in each data field.
Suppose that:
α11, α12,……. α1Ka
α21, α22,……. α2Ka
Rn -1 = Rd-1U Rt -1 = Rd -1 U I=
U
Ka
I
NQ+W-1
α Ka,1, αKa,2 ,……. α Ka,Ka
NQ+W-1
Ka
Figure 4-2 Estimation of the Spatial Covariance Matrix
We have
AHRn
−1
−1
= [ A (1)H A (2)H ,....., A (Ka)H ]R d ⊗ I = [A ' (1)H , A' (2)H ,...., A '(Ka)H ] (31
)
Where A’(ka)H =
Σ
Ka
i=1
αi,ka A(ka)H
Then:
AHRn-1e = Σka=1 Ka A’(ka)H e(ka)
Maximum ratio combining
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From above equation, the output of the whitening matched filter is the coherent
maximum ratio combining of all Ka antennas. Thus Ka elements of the antenna array
work as a diversity array and no beam is formed.
4.3.
Computation of the Zero Force Equalizer
We now turn our attention to the computation of the Zero Force Equalizer (Figure 4-1).
We define the zero force equalizer matrixes as
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H
-1
H
-1
C-1 = (A Rn A )-1 and C = A Rn A
(33)
C = [A’(1)H A’(2)H….. A’(Ka)H] [A(1)T A(2)T….. A(Ka)T]T = Σka=1Ka A’(ka)H A(ka)
(34)
= Σka=1Ka C(ka)
The matrix C is the summation of the matrix C(ka) .Which indicate that Ka antenna
elements are coherently combined.
C
=
(ka)
Q+W-1
~(ka)
~
b
A(ka)
~(ka) H
b
ka=1
~
b(ka)
A
(ka)
b
(ka
)
C0
C1
C2
C1 H
C0
C1
C1 H
C0
C1
=
b(ka)
b(ka)
C1 H
C1
C1 H
C0
Figure 4-3 Zero Force Equalizer Matrix
From Figure 4-3 the sub-matrixes C0 and C1 can be computed from:
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Q+W-1
K
~(1,ka)
b
H
~
b(2,ka)
H
b(1,ka b(2,ka
)
C0 =
b(K,ka
)
)
Q+W-1
~
b(K,ka)
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H
b(1,ka)
H
C1 =
~(1,ka)
b
H
~
~
b(2,ka)
C0 =
0
b(2,ka)
H
Q+W-1
H
Q
K
Q+W-1
First W-1 rows
b(1,ka b(2,ka
b(K,ka
)
)
)
b(1,ka b(2,ka
b(K,ka
)
)
)
Q+W-1
~(K,ka)
b
H
Figure 4-4 C0 and C1 submatrices
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5.
Joint Detection Receiver Implementation
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Figure 5-1 gives the logical block diagram of the joint detector that has been discussed in this paper. Joint
Detection algorithms are complex and computationally intensive (complexity grows exponentially as the
number of codes increases) and as such are not suitable for use in other CDMA systems because of the high
number of codes used in those systems. In the Joint Detection block diagram, most of the operations are
matrix and vector operations. As the size of the matrices and vectors increases, so does the complexity of
the system and the computational power that is required to separate the users.
Noise
Variance
Estimation
Antenna
Data
Data
Extract
e(a)
Midamble
extraction
e(a)
Whitening
Matched Filter
A(a)HRn(a)-1
Channel
Estimation
Matrix
A(a)
Generator
MaxRatio
Antenna
combining
Calculate
(a)H (a)-1 (a))-1
(A Rn A
Decorrelator
(AHRn-1A(a))-1
User’sdata
MaxRatio
Antenna
combining
Spreading
Code
Generator
Figure 5-1 Joint Detection Based Receiver
The analysis of the Joint Detection algorithm presented in this work shows very clearly that a very large of
matrix computations are involved. Because of this, traditional DSPs are not suited to this task. One could
argue that a matrix-coprocessor could be used in the computations, however the variety in the dimensions
of the matrices involved would make such a coprocessor very inefficient and therefore very expensive to
use. An approach with a structure that can reconfigure and adapt would be the ideal solution to the
problem.
The inherent parallelism in the implementation of the various blocks in the Joint Detector makes it an ideal
fit for the Motorola MRC6011 Reconfigurable Compute Fabric. The multicore architecture provides a very
high degree of flexibility and scalability and facilitates the integration of the Joint Detection operation with
the other receiver blocks such as the channel estimation processor. When coupled with Motorola’s
advanced DSPs, the MRC6011 provides the ideal solution for the implementation of a TD-SCDMA
receiver.
For more complete details on the implementation of the receiver with the MRC6011, the reader is referred
to other publications in this series or contact your local Motorola Field Applications Engineer.
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User 1
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Analog
Front
End
A/D
Burst
Split
Channel
Estimation
Joint
Detector
MRC6011
Symbol Rate
Processor
User n
MSC8102/MSC81
26
Figure 5-2 MRC6011 Based TD-SCDMA Receiver
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User 2
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References
1.
Rappaport, T. S., Wireless Communications, Upper Saddle River, NJ: Prentice Hall, 1996.
2.
Viterbi, A.J., CDDMA: Principles of Spread Spectrum Communications. Reading. MA: AddissonWesley, 1995.
3.
M. Haardt, A. Klein, R. Koehn, S. Oestreich, M. Purat, V. Sommer. “The TD-CDMA Based
UTRA TDD Mode” IEEE Journal on Selected Areas in Communications, Vol 18, No. 8, August
2000.
4.
Bernd Steiner, Peter Jung: Optimum and suboptimum Channel Estimation For the Uplink of
CDMA Mobile Radio System with Joint detection.
5.
3GPP TR 25.928 V4.01 – 1.28 Functionality for UTRA TDD Physical Layer (Release 4). 2001
6.
3GPP TS 25.221 V5.5.0 (2003-6). Physical Channels and mapping of transport channels onto
physical channels (TDD) – Release 5.
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Go to: www.freescale.com
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