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
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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 µs
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)
dˆ
(1)
e
Data
Esti mation
h(k)
(k )
h(K)
(k )
dˆ
(K )
dˆ
(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 )
∑eφ
j ( k , ka , kd )
hd
( k , kd )
(17)
kd =1
where φ(k,ka,kd) = {2πL(ka)cos(β(k,kd) - α(ka) )}/λ
(k)
1…Kd ;
k=1…K ka = 1…Ka and kd =
Interference ki
Antenna ka
γ(ki)
α
(ka)
β(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 jφ(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
dˆ = (A H R n A) A H R n x
(20)
ˆ 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
hˆ = {( 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
jφ ( ki ,i )
nd
( ki )
ki =1
Ki
∑e
− jφ ( kj , j )
nd
( kj ) H
}
kj =1
Ki
= E{∑ e j [φ ( ki ,i )−φ ( ki , j )] nd
( ki )
nd
( ki ) H
}
ki =1
Ki
~ ( ki )
= ∑ e j [φ ( ki ,i )−φ ( ki , j )] Rm σ ( ki ) 2
ki =1
~
where R m
( ki )
= E{n d
( ki )
nd
( ki ) H
~ ( ki )
} / σ ( 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 = ∑ (σ ( ki ) 2 )e j[φ ( ki ,i )−φ ( 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
hˆ = {( 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
hˆ = { 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
hˆ 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
dˆ = ( 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
dˆ = 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
dˆ = 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
dˆ = 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! Reference source not found.
22
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