聖約翰技術學院
專題研究
階層式 DS-CDMA 多路徑無線通道
參數估測演算法之設計
計畫主持人：王永宜
單 位：電腦與通訊工程系
級 職：副教授
中
華
民
國
年
92
1
11
月
12
日
Abstract:
This project proposes a one dimensional (1-D) based direction of arrival
(DOA) and delay joint estimation algorithm for a DS-CDMA wireless multipath
channel. In conjunction with the complementary orthogonal projection (COP)
methods, the proposed algorithm, in a tree structure, uses the spatial-temporal
geometric distribution of the channel to hierarchically group, isolate each single
ray and then identify the channel contents, so as to jointly estimate the DOAs
and the delays of multipath cahnnel. In addition to significantly mitigating the
computation complexity, the proposed algorithm performs less estimation error
than the recently developed 2-D based methods.
1. INTRODUCTION:
DOA-Delay joint estimation plays a prior role in wireless
communication systems. Receivers of wireless communication systems use the
DOA-Delay information to improve system performance, such as bit error rate
mitigation, capacity increase, and diversity combining. Specifically, in a
DS-CDMA system with multiple receive antennas, it is used for synchronizing
the received data, suppressing the interference from other communication
applications, and thus promote the overall system performance.
Many researchers have proposed algorithms for the DOA-Delay joint
estimation [1-3]. Among them, [1-2] developed the JADE-MUSIC and the
JADE-ESPRIT algorithms for TDMA systems, which evolve from the 2-D
ESPRIT algorithms for frequency retrieval problems. [3] provides the maximum
likelihood algorithm for the path delay estimation and it regards the DOA
estimation as a least square problem.. However, [1] cost extremely high
computations on eigen-decomposition and target search. [2] can not be applied
to CDMA systems due to the multiple access interference(MAI). [3] has the
initialization problem sometimes making the algorithm diverge. In this project
we propose a hierarchical 1-D based tree structure DOA-Delay joint estimation
algorithm for DS-CDMA systems. According to the space-time distribution of
the received signals, the proposed algorithm uses the COP method to group,
isolate, and then identify the received signals on the DOA-Delay plane. Two
spatial MUSIC (S-MUSIC) algorithms and one temporal MUSIC algorithm are
used for parameter estimating and providing guard information to each step of
the algorithm. The tree structure of the algorithm ensures that the pairing of the
estimated DOAs and delays is uniquely determined.
Compared with the other algorithms, the proposed 1-D based algorithm
approach is computational saving and accurate. In addition, the proposed
algorithm can resolve the rays with close delays or with close DOAs. The rest of
this report is organized as follow. Section 2 introduces the data model of a
DS-CDMA reverse link channel. Section 3 describes the proposed algorithm.
Section 4 conducts simulations to verify the proposed algorithm.
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2. DATA MODEL
A DS-CDMA communication system usually uses a spreading sequence
for the purpose of multiple access. At the receiver, ignoring the additive noise,
the received signals, after sampling, can be expressed as
X (t n )  A( )BGT ( τ )SD ,
(1)
T
where the superscript denotes the matrix transpose operation, the
spatial signature A( )  a( 1 )  a( Q ) with a( k )  1 e j sin  e j ( M 1) sin 
which denotes the array response vector of the uniform linear array (ULA) with
M antenna elements, B  diag  1   Q  represents the Q complex Gaussian
fading amplitudes , G( t)  g ( 1 )  g ( Q ) is the temporal signature matrix
k
k
with g ( k ) denoting the samples of the delayed pulse shaping function, S and
D both are Toeplitz matrices consisting of the spreading sequence and the data
symbols respectively.
3. The S-MUSIC and the T-MUSIC
The proposed algorithm is based on the second order statistical eigen-structures
of the spatial covariance matrix and the temporal covariance matrix of the
received data, respectively. The spatial covariance matrix of the received data
is
R s  E X t X tH   AR BBA H
V Λ V V Λ V
s
s
s
s
sH
s
s
n
s
n
sH
n
(2) Obviously, after performing the
eigen-decomposition, the signal subspace of R s , which is constituted by the
eigen-vectors with nonzero eigen values, shares the same column space with the
spatial signature matrix A . On the other hand, we observe that the row space
of (1) contains the delay information of the received signal. The temporal
covariance matrix is thus


R t  E X t X *t  GR BB G
T
H
V Λ V V Λ V
t
s
t
s
tH
s
t
n
t
n
tH
n
(3)
where
G  G S denotes the composite temporal signature matrix. By using the facts
T
that the spatial signatures and temporal signatures share the same signal
subspace with R s and Rt , respectively. The S-MUSIC and the T-MUSIC
algorithm are respectively summarized as
(4)
min aH   I  Vss Vss a  

and


min g H   I  Vst Vst

H
H

 g   .
(5)
4. THE PROPOSED ALGORITHM
Fig. 1 illustrates the tree structure of the proposed approach. According to
the DOA-Delay geometric distribution of the multipath channel, as shown in
Fig. 1, the proposed approach hierarchically decomposes the multipath channel
into several single path structures. The hierarchical decomposition is consist of
the temporal grouping and the spatial isolating. To achieve the hierarchical
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decomposition, in conjunction with the orthogonal projection techniques, the
S-MUSIC algorithm and the T-MUSIC algorithm provide the spatial
information and the temporal information respectively to facilitate the temporal
grouping and the spatial isolating.
Fig. 2 shows a path structure evolution diagram of the proposed algorithm
for estimating the DOA-delays of a three-path channel. In Fig. 2, we assume
that path 1 and path 2 are with distinct delays but are spatially close by, i.e.
 1   2 , 1   2 , while path 1 and path 3 are with different DOAs but are
temporally close by, i.e.  1   3 , 1   3 . The proposed algorithm first applies
the T-ESPERIT algorithm to X t for delay estimation. The temporally close by
paths makes only two delays, ˆ1 and ˆ2 , are obtained by the T-MUSIC algorithm.
Using ˆ1 and ˆ2 , the proposed algorithm generates the temporal projection
matrice by
U1t  I  g(ˆ2 )  g(ˆ2 ) H , and
U t2  I  g(ˆ1 )  g(ˆ1 ) H
.
(6)
Using (6), the proposed algorithm then generates two group matrice
X1  X t  U1t and X 2  X t  U t2 , respectively. Apparently, the orthogonal projection
referred to as the temporally grouping operation renders that the group matrix
X1 contains the spatially diverse paths, path 1 and path 2, while the other
group X 2 contains path 3 only. The temporally grouping operation implies that
ˆ1 ,ˆ2 , and ˆ3 can be accurately obtained by applying the S-MUSIC algorithm
to X1 and X 2 , respectively. The spatial projection matrice are then generated by
U 1s  I  a(ˆ2 )  a(ˆ2 ) H , and
,
U s  I  a(ˆ )  a(ˆ ) H
2
1
(7)
1
Similar to the temporally grouping process, the proposed algorithm spatially
decomposing, or isolating, the group matrix X1 into two single path structure
by multiplying the spatial projection matrice in (7) to X1 .
X1,1  U1s  X1 , and X 2,2  U 2s  X1 (8)
Notice that X 1,1 and X 2, 2 contains path 1 and path 2 with the known
corresponding DOA estimates. The estimation of the path delay is then achieved
by applying the T-ESPERIT algorithm again to X1,1 and X 2, 2 , respectively.
Also, as shown in Fig. 2, the tree structure of the proposed algorithm renders
that the pairing of each estimated DOA with the corresponding estimated path
delay is automatically determined.
Supposed that there are Q paths distributed in q temporal groups are
presented in a wireless channel. The whole procedures of the proposed
algorithm is summarized as follows:
I. Temporally Grouping:
Applying the T-MUSIC algorithm to X t , we can obtain the average
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group delay, tˆ1 , , tˆq , of each temporal group. According to the average
group delays, we form the projection matrix, U tn  I  g(tˆn )  g(tˆn ), n  1, q ,
and then decompose X t into q group matrice by
(9)
X k  X t   U tn
nk
II. Spatially Isolating:
Applying the S-ESSPRIT algorithm to each group matrix, we can
obtain the estimated DOAs corrresponding to the paths contained in each
group matrix. The spatially projection matrice are thus obtained by
U ks ,n  I  a(ˆk ,n )  a(ˆk ,n ) , where ˆk , n denotes the estimated DOA of the n-th
path of the k-th group. The isolated single path matrice are generated by
(10)
X k ,m   U ks ,n  X k
nm
III.
Delay Estimating and Pairing
Applying T-MUSIC algorithm again to each X k ,m , we thus can
estimate the propagation delay for each isolated path, and then pair each path
delay with the associated DOA obtained in step II.
4. SIMULATION RESULTS
In this section, some simulations are conducted to assess the proposed
algorithm. We assume that narrowband signals are transmitted through a
three-ray channel with flat fading amplitudes and additive noise. At the
basestation, the receiver uses a three-element ULA and samples the received
training sequence for 20 bursts. The spatial / temporal parameters of the three
paths are set to be 25 27  38 /.2 1.1 .3T , where T  3.68s is the symbol
period of the GSM system. All three fading amplitudes are set to be 0 dB. Fig. 3
demonstrates the scatter-gram of the proposed algorithm, based on 0 dB noise
power and 200 independent trials. We can observe in Fig. 3 that the proposed
algorithm successfully identifies, with very small estimation variance, each path
on the DOA-Delay plane.
REFERENCE:
[1] M. C. Vanderveen, C. B. Papadias, ans A. Paulraj, “ Estimation of Multipath
Parameters in Wireless Communications,” IEEE Trans. Signal Processing, pp.
682-690, Mar, 1998.
[2] A. J. Vanderveen, M. C. Vanderveen, and A. Paulraj, “ Joint Angle and
Delay Estimation (JADE) for Multipath Signals Arriving at an Antenna Array,”
IEEE Comm. Lett., pp. 12-14, Jan, 1997.
[3] M. P. Clark, and L. L. Scharf, “ Two Dimensional Modal Analysis Based on
Maxium Likelihood,” IEEE Trans. Signal Processing, pp.1443-1552, June
1994.
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Fig. 1: The tree structure of the proposed algorithm
Fig. 2: An example of the channel content evolution in the proposed
algorithm
6
80
Noise power = 0 dB
60
200 shots
40
DOAs (degree)
20
0
-20
-40
-60
-80
-1
0
1
2
Delay (T)
3
4
5
Fig. 3: The scatter diagram of the proposed algorithm based on 200
independent trials
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