基於多重輸入/多重輸出正交分頻多工通訊系統的聯合頻率偏移---入射角估測與信號偵測

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行政院國家科學委員會專題研究計畫成果報告

基於多重輸入-多重輸出正交分頻多工通訊系統的聯合頻率偏移-入射角估測與信號偵測

計畫類別：個別型計畫

計畫編號： NSC94-2213-E-011-013-

執行期間： 94 年 08 月 01 日至 95 年 07 月 31 日執行單位：國立臺灣科技大學電子工程系

計畫主持人：方文賢

計畫參與人員：林仁得,盧晃瑩,巫國雄,楊萬興,劉嘉全,羅志文,王冠雄

報告類型：精簡報告

報告附件：出席國際會議研究心得報告及發表論文處理方式：本計畫可公開查詢

中華民國 95 年 10 月 30 日

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行政院國家科學委員會專題研究計畫成果報告

基於多重輸入-多重輸出正交分頻多工通訊系統的聯合頻率偏移- 入射角估測與信號偵測

Joint Frequency Offset-DOA Estimation and Symbol Detection in MIMO-OFDM System

計畫編號: NSC 94－2213－E－011－013 執行期限:94/08/01 - 95/07/31

主持人:方文賢國立臺灣科技大學電子系

計劃參與人員: 林仁得,盧晃瑩,巫國雄,楊萬興,劉嘉全,羅志文,王冠雄

一、中文摘要

本計畫發展一種基於天線陣列的樹狀結構演算法則，可同時估測多重輸入多重輸出- 正交分頻多工通訊系統中的信號重要參數：

入射方位角(DOAs)以及頻率偏移(Frequency offsets)。此演算法運用一個空間-頻率-空間的樹狀結構分別在兩個空間域上(S-MUSIC)及時間域上(F-MUSIC)輪流估測信號到達方位角及頻率偏移，並結合空間波束形成及時域濾波來有效將信號分群並抑制傳遞誤差，因而提高整體效能。此外，基於所估測之方位角及頻率偏移，本計畫亦發展一資料偵測演算法。模擬結果驗證此低複雜度演算法的優異效能。

關鍵詞︰信號到達方向、信號延遲時間、分碼多工、通道參數估測

Abstract

This project presents an antenna array-assisted approach to jointly estimate nominal directions of arrival (DOAs) and frequency offsets, and detect data in uplink multiple-input-multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) wireless networks. To alleviate the computational overhead, the approach determines the nominal DOAs and frequency offsets of the incoming rays in a

space-frequency-space (SFS) tree structure, in which two S-MUSICs and one F-MUSIC are invoked alternatively to estimate the nominal DOAs and the frequency offsets, respectively In between every other MUSIC, a spatial beamforming process and a temporal filtering process are employed to decouple the uplink signals from different transmitters, thus enhancing the estimation accuracy. In addition, based on the estimated nominal DOAs and frequency offsets, a data detection procedure is also addressed. Furnished simulations show that the proposed algorithm can provide satisfactory performance, but with lower computational complexity.

Keywords: DOA, Frequency offset,

MIMO-OFDM, Parameter estimation 二、研究與目的及相關文獻探討

MIMO-OFDM networks possess the characteristics of high channel capacity and bandwidth efficiency [1], which make them very suitable for high data rate access in wireless local area network (WLAN). However, OFDM signalling is very sensitive to frequency offset [2] and the system performance deteriorates substantially with an increase in the

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frequency offsets. Various algorithms for estimating frequency offsets have been reported [3]-[5]. For example, [3] develops a low complexity, yet reasonably accurate frequency offset estimation algorithm, where a training symbol composed of two or more identical parts in the time domain is adopted so the estimation range can be dynamically extended to be wider than the subcarrier spacing. This approach, however, is not applicable to multi-user environment. In [4], [5], the frequency offset estimation problem is addressed in the MIMO-OFDM or single user scenario, where antenna arrays are used to greatly improve the estimation accuracy. However, if we allow channel interferences (CCIs) and multiple access interferences (MAIs) to exist in the same frequency band as the target signal so as to increase the overall network throughput, the aforementioned frequency offset estimation algorithms, blind or non-blind, with single or multiple antennas, would simply fail. Also, in current wireless OFDM WLAN, active and passive CCIs protection mechanism such as carrier sense multiple access/carrier avoidance (CSMA/CA) and clear to send/request to send (CTS/RTS) are employed to prevent CCIs and packet collision. However, both schemes consume additional overhead, thus reducing the total throughput. Therefore, we present an antenna-array-assisted approach to jointly estimate the nominal DOAs and frequency offsets, and detect data in uplink MIMO-OFDM wireless networks. The proposed approach can cooperate with upper medium access control (MAC) layer to allow the co-existence of CCIs and MAIs to enhance the data rate, thus tailing high channel capacity in MIMO-OFDM. To

achieve this, two MUSIC[6]-based algorithms are first considered to jointly estimate the nominal DOAs and frequency offsets of the incoming rays. The first algorithm is to simultaneously estimate these two parameters based on the 2-D MUSIC. To alleviate the computational overhead, the second algorithm utilizes the spatial and temporal data structures to estimate the nominal DOAs and frequency offsets in an SFS hierarchical tree structure, where two S-MUSICs and one F-MUSIC are employed alternatively to estimate the nominal DOAs and frequency offsets, respectively. Also, a spatial beamforming process and a temporal filtering process are invoked after the S-MUSIC and F-MUSIC, respectively, to partition the signals into appropriate groups to enhance the estimation accuracy. Furthermore, the estimated nominal DOAs and frequency offsets are automatically paired due to the tree-structured estimation scheme. Thereafter, a data detection procedure, based on the estimated nominal DOA and frequency offset, is also addressed to detect the transmitted symbols.

三、研究方法及成果 Data Model

Consider an indoor MIMO-OFDM WLAN uplink scenario as shown in Fig. 1. Assume that the number of antennas at the access point (AP) is

M

_R and that at the STA is

M

_T , The received equivalent diffused baseband symbol can be written as

(1) where

a

_R(

θ

_{R , ,}_{k l}) , [

a

_T(

θ

_{T, ,}_{k l})] _m ,

β

_{k l j}_{, ,} and

f

k

Δ are the receive array response vector,

k T

k

k l

n

L M

K j f

R R k,l N T T k,l m

k l m

J

k l j k j

n θ e θ

β s n n

,

, ,

, ,

x( ) a ( ) ( [a ( )] )

( ) ( ) n( )

2π

1 1 1

1

Δ

= = =

=

≅ ⋅ ⋅

⋅ ⋅ +

∑∑ ∑

∑

(4)

m

thelement of the transmit array beamforming vector, fading gain and the carrier frequency offset normalized to subcarrier spacing in the

l

thpath cluster of the

k

^thSTA, respectively.

K

denotes the total number of STAs. Without loss of generality, we assume k

= 1

is the desired STA and others

k

= 2,...,

K

are interference STAs. The number of scattering path clusters in the

k

^thSTA is

L

_k. The signal can be expressed as

= [ (0), (1), , (N−1)] = ( R) ^T(Δ +)

X x x x A Θ BG f N

(2) whereB

=

diag B

{

_1,1^' , B_1,2^' , , _, }

'

B

K LK is the L*L composite fading matrix with

, , , ,

1

' [ ( )]

MT

K L K L T K T L

m m

B β a θ

=

= ∑ ^and

R R R ,1,1 R R ,1,2 R R , ,

( ) = [ (

θ

), (

θ

), , (

θ _{K LK}

)]

A Θ a a a

are diagonal fading matrix and spatial signature matrix, respectively. G f

( ) =[ ( Δ

g_1,1

Δ

f_1,1

),

g_1,2

( Δ

f_1,2

),

, ,

, _{K L} ( _{K L} )

K Δ

f

K

g ] =

S G

:

^' is the temporal signature matrix with

S

= [ ,

s

₁ , ,

s s

₁ ₂, ,

s ,

₂ ,

s

_K, ,

s

_K] is the temporal signal matrix with

s

_k = [ (0),

s

_k

s

_k(1), ,

s N

_k( −1)]^Tand

G

^'

=

[

g g_1,1^'

,

_1,2^'

, ,

g'_{K LK}_, ] is the matrix with

2 , /

,

= [1,

^j ^f ^N

' i j

i j e ^πΔ

g , ,

e

^j²^πΔ^f^{i j}^, ⁽^N⁻^{1) /}^{N T}] and

:

denotes the Hadamard product(7).

To follow, we address two MUSIC-based algorithms, namely SODE MUSIC and SFS MUSIC, to estimate the nominal DOAs and the frequency offsets of the incoming rays.

SODE MUSIC：

The SODE MUSIC begins with stacking the

M

_R×

N

matrix

X

into a vector

=

vec

{ } = [ ^T(0), ^T(1)

y X x x

, ,

x

^T(

N

−1)]^T, which can be expressed as

R R

= { ( ) ( )} { }

= ( , ) {

T

'

vec vec

vec

Δ +

Δ ⋅ +

y A Θ BG f N

U Θ f B N}

where ( ) = [ _1,1, _1,2, , _, ]

' ' '

' T

n B B B

K LK

B

and

R R

( ,Δ ) = ( )◊ Δ

U Θ f A Θ G( f) , in which

◊ denotes the Khatri-Rao matrix product(7).

Determining the covariance matrix of

y

,

= {

E ^H

}

Ryy yy , we can get

2

R R

= ( , ) ( , )

R

H

n M N

σ

Δ Δ + ⋅

Ryy U Θ f PU Θ f I where

P

= {

E B B

^' ^'H} represents the fading covariance matrix. Taking the eigendecomposition of

R

_yy yields

s s s n n n

=

^H

+

^H

Ryy V Λ V V Λ V

where the column vectors of

V

_s and

V

_n are the eigenvectors that span the signal subspace and noise subspace of

R

_yy, respectively. We can get the

L

pairs of nominal DOAs and frequency offsets

1 1

{( Δ

f

ˆ ˆ , ),

θ

( Δ

f

ˆ ˆ

₂

,

θ₂

}, , ( Δ

f

ˆ

_L

,

θ

ˆ

_L

)}

via the 2D-MUSIC algorithm given by

,

ˆ 1

{ , } = arg max

( , ) ( , )

H H

f n n

f

^θ

f f

θ

^Δ ^Δ

u θ

Δ

V V u θ

Δ where

u

( ,

θ

Δ

f

) =

a

_R( )

θ

⊗ Δ

g

(

f

).

SFS MUSIC:

The SODE MUSIC algorithm addressed above suffers from huge computational complexity due to high-dimensional eigendecomposition of

R

_yy and an additional 2-D search for simultaneously locating the nominal DOAs and frequency offsets. To alleviate the computational overhead, to follw we address an SFS tree structure which involves only 1-D MUSICs. The approach begins with computation of the spatial covariance matrix, (3)

(4)

(5)

(6)

(5)

= 1 { }

s

E

H

R N XX

, and we can get

s 2

R s R R

= 1 ^H( ) _n _M

N

+

σ

⋅

R A(Θ )P A Θ I

where

P

_s = {[

E BG f

(Δ ) ][^T

BG( f)

Δ ^{T H}] } is a diagonal matrix. Taking the eigendecomposition of

R ,

^s we have

R

^s =

V L V

_s^s ^s_s _s^s^H +

V L V

_n^s ^s_n _n^s^H,

where the column vectors of

V

_s^s and

V

_n^s are the eigenvectors that span the signal subspace and noise subspace of

R

^s, respectively. We can then have a rough estimate of the nominal DOAs, say

{

^{θ θ}¹

^,

²

^, ^… ^,

^θ^p

}

, via the 1-D S-MUSIC by

s s

n n

= arg max 1

( ) ( )

H H

θ

θ θ

a V V a

The estimated coarse nominal DOAs can, nevertheless, help us decouple the signals into several groups with signals in each group having very close (or the same) nominal DOAs but different frequency offsets. Such a decoupling process can enhance the estimation accuracy of the MUSIC algorithm.

To achieve the grouping process, we construct

p

spatial beamforming matrices

{ } F

_i^s , = 1, 2,...,

i p

, where

F

_i^s is a complementary projection matrix given by

s s s

= , = 1, 2,...,

i^⊥ − i ⋅ i

i p

F I F F

where i^s= ( )⎡

θ

1 (

θ

i−1) (

θ

i+1) ( )

θ

p ⎤

⎣ ⎦

F a a a a .

and the superscript + denotes matrix Pseudo inverse[7].

The spatially-filtered signals can then be

written as

= s , = 1, ,

i i^⊥⋅

i p

X F X

which includes only the

i

^th signal group corresponding to the estimated

θ

i. Next, we compute the temporal covariance matrix of each group of spatially-filtered signals,

f 1

= { ^H }

i i i

R

M E

R X X

, and can obtain

f 2

= f , = 1, ,

i Δ ^H Δ +

σ

n⋅ N

i p

R G( f)P G ( f) I

where P_f

= {[

E F A Θ B F A Θ B_i^s^⊥

(

_R

) ] [

^H _i^s^⊥

(

_R

) ]}

is a diagonal matrix.

Taking the eigendecomposition of

R

^f_i

results in

R

^f_i =

V L V

_i^f_s ^f_i_s _i^f_s^H +

V L V

_i^f_n ^f_i_n _i^f_n^H, where

the column vectors of

V

_i^f_s and

V

_i^f_n are the eigenvectors that span the signal subspace and noise subspace of

R

^f_i , respectively. We can then estimate the frequency offsets

ˆ,1

{Δ ,

f

_i Δ

f

ˆ ,_i_,2

… , Δ

f

^ˆ

_{i Qi}_,

}

, = 1, 2,

i

,

p

via the F-MUSIC given by

f f

n n

ˆ = arg max 1

( ) (

H H

f i i

f ^Δ f f

Δ

g

Δ

V V g

Δ

)

where

Q

_i denotes the number of signals in

i.

X

Along the same line as the above, to get a precise estimate of the nominal DOAs, we can decouple the signals into groups with the estimated frequency offsets. To achieve this, we form a set of temporal filtering matrices given by

f f f

,

=

, ,

, = 1, 2,..., , = 1, 2,...,

i j^⊥

−

i j

⋅

i j i p j Qi

F I F F (7)

(8)

(9)

(10)

(11)

(12)

(13)

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whereF_{i j}^f_, =[ (gΔfˆ_i_,1), , (

g

Δ

f

ˆ_{i j}_{, 1}₋),

g

(Δ

f

ˆ_{i j}_{, 1}₊), , (

g

Δ

f

ˆ_{i Qi}_, )]

The temporally-filtered signals can be written as

f

,

=

,

, = 1, 2, , , = 1, ,

i j i i j^⊥ i p j Qi

X X F

where

X

_{i j}_, contains only the single path cluster signal. Thereafter, we can perform the S-MUSIC again to calculate the nominal DOAs.

Similar as the above, using the filtered scanning vector, we can obtain a more precise estimate of the nominal DOAs as {

θ

ˆ_i_,1,

θ

^ˆ_i_,2, ,θ

^ˆ

_{i Qi}_,

}

. It is noteworthy that, due to the tree-structured estimation scheme, the nominal DOAs estimated are automatically paired with the frequency offsets perviously determined, i.e.,

1,1

{(Δ

f

ˆ ,

θ

ˆ ), ,(_1,1 Δ ,

f

ˆ_P_,1

θ

ˆ )_P_,1 , ,( ˆ_{P Q}_, , ˆ_{P Q}_, )}

p p

f θ

Δ .

The overall procedures of the SFS MUSIC can be summarized as follows:

Step 1: Rough nominal DOA Estimation:

Estimate the spatial covariance matrix by

s 1

= { ^H}

N

∑

R XX

and use the S-MUSIC to

get a set of coarse group nominal DOAs estimates

{

^{θ θ}¹

^,

²

^, ^… ^,

^θ^p

}

^.

Step 2: Spatial Beamforming:

Form a set of spatial complementary orthogonal projection matrices by (9) to separate the signals into different signal groups by (10).

Step 3: Frequency Offset Estimatoin:

For each signal group, determine the temporal covariance matrices to estimate the frequency offsets via(12).

Step 4: Temporal Filtering:

Use temporal complementary orthogonal projection matrices constructed in (13) to decouple signals into groups which only consist of a single signal after temporal filtering by (14).

Step 5: Precise nominal DOA Estimation:

Invoke the nominal DOA estimation again in each decoupled group with different array manifold

F a

_i^s^⊥ ( )

θ

. Note that the estimated nominal DOAs are automatically paired with the frequency offsets estimated in Step. 3.

Data Detection

In this part, we address a data detection process based on the estimated nominal DOAs and frequency offsets. Assume the target signals to be detected in the uplink network are from STA1. The estimated nominal DOAs and frequency offset of the path clusters from STA1 are {

θ

ˆ_{R ,1,1},

θ

^ˆ_{R ,1,2}, _{R ,1,}

1

,

θ

ˆ

_L

}

and

Δ ˆf

₁ . To detect one of these path clusters from STA1, say path 1 from STA1, the received signal X in (1) is first spatially filtered by

F

^s^⊥ =

I F F .

− ^s⋅ ^s^† Note that the spatially filtered signal

F

^s^⊥

X

only consists of the desired signal and the CCIs from different nominal DOAs have been removed.

Thereafter, premultiplying the spatially

filtered

F

^s^⊥

X

by

s

R R ,1,1 s 2

R R ,1,1

( ˆ )

= ( ˆ )

H

θ θ

⊥

⎛ ⋅ ⎞

⎜ ⎟

⎜ ⋅ ⎟

⎝ ⎠

F a M

F a

and followed by taking the Hadamard product with g^'

( Δ

f

ˆ

₁

)

^H to compensate for the frequency offset, we can obtain

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T s

1 1 T , , 1

=1

'( ˆ) = ( ) ( )

M

H T

i m m

f β n a n

⊥ Δ ∑ +

MF X

:

g s n

where

:

denotes Hadamard product and

s '

1

( ) = (

n

⋅

^⊥

⋅ ( ))

n ^H

( Δ

f

ˆ )

n M F n

:

g .

The transmitted symbol can then be detected by

s '

1

1,1 1 1 1

ˆ ( ) = ( ) ( ˆ )

[ (1), (2),.., ( )] ( )

H

'

n f

B s s s N n

⋅

⊥

⋅ Δ

≅ ⋅ +

x M F X g

n

:

Next,let

ˆ =

s_1,_l

[

s

ˆ

_1,_l

(0),

s

ˆ (1),

_1,_l ,

s N−

ˆ_1,_l( 1)]^Tdenote the detected symbol belong to

l

^th path cluster from STA1. Collecting the signals from different paths of STA1 and stacking them,

ˆ1,1

= [

s

,

u s

ˆ ,_1,2 _1, ˆ 1

,

s

_L ] =^T

s

ˆ '₁

b n

+ ′, where b

'

denotes the fading vector of the multipaths from STA1, then b

ˆ '

is the dominant eigenvector of the covariance matrix

R

_u = {

E uu

^H} with an ambiguity of a complex factor α. After b

ˆ '

is estimated,

s

ˆ =₁

b u

ˆ'^H =

s

₁

αβ

+b nˆ'^H ^′=

s

₁

γ

+b nˆ'^H ^′,

where

β

= '

b b

ˆ^H and

γ αβ

= is an unknown complex constant.

The ambiguity of

γ

can be overcome by differential encoding and decoding. Single path OFDM signal can be detected by taking the inverse fast Fourier transform of { ( )}

s n

ˆ₁ and the detection performance can be improved by maximal ratio combining (MRC).

As a whole, the proposed joint parameters estimation and data detection procedure is as illustrated in Fig. 2.

Simulations and Discussions

Computer simulations are conducted in

this section to demonstrate the proposed approaches. Assume that the numbers of antennas at AP1 and STA are both equal to 4, the number of subchannels in OFDM networks is N=64, the number of STAs is

K

=2 and the number of path clusters is L

= 3

. There are two targeted path clusters for STA1. The nominal DOAs of the STAs are [-3 5 25]^o, and the frequency offsets between the AP1 and STAs are [-0.5 0.33 0.33] with respect to the intercarrier spacing. The average fading amplitude for all signals are equal and normalized to 0 dB. Both of the SODE MUSIC and SFS MUSIC are carried out for joint nominal DOA-frequency offset estimation. 50 symbols across packets are employed in the uplink MIMO-OFDM network for the estimation of nominal DOAs and frequency offsets.

Figs. 3 and 4 illustrate the root mean square errors (RMSEs) of the estimates of the nominal DOAs and frequency offsets, respectively, based on the estimates of SODE MUSIC and SFS MUSIC. The RMSEs of the nominal DOAs and frequency offsets using the S-MUSIC and F-MUSIC alone without the beamforming/filtering processes and the Cramer-Rao lower bound (CRLB) are also furnished for comparison. Fig. 5 shows the resulting BER performance based on the estimated nominal DOAs-frequency offsets using these three algorithms, based on perfect channel state information (know nominal DOAs and frequency offsets) and single user bound (SUB). We can note that from Figs. 3 and 4 that the 1-D F-MUSIC and 1-D S-MUSIC alone can not resolve the nominal DOAs and frequency offsets, respectively, with close nominal DOAs (15)

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or frequency offsets. Also, SODE MUSIC, as expected, outperforms the SFS MUSIC as it estimates these two parameters simultaneously.

The latter, however, calls for substantially less computations. We can also find from Fig. 5 that both of the proposed algorithms yield very close and satisfactory BER performance.

Conclusions

In this paper, an antenna-array-assisted approach is proposed to jointly estimate the frequency offsets and nominal DOAs, and detect data in uplink MIMO-OFDM networks.

The approach begins with estimating these two parameters based on the high-resolution SODE MUSIC or computationally less demanding SFS MUSIC, followed by a path-wise data detection by making use of this estimated channel information. Simulations show that the new approach can provide satisfactory performance even with close frequency offsets or nominal DOAs.

四、計劃成果自評

Compared with current wireless OFDM LAN, proposed algorithms possess the following attractive attributes: (1) the overhead of the CSMA/CA and CTS/RTS mechanism in the MAC layer can be reduced; (2) the frequency reuse factor in the network can be greatly reduced to be less than one to enhance the overall network throughput and achieve multiplexing gain; (3) the short symbols and long symbols in the preambles from different stations (STAs) can be arbitrarily assigned without any restriction; (4) the MAIs and CCIs suppression capability is enhanced by spatial filtering based on the estimated nominal DOAs.

Simulation results are also furnished to justify the proposed approach. The about research

results have been presented at IEEE VTC 2006.

五、參考文獻

[1] G.J. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multiple antennas,” Bell Labs Tech., pp. 41-59, Aut.

1996.

[2] Y. Zhao, S.-G. Haggman, “BER analysis of OFDM communication systems with intercarrier interference,” in Proc. IEEE Communication Technology Conf., pp.

1998.

[3] M. Morelli and U. Mengali, “An improved frequency offset estimator for OFDM applications,” IEEE Comm. Letters, vol. 3, no. 3, pp. 75-77, Mar. 1999.

[4] G.L. Stuber, J.R. Barry, S.W. Mclaughlin, Y.

Li, M.A. Ingram and T.G. Pratt, “Broadband MIMO-OFDM Wireless Communications,”

IEEE Proc. vol. 92, no. 2, Feb. 2004.

[5] J.J. van de Beek, M. Sandell and P.O.

Borjesson, “ML estimation of time and frequency offset in OFDM systems,” IEEE Trans. on Signal Processing., vol. 45, pp.

1800-1805, July, 1997.

[6] R.O. Schmidt, “Multiple emitter location and signal parameter estimation,” in Proc.

RADC Spectral Estimation Workshop, pp.

243-258, 1979.

[7] G.H. Golub and C.F. Van Loan, 3rd ed., Matrix Computations, Johns Hopkins, 1996.

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ÓÓÓÓ

ÄÄÄÄÔDÕ

ÔDÕ ÔDÕ ÔDÕ

Fig.1 The scenario of MIMO-OFDM uplink network

X

ˆ )}

ˆ , ( , ˆ ), ˆ , ( ˆ), ˆ,

{(∆f1,1θ1,1 ∆f1,2θ1,2 ∆fP,Q_PθP,Q_P

)}

ˆ( {d1i

Fig.2 The flow graph of the propose SFS algorithm

Fig. 3 Comparison of RMSE of nominal DOA Estimates

Fig. 4 Comparison of RMSE of frequency offsets estimates

Fig. 5 Comparison of BER