IEICE TRANS. FUNDAMENTALS, VOL.E89–A, NO.3 MARCH 2006
670
PAPER
Special Section on Multidimensional Signal Processing and Its Application
Design of MIMO Communication Systems Using Tapped Delay Line Structure in Receiver Side Tetsuki TANIGUCHI†a) , Member, Hoang Huy PHAM† , Student Member, Nam Xuan TRAN†† , and Yoshio KARASAWA† , Members
SUMMARY This paper presents a simple method to determine weights of single carrier multiple input multiple output (MIMO) broadband communication systems adopting tapped delay line (TDL) structure in receiver side for the effective communication under frequency selective fading (FSF) environment. First, assuming the perfect knowledge of the channel matrix in both arrays, an iterative design method of transmitter and receiver weights is proposed. In this approach, both weights are determined alternately to maximize signal to noise plus interference ratio (SINR) by fixing the weight of one side while optimizing the other, and this operation is repeated until SINR converges. Next, considering the case of uninformed transmitter, maximum SINR design method of MIMO system is extended for space time block coding (STBC) scheme working under FSF. Through computer simulations, it is demonstrated that the proposed schemes achieves higher SINR than conventional method with delay-less structure, particularly for the fading with long duration. key words: MIMO, STBC, maximum ratio combining, frequency selective fading, spatio-temporal processing, tapped delay line
1.
Introduction
As an answer to increasing requirement for the high data rate transmission, MIMO communication systems using array antennas both in transmitter and receiver sides are collecting attentions [1], [2]. In the case of flat fading (FF), the singular value decomposition (SVD) based design with power allocation scheme by water filling (WF) is known to be effective under the assumption of perfect channel state information (CSI) in both transmitter and receiver [3], [4], and various space-time coding techniques are used when transmitter (and receiver) is uninformed [2]. Under frequency selective multipath fading environment, however, those methods could not be simply applied due to the inter symbol interference (ISI) caused by signals arriving through delay paths. Multicarrier MIMO system (ex., MIMO-OFDM [5]) is one attractive candidate to mitigate the influence of FSF since the well-investigated fundamental theory of flat fading environment could be simply applied to each subchannel. Other approaches use cyclic prefix (CP) [6] or zero guard symbols [7] (this paper deals Manuscript received June 27, 2005. Manuscript revised October 3, 2005. Final manuscript received November 17, 2005. † The authors are with the Department of Electronic Engineering, The University of Electro-Communications, Chofu-shi, 1828585 Japan. †† The author is with the Department of Information and Communication Engineering, The University of Electro-Communications, Chofu-shi, 182-8585 Japan. a) E-mail:
[email protected] DOI: 10.1093/ietfec/e89–a.3.670
with the most general case adopting data multiplexing transmission by space-time processing in both array sides) for single carrier transmission, but they bring the reduction of the transmission rate due to the addition of CP or the extension of the data. Single carrier approaches without data extension are also examined, but we have few literatures describing practical design of them. The method given in [8] achieves mitigation of FSF by suppressing the waves arriving at the receiver with time delay only by spatial filtering, but the number of delayed waves to be cancelled is restricted by the number of array elements. To cope with the delay of long duration, MIMO communication systems with tapped delay line (TDL) have been also considered. In [9], continuous time system is investigated, and recent papers [10], [11] deal with the case of matrix modulation, but they require complicated nonlinear optimization procedure. Reference [12] formulates the input output relation of a MIMO system consisting of cascade connection of beamformer for spatial processing and time-domain equalizer. In [13], the performance of a MIMO system using a spatio-temporal filter in transmitter is examined through computer simulations. The cascade connection of array antenna and decision feedback equalizer is described in [14]. Our final objective is to establish a mathematically simple procedure to determine weights of MIMO systems with TDL configuration based on maximum SINR criterion for the effective broadband communication without data extension under FSF. In this paper, as a first step of a series of works, a design method of MIMO systems having TDL structure only in receiver side is presented for two cases: (i) Perfect CSI at transmitter and receiver, and (ii) Space time block coding (STBC) scheme assuming uninformed transmitter and receiver with perfect CSI. This approach could be applied in the situation, e.g., where a mobile station with simple structure is working with a base station equipped with TDL, and/or small amout of feedback is allowed. The organization of this paper is as follows: In Sect. 2, MIMO communication system under FSF is briefly described. In Sect. 3, the proposed design scheme of TDLMIMO communication system is given. Section 4 provides computer simulations to investigate the performance of the proposed method. Sections 5 and 6 describe TDL structure which works under STBC transmission in FSF. Finally in Sect. 7, the conclusions and future works are described.
c 2006 The Institute of Electronics, Information and Communication Engineers Copyright
TANIGUCHI et al.: DESIGN OF MIMO SYSTEMS USING TDL STRUCTURE IN RECEIVER SIDE
671
Fig. 1 Multiple-input-multiple-output (MIMO) communication system under FSF. System considered in this study has TDL structure only in receiver side.
2.
Description of MIMO Communication System under FSF
Consider a MIMO communication system as shown in Fig. 1, in which the transmitter and the receiver arrays have Nt and Nr antenna elements, respectively. Each receiver element is followed by Lr − 1 tapped delay line units accompanied by Lr weights. As a propagation channel, a quasi-static i.i.d. (independent and identically distributed) Rayleigh fading channel with frequency selectivity is assumed. The propagation channel under FSF environment is expressed by channel matrix series with the size of Nr × Nt and duration L denoted by {H(); = 0, · · · , L − 1}, where (nr , nt ) element Hnr ,nt () denotes the transmission coefficient from nt -th element in the transmitter to nr -th element in the receiver with the delay T S , where T S denote the symbol period. Here, we assume that this matrix series {H()} is completely known at the both sides of the system (perfect knowledge of CSI=Channel State Information). The input signal s(t)(t ∈ Z) is multiplied by Nt dimensional transmitter weight vector wt , then radiated into multipath channel represented by {H(); = 0, · · · , L − 1}, and reproduced through the set of Nr -dimensional receiver weight vectors {wr (r ); r = 0, · · · , Lr − 1}. As a result, the output signal sˆ(t) is formulated as follows: sˆ(t) =
L r −1
L−1 wrH (r ) H()wt
r =0
=0
× s(t + r − ) + n(t + r )
are derived based on singular value decomposition (SVD) of H(0) [4], design approach under FSF is required to eliminate or utilize the multipath waves arriving with time delay. The former strategy has been adopted in [8], and the latter is described in this paper. 3.
Design Method of MIMO Communication Systems under FSF
3.1 Design Method of MIMO Communication Systems without TDL [8] In this subsection, the design method of MIMO communication systems without delay line (Lr = 1) assuming FSF and perfect knowledge of CSI is briefly described. As shown in Sect. 2, the received signal contains delayed versions of previous signals corresponding {H(); 0}, and which causes ISI between s(t) and {s(t−1), · · · , s{t− (L − 1)}}. Therefore, if we can extract the propagating wave coming through the delayless path H(0) and eliminate delayed components, the influence of FSF could be avoided. Hence, the transmitter and receiver weights are determined to maximize SINR defined by following equation: 2 wH H(0)w P t S r (2) SINR = 2 L−1 H 2 wr H()wt PS + ||wr || PN =1
(1)
where Nr -dimensional vector n(t) denotes the additive white Gaussian noise (AWGN) generated at the receiver array. The following assumptions are made for the signal s(t) and the noise n(t): E[s(t)s∗ (t − τ)] = PS δτ,0 , E[n(t)n∗ (t − τ)] = PN δτ,0 , and E[s(t)n∗ (t − τ)] = 0, where δm,n denotes the Kronecker’s delta. Different from the flat fading case (L = 1) where the optimum weights maximizing signal to noise ratio (SNR)
where PS = E[|s(t)|2 ] and PN = E[|n(t)|2 ] are the power of signal and noise. In [8], it has been shown that the number of delayed waves (H() O, = 1, · · · , L − 1) is restricted to Nt + Nr − 2 which corresponds to the degrees of freedom of the MIMO communication system. To remove this restriction, array structure with TDL is required. In the next subsection, the approach described in [8] is extended to the design of MIMO system using TDL receiver.
IEICE TRANS. FUNDAMENTALS, VOL.E89–A, NO.3 MARCH 2006
672
3.2 Design Method of MIMO Communication Systems Using TDL The advantage of TDL structure is that the multipath waves arriving with the time delay are not only eliminated but can be utilized to enhance the desired component. In the MIMO communication system considered in this study, the transmitter uses only a spatial filter while the receiver array is equipped with delay elements which enable us spatio-temporal processing of the received signal. Being conscious of SNR maximization design of MIMO systems in FF environment, the transmitter weight wt and the set of receiver weights {wr (r ); r = 0, · · · , Lr − 1} which is summarized to a vector wr = [wTr (0), · · · , wTr (Lr −1)]T are determined to maximize SINR at the output of the receiver. Namely, the following objective function is considered |wrH H s wt |2 PS wtH Ri,r wt PS + ||wr ||2 PN |wrH H s wt |2 PS = H . wr Ri,t wr PS + ||wr ||2 PN
SINR =
(4)
The correlation matrix of interference signal Ri,t is a Nr Lr by-Nr Lr Hermitian matrix with (r,0 , r,1 )-th block represented by following Nt -by-Nt submatrix [Ri,t ]r,0 ,r,1 =
L−1
(1 − δ0 −r,0 ,0 ) (1 − δ1 −r,1 ,0 )
0 ,1 =0
× δ0 −r,0 ,1 −r,1 H(0 )wt wtH H H (1 )
(5)
while Ri,r representing interference correlation is a Nt -by-Nt Hermitian matrix, which is expressed as Ri,r =
L r −1
L−1
wtH Ri,r wt PS + ||wr ||2 PN wtH H sH wr PS −1 × Ri,r PS + ||wr ||2 INt PN H sH wr .
wt,o =
wrH Ri,t wr PS + ||wr ||2 PN wrH H s wt PS × Ri,t PS + INr Lr PN −1 H s wt .
wr.o =
× δ0 −r,0 ,1 −r,1 H H (0 )wr (r,0 )wrH (r,1 )H(1 ).
4.
Simulation Examples
In this section, computer simulations are carried out to verify the effectiveness of the proposed method. In this study, a MIMO system with Nt = 3, Nr = 4, and Lr = 10 is considered. The propagation channel is simulated by truncating delay profile of exponential Rayleigh fading model (delay spread 3T S ) by L (The finite duration is unnatural as an actual environment, but suitable to evaluate the influence of duration of H()). For the evaluation of the performance, the output SINR of the system is defined as follows by using the normalized correlation of input and output signals: ρ=
(6)
Since this optimization problem is not easy to solve in closed form, we consider to calculate wt and wr alternately. Actual steps are as follows: After giving certain initial values to all weights (In this paper, we use a uniform weight of unit length. The investigation on the choice of a better initial weight is included in the future works), the transmission weight wt which maximize SINR is calculated for a fixed
(8)
Though the constraint of unit norm is not necessary in the case of the receiver weight determination since its norm has no influence on SINR, wr is also normalized for convenience. The above procedure is repeated until the change of SINR fall below a certain threshold (ε = 10−3 in this study). Though the convergence of this algorithm is not proven theoretically, the experience shows it works successfully.
(1 − δ0 −r,0 ,0 ) (1 − δ1 −r,1 ,0 )
r,0 ,r,1 =0 0 ,1 =0
(7)
Equation (7) still contains wt in the right-hand-side and it seems that the complete solution has not derived, but the influence of the variation of wt is restricted only to the length of the vector (because it is contained only in the scalar term wtH Ri,r wt PS +||wr ||2 PN ), and Eq. (7) should be satisfied to maxiwtH H sH wr PS mize SINR, which means the result of above equation indicates correct direction of optimum solution. Therefore, we can get desired transmission weight after normalization. Then wr to achieve maximum SINR is determined keeping wt constant. The solution is
(3)
Here, two expressions of SINR are used for the convenience of optimization to be described. In above equations, the numerator and denominator represent the energy of desired and interference components contained in the output signal sˆ(t). Consequently, the system works to minimize the error of output signal fully utilizing the desired components in propagation wave within the length of TDL. The transmission path H s for the target signal is defined by next equation H s = [H T (0), · · · , H T (Lr − 1)]T .
wr . Since the SINR is improved as the norm of wt becomes larger† , ||wt || should be constrained to 1. By solving above problem using method of Lagrange multiplier, the optimum weight of transmitter is given by next equation:
E[ sˆ(t)s∗ (t)]
E[| sˆ(t)|2 ]E[|s(t)|2 ] |ρ|2 SINR = . 1 − |ρ|2
(9) (10)
The input SNR, the power ratio between the input signal † If weigh vector wt is multiplied by c(> 1), after dividing numerator and denominator of Eq. (3) by c2 , only the second term of the denominator is still multiplied by 1/c2 . Hence, as the constant number c is large, SINR becomes large.
TANIGUCHI et al.: DESIGN OF MIMO SYSTEMS USING TDL STRUCTURE IN RECEIVER SIDE
673
(a) L = 5
Fig. 3 Distribution functions of SINR for conventional [8] (broken line) and proposed (solid line) approaches assuming infinite length delay profile with exponential average power.
(b) L = 7 Fig. 2 Comparison of performance between conventional [8] (broken line) and proposed (solid line) approaches based on distribution functions of SINR. Fig. 4
Duration of delay profile versus output SINR.
s(t) to the transmission array and noise n(t) generated in the receiver, is defined by next equation SNR =
E[|s(t)|2 ] PS . = PN E[|n(t)|2 ]
The output SINR is calculated for BPSK signals with SNR = 20 dB, and the distribution function of SINR given in Fig. 2 is derived repeating this operation. The performance of the proposed method is compared with that of the conventional delay-less structure shown in [8]. In case that the maximum number of delayed waves L − 1 = 4 is within the degrees of freedom of conventional method (Nt + Nr − 2 = 5) [8], the performance of the proposed method is better since it utilizes delayed versions of s(t) to enhance the desired signal instead of excluding them (Fig. 2(a)), but their difference is small. On the other hand, in the case in which the duration of channel matrix L − 1 exceeds Nt +Nr −2 = 5, the proposed method brings significant efficiency as shown in Fig. 2(b). Figure 3 is a simulation assuming a realistic environment with infinite exponential
Fig. 5 An example of convergence curves of conventional [8] (broken line, 22.6 dB) and proposed (solid line, 24.4 dB) approaches.
IEICE TRANS. FUNDAMENTALS, VOL.E89–A, NO.3 MARCH 2006
674
delay profile (actually, it is calculated for L = 20, which contains 98% energy of infinite case, i.e., L = ∞). Though it could be predicted from the result of Fig. 2, Fig. 3 demonstrates the dominance of the proposed approach under this practical condition for actual communications. Figure 4 denotes the change of SINR along with the duration of the delay profile. The SINR of receiver-TDL-MIMO system reduces gradually even after L − 1 exceeds the length Lr − 1 of receiver weights, while that of non-TDL system suddenly degrades after L − 1 becomes larger than degrees of freedom Nt + Nr − 2 = 5. An example of convergence curves of TDL-MIMO schemes is shown in Fig. 5. Those results show that the proposed method achieves higher performance than the conventional scheme, but the convergence speed of the weights in TDL-MIMO is slower than that of conventional one. Hence the development of a fast algorithm to carry out the proposed design method is strongly required. 5.
MIMO System with TDL Structure for STBC Transmission
When CSI is possessed only at the receiver side, i.e., a uninformed transmitter is considered, STBC is known to be one good choice as a data transmission scheme [15], [16]. As is the case of FF, the maximum likelihood (ML) estimation using the information of frequency selective channel could be adopted at the receiver for the detection, but it requires large computational cost. In this section, the SINR maximization design approach for MIMO system with TDL proposed in Sect. 3 is extended to work under the transmission scheme adopting STBC. The block diagram of the proposed system is depicted in Fig. 6. Since the data transmission scheme is ruled by the design of STBC and equal power is allocated to each antenna element, only the optimization of receiver weights is required and the receiver works like a broadband array antenna using TDL structure. The primal difference of the receiver structure from that of Fig. 1 is the operator for the complex conjugation and existence of a sets of two weight s) vectors (wR(ns ) and w(n I ) for the derivation of one target sym-
bol. Assume a block of STBC consists of N s symbols {sns (k); n s = 0, · · · , N s − 1}, where k(∈ Z) denotes the block index. In STBC, those symbols are converted through Nt -by-N matrices CR,ns and C I,ns , into Nt -by-N code matrix: S (k) = [s(kN), · · · , s{ kN + (N − 1)}] =
N s −1
CR,ns sns (k) + C I,ns s∗ns (k)
(11)
n s =0
where the notation s(kN + n) represents n-th column vector of S (k). The (nt , n) element of S (k) is transmitted from the nt -th antenna element at time slot t = kN + n. Define [A]m,n as the (m, n) element of matrix A. In the case of the simple Alamouti scheme, [CR,0 ]1,1 = 1, [C I,0 ]2,2 = −1, [CR,1 ]2,1 = 1, and [C I,1 ]1,2 = 1, and other components of those matrices are zero. Considered in this paper is the case where sns (k) appears in each column of S (t) only once including their complex conjugated version (Alamouti scheme [16] and all examples in [2] satisfy this assumption). Since the desired symbol sns (k) is contained in the received signal not only as it is but also in conjugated form, the combination scheme fully utilizing all available signal is given by next equation: sˆns (k) =
L r −1 r =0
(n )H wR s (r )r(kN + r ) s )H + w(n (r )r∗ (kN + r ) I
(12)
s) where wR(ns ) (r ) and w(n I (r ) are Nr -dimensional weight vectors which is used to extract sns (k) from the Nr -by-1 vector of the received signal r(kN + r ) which is represented by
r(t) =
L−1
H()s(t − ) + n(t)
(13)
=0
and its conjugate r∗ (kN + r ) at time t = kN + r . By defining 2Nr Lr -dimensional weight vector w(ns ) , received signal vector r˜ (t), and noise vector n(k) as follows
s) Fig. 6 Structure of MIMO system with TDL for STBC. The weight block w(n (r = I in this figure) I contains complex conjugation operator denoted by ∗, which is not work in case of wR(n s ) (r = R in this figure).
TANIGUCHI et al.: DESIGN OF MIMO SYSTEMS USING TDL STRUCTURE IN RECEIVER SIDE
675 s )T w(ns ) (r ) = [wR(ns )T (r ) w(n (r )]T I
where matrices [Ri(ns ) ]R,r,0 ,r,1 ,nt,0 and [Ri(ns ) ]I,r,0 ,r,1 ,nt,1 with the size of 2Nr × 2Nr are defined by next equations:
w(ns ) = [w(ns )T (0), · · · , w(ns )T (Lr − 1)]T r˜ (k, r ) = [rT (k + r ) rH (k + r )]T
[Ri(ns ) ]R,r,0 ,r,1 ,nt,0 (R,R) nt,0 ,r,0 ,0 H Cns n , , hc,nt,0 (0 )hc,n (1 ) t,1 t,1 r,1 1 = (I,R) nt,0 ,r,0 ,0 ∗ H Cns nt,1 ,r,1 ,1 hc,nt,0 (0 )hc,nt,1 (1 )
r˜ (k) = [˜rT (k, 0), · · · , r˜ T (k, Lr − 1)] n(kN + r ) = [nT (kN + r ) nH (kN + r )}]T
nt,0 ,r,0 ,0 T Cn(R,I) s nt,1 ,r,1 ,1 hc,nt,0 (0 )hc,nt,1 (1 ) (I,I) nt,0 ,r,0 ,0 ∗ T h ( )h ( ) C
n(k) = [nT (kN), · · · , nT { kN + (Lr − 1)}]T , a simplified expression of the estimate of n s -th signal in the block is derived as sˆns (k) =
L r −1
w(ns )H (r )˜r(k, r )
ns
(14)
In this study, as the case of Sect. 2, the maximization of SINR is adopted as a criterion of the optimization. Since the real and imaginary part of s(t) and n(t) are uncorrelated for time shift, the relation E[s(t)s(t − τ)] = 0 and E[n(t)n(t − τ)] = 0 consist (even for τ = 0). From this fact, the following relation is derived. SINR =
s) 2 |w(ns )H h(n s | PS s) (n s ) w(ns )H (R(n i PS + Rn )w
(18)
s) is determined as follows where vector h(n s
s) h(n s,R (r ) =
L−1 N t −1
δQ[r ,],0 sgn([C R,ns ]nt ,R[r ,] )hnt ()
ns
=
δQ[r ,],0 sgn([C I,ns ]nt ,R[r ,] )h∗nt ()
(24)
1
nt,1 ,r,1 ,1
c,nt,0
0
c,nt,1
(25)
1
n , ,
n , ,
r,0 0 Cn(rs0 ,r1 ) nt,0 t,1 ,r,1 ,1
= sgn[Cr0 ,ns ]nt,0 ,R[r,0 ,0 ] sgn[Cr1 ,ns ]nt,1 ,R[r,1 ,1 ]
(26)
and hc,m () denotes the m-th column vector of channel matrix H(). The matrix Rn shows the correlation of AWGN component represented by Rn = E[n(k)nH (k)] = PN I2Nr Lr
(27)
which results in the noise term in Eq. (18). Different from Eq. (3), Eq. (18) has only one vector to be optimized, hence a closed form solution is derived without circular iteration. In the similar manner as the case in Sect. 2, the optimum receiver weight is derived by following equation: s) wo(ns ) = (Ri PS + I2Nr Lr PN )−1 h(n s .
(19) L−1 N t −1
c,nt,1
r,0 0 could be In above equations, the coefficient Cn(rs0 ,r1 ) nt,0 t,1 ,r,1 ,1 determined as follows:
=0 nt =0
s) h(n s,I (r )
0
nt,0 ,r,0 ,0 T Cn(I,R) s nt,1 ,r,1 ,1 hc,nt,0 (0 )hc,nt,1 (1 ) . (R,R) nt,0 ,r,0 ,0 ∗ T h ( )h ( ) C
(15)
For the convenience of the following discussions, here introduced are two operators defined by next equations:
kN + r − Q[r , ] (16) N (17) R[r , ] r − (mod N).
c,nt,0
[Ri(ns ) ]I,r,0 ,r,1 ,nt,1 (I,I) nt,0 ,r,0 ,0 H Cns n , , hc,nt,0 (0 )hc,n (1 ) t,1 t,1 r,1 1 = (R,I) nt,0 ,r,0 ,0 ∗ H Cns nt,1 ,r,1 ,1 hc,nt,0 (0 )hc,nt,1 (1 )
r =0
= w(ns )H r˜ (k).
nt,1 ,r,1 ,1
(28)
The normalization could be carried out without an influence on the resultant SINR.
=0 nt =0
(20) T T T s) h(n s (r ) = [h s,R (r ) h s,I (r )] s) s )T s )T h(n = [h(n (0), · · · , h(n (Lr s s s
(21) − 1)]T .
(22)
The 2Nr -dimensional square submatrix [Ri(ns ) ]r,0 ,r,1 representating (r,0 , r,1 )-th block of 2Nr Lr -dimensional square matrix Ri(ns ) is defined by next equation: [Ri(ns ) ]r,0 ,r,1 =
L r −1
L−1
N t −1
r,0 =0,r,1 =0 0 ,1 =0 nt,0 ,nt,1 =0
δQ[r,0 ,0 ],Q[r,1 ,1 ] δR[r,0 ,0 ],R[r,1 ,1 ] × 1 − min{δQ[r,1 ,1 ],0 , δR[r,0 ,0 ],ns } (n s ) s) × [R(n ] + [R ] R, , ,n I, , ,n r,0 r,1 t,0 r,0 r,1 t,1 i i
(23)
6.
Example of STBC Processing and Discussion
In this section, the effectiveness of the proposed approach in Sect. 5 is demonstrated through examples. The simulation considered here is for the transmission using Alamouti scheme [16]. The distribution function of the output SINR in 2 × 2 STBC-based MIMO system is calculated for QPSK signals with SNR = 10 dB. The channel duration is set to L = 10 and the delay spread is assumed to be σS = 3T S . Observed from the result shown in Fig. 7, the output SINR improves as the length of TDL Lr becomes longer, and the effectiveness of the proposed method is verified. Figure 8 compares the distribution functions of SINR for two transmission schemes described in Sect. 3 (BF, Lr = 4), and Sect. 5 (STBC, here Lr = 5 is used so that both s) {wR(ns ) (r )} and {w(n I (r )} can utilize signal components of at
IEICE TRANS. FUNDAMENTALS, VOL.E89–A, NO.3 MARCH 2006
676
considered corresponding to the constellation of the type of STBC. Here we proposed is the generalized theory containing those variations as a special case. 7.
Fig. 7 Distribution functions of SINR in 2 × 2 MIMO system for various TDL length under FSF with the channel duration L = 10 and delay spread σS = 3T S .
Fig. 8 Distribution functions of SINR in 4 × 4 MIMO system for two transmission approaches under FSF with the channel duration L = 7 and delay spread σS = 5T S . BF denotes the result of beamforming method in Sect. 3, and STBC shows that of the scheme described in Sect. 5.
least four time slots. Remark that in examples in this paper, the complex conjugated signals first appear at the second column of S (k)). The code matrix of STBC used here is s as follows [2]: s0 (k) −s∗1 (k) −s∗2 (k) s3 (k) s (k) s∗ (k) −s∗ (k) −s (k) 2 . 0 3 S (k) = 1 s2 (k) −s∗3 (k) s∗0 (k) −s1 (k) s∗1 (k) s0 (k) s3 (k) s∗2 (k) Figure 8 shows the performance of BF method assuming perfect CSI at both sides overcomes that of STBC approach which is usually used when CSI is possessed only in receiver side (even though STBC scheme is advantageous in its weight number), and this result coinsides with the case of FF [16]. Here we used the example of Alamouti type STBC, but the proposed method is applicable to other various spacetime codes such as layered type (ex. BLAST) without modifications. In so doing, a variety of modifications (ex., variable length of TDL depending on symbol index n s ) could be
Conclusions
In this paper, we presented a novel maximum SINR design method of MIMO communication systems having TDL structure in receiver side for the high data rate transmission under FSF. First, assuming perfect knowledge of CSI in both array sides, a procedure for the iterative decision of transmitter and receiver weights was proposed, in which both weights are determined alternatively, fixing one side and optimizing the other based on maximum SINR criterion. Repeating this operation until the convergence of SINR, the final version of transmitter and receiver weights is derived. Then, assuming uninformed transmitter, we gave a design method of TDL-MIMO system to derive a maximum SINR output for the signal transmitted using STBC scheme. Through computer simulations, the effectiveness of the proposed method, particularly in the case of large delay spread, was demonstrated. The proposed method requires large computational cost, but it enables us to achieve high SINR communication without the expense of data transmission rate. As future works, further investigation on the potential and detailed performance analysis of TDL-MIMO as well as more effective strategy for weight optimization (particularly, direct solution of Eq. (3) without iterative procedure) should be considered. The design methods of MIMO system with TDL structure in transmitter, in both array sides, and furthermore multimode transmission using those strategies are also important themes of study. Acknowledgment The authors would like to thank Japan Society for the Promotion of Science (JSPS) for their support of this work under Grant-in-Aid for Young Scientists (B) (No. 16760291). References [1] H. B¨olcskei and A.J. Paulraj, “Multiple-Input Multiple-Output (MIMO) wireless systems,” in The Communications Handbook, 2nd ed., ed. J. Gibson, pp.90.1–90.14, CRC Press, 2002. [2] Y. Karasawa, “MIMO,” in Next Generation Wireless Techniques, ed. N. Nakajima, pp.70–108, Maruzen, Tokyo, 2004. [3] J.B. Andersen, “Array gain and capacity for known random channels with multiple element arrays at both ends,” IEEE J. Sel. Areas Commun., vol.18, no.11, pp.2172–2178, Nov. 2000. [4] Y. Karasawa, Radiowave Propagation Fundamentals in Digital Mobile Communications, pp.135–143, Corona-sha, Tokyo, 2003. [5] K. Wong, R.S.-K. Cheng, K.B. Letaief, and R.D. Murch, “Adaptive antennas at the mobile and base stations in OFDM/TDMA system,” IEEE Trans. Commun., vol.49, no.1, pp.195–206, Jan. 2001. [6] N. Al-Dhahir, “Single-carrier frequency-domain equalization for space-time block-coded transmissions over frequency-selective fading channels,” IEEE Commun. Lett., vol.5, no.7, pp.304–306, July 2001.
TANIGUCHI et al.: DESIGN OF MIMO SYSTEMS USING TDL STRUCTURE IN RECEIVER SIDE
677
[7] H. Sampath, P. Stoica, and A. Paulraj, “Generalized linear precoder and decoder design for MIMO channels using the weighted MMSE criterion,” IEEE Trans. Commun., vol.49, no.12, pp.2198–2206, Dec. 2001. [8] H.H. Pham, T. Taniguchi, and Y. Karasawa, “The weights determination scheme for MIMO beamforming in frequency-selective fading channels,” IEICE Trans. Commun., vol.E87-B, no.8, pp.2243– 2249, Aug. 2004. [9] J. Salz, “Digital transimission over cross-coupled linear channels,” AT&T Technical Journal, vol.64, no.6, pp.1147–1159, July-Aug. 1985. [10] K. Wong, R.D. Murch, and K.B. Letaief, “Optimizing time and space MIMO antenna system for frequency selective fading channels,” IEEE J. Sel. Areas Commun., vol.19, no.7, pp.1395–1407, July 2001. [11] D.P. Palomar and M.A. Lagunas, “Joint transmit-receive space-time equalization in spatially correlated MIMO channels: A beamforming approach,” IEEE J. Sel. Areas Commun., vol.21, no.5, pp.730– 743, June 2003. [12] T. Sawazaki, K. Ishii, H. Yamasuge, and R. Kohno, “A study on optimal equalization of transmitter and receiver in space and time domains using adaptive array antenna,” IEICE Technical Report, RCS2001-48, June 2001. [13] T. Sawazaki and R. Kohno, “A study on optimal equalization of transmitter and receiver using adaptive array antenna,” IEICE Technical Report, RCS2001-288, March 2002. [14] D. W¨ubben and K.-D. Kammeyer, “Impulse shortening and equalization of frequency-selective MIMO channels with respect to layered space-time architectures,” Signal Process., vol.83, no.8, pp.1643–1659, Aug. 2003. [15] V. Tarokh, N. Seshadri, and A.R. Calderbank, “Space-time codes for high data rate wireless communication: Performance criterion and code construction,” IEEE Trans. Inf. Theory, vol.44, no.2, pp.744– 765, March 1998. [16] S.M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Sel. Areas Commun., vol.16, no.8, pp.1451–1458, Oct. 1998.
Tetsuki Taniguchi received the B.S. and M.S. degrees in electrical engineering from Tokyo Metropolitan University, Tokyo, Japan, and D.E. degree in natural science from Kanazawa University, Kanazawa, Japan, in 1989, 1991, and 1996, respectively. In 1992, he joined Kanazawa University, where he worked as a research assistant at Department of Electrical and Information Engineering, and a researcher at MAGCAP (Laboratory of Magnetic Field Control and Applications). In 2001, he joined the University of Electro-Communications, where he is currently a research assistant at Department of Electronic Engineering. His research interests are in digital signal processing, digital communications, and nondestructive evaluation. He is a member of IEEE, The Institute of Electrical Engineers of Japan, and The Japan Society of Applied Electromagnetics and Mechanics.
Hoang Huy Pham received B.E. degree from Ho Chi Minh University of Technology, Vietnam in 1999 and M.S degree from the University of Electro-Communications, Tokyo, Japan in 2003. He is currently a Ph.D. student in Department of Electronic Engineering, The University of Electro-Communications, Tokyo, Japan. His research interests are in the areas of adaptive array antenna, space-time adaptive beamforming, DS-CDMA for FDD system, flat and frequency selective fading channels, multiple-input multiple-output and multiuser systems.
Nam Xuan Tran was born in Thanh Hoa, Vietnam on 8th September 1971 in Thanh Hoa, Vietnam. He received his B.E. degree in radioelectronics from Hanoi University of Technology, Vietnam in 1993, M.E. in telecommunications engineering from University of Technology, Sydney, Australia in 1998, and D.E. in electronic engineering from The University of Electro-Communications, Tokyo, Japan in 2003. Since November 2003, he has been a research associate at the Information and Communication Engineering, The University of Electro-Communications. His research interests are in the areas of adaptive array antenna space-time processing, space-time coding and MIMO systems. Dr. Tran is a recipient of the 2003 IEEE AP-S Japan Chapter Young Engineer Award. He is a member of IEEE, and Society of Information Theory and its Applications.
Yoshio Karasawa received the B.E. degree from Yamanashi University, Japan, in 1973 and the M.S. and Dr. Eng. degrees from Kyoto University, Japan, in 1977 and 1992, respectively. In 1977, he joined KDD R&D Labs., Tokyo, Japan. From July 1993 to July 1997, he was a Department Head of ATR Optical and Radio Communications Res. Labs. (1993–1996) and ATR Adaptive Communications Res. Labs. (1996–1997), both in Kyoto, Japan. From 1997 to 1999, he was a Senior Project Manager of KDD R&D Labs. now he is a professor of The University of ElectroCommunications, Tokyo. He was also a visiting professor of Osaka University, Osaka, Japan (2000–2001). Since 1977, he has been engaged in studies on wave propagation and radio communication antennas, particularly on theoretical analysis and measurements for wave-propagation phenomena, such as multipath fading in mobile radio systems, tropospheric and ionospheric scintillation, and rain attenuation. His recent interests are in frontier regions bridging “wave propagation” and “digital transmission characteristics” in wideband mobile radio systems and digital and optical signal processing antennas. Dr. Karasawa received the Young Engineers Award from the IECE of Japan in 1983 and the Meritorious Award on Radio from the Association of Radio Industries and Businesses (ARIB, Japan) in 1998. He is a member of the IEEE, URSI and SICE (Japan).
