IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 6, JUNE 2008
1987
MIMO Block Spread CDMA Systems for Broadband Wireless Communications Tio Surya Dharma, A.S. Madhukumar, Senior Member, IEEE, and A.B. Premkumar, Senior Member, IEEE
Abstract—This paper studies two MIMO architectures for single-carrier CDMA system employing block spreading, namely Layered Space-Time Block Spread CDMA (LST BS-CDMA) and Space-Time Coded Block Spread CDMA (STC BS-CDMA). It is shown that under low mobility conditions, the proposed systems are virtually free from Multiple User Interference (MUI) and the block processing technique used leads to considerable reduction in the overall processing complexity. Extensive simulation was performed to study the impact of the spreading factor and Doppler frequency on the proposed systems. A new parameter called Channel Coherence Ratio (CCR) is introduced as a key parameter in determining the performance of MIMO BS-CDMA. Index Terms—Block spread CDMA, MIMO, single-carrier systems.
I. I NTRODUCTION
F
UTURE mobile communication system is faced with the challenge to deliver the transmission rate that meets the needs of bandwidth hungry applications while maintaining hardware and transmission costs low. Orthogonal Frequency Division Multiplexing (OFDM) seems to be an obvious choice to combat frequency-selective channels in high-rate mobile communication systems and has been adopted widely in various standards for high rate wireless transmission systems. However, OFDM system is well-known to suffer from high peak-to-average power ratio (PAPR) and higher sensitivity to carrier frequency offset as compared to single-carrier (SC) transmission scheme. In this context, a SC system with frequency-domain equalization (SC-FDE) was proposed in [1]. The SC transmission used in [1] simplifies the transmitter structure and minimizes the PAPR that plagues OFDM transmitter. It also gives SC-FDE additional robustness against deeply faded narrowband channels compared to OFDM as energy of individual bit is distributed over the whole spectrum during equalization. Based on SC-FDE, cyclic-prefix (CP) assisted SC CDMA (CP-CDMA) was proposed in [2] as an alternative to multicarrier CDMA (MC-CDMA) systems. Conventional CDMA schemes as such employ chip-wise processing. In other words, considerable amount of processing (such as FFT/IFFT and channel equalization) is performed in between the spreading and despreading blocks. This results
Manuscript received June 1, 2006; revised September 24, 2006, June 27, 2007, and September 6, 2007; accepted January 11, 2008. The associate editor coordinating the review of this letter and approving it for publication was S. Kishore. The authors are with Nanyang Technological University, School of Computer Engineering, BLK N4, Nanyang Avenue, N4-02A-13, Singapore, 639798 (e-mail:
[email protected]; asmadhukumar,
[email protected]). Digital Object Identifier 10.1109/TWC.2008.060205.
in two major issues: 1. Processing complexity is directly proportional to spreading factor (SF); 2. Chip-wise processing destroys code orthogonality during asynchronous transmission. To overcome these limitations, block spread CDMA (BSCDMA) was proposed in [3]. Rearrangement of the processing modules at the receiver allows symbol-wise processing which leads to a reduction in processing complexity by a factor that is equal to SF, while the block structure allows MUI-free transmission and preserves the code orthogonality even during uplink transmission. Formation of multiple-input-multiple-output (MIMO) channels through the use of multiple transmit and receive antennae promises dramatic performance and capacity improvements. The first way of exploiting the additional data pipe is to transmit encoded data from different antenna that will reach the receiver through different paths, creating diversity and hence additonal reliability. In [4], Alamouti discovered one such remarkable architecture. The second way is to enhance data rate by transmitting different data in parallel, leaving the task of separating the transmitted signals to the receiver. Vertical Bell Laboratories Layered Space-Time (VBLAST) [5] is one such architecture. The wedding of the two MIMO architecture with BS-CDMA was proposed in [6][7] and were shown to offer improved performance and lower processing complexity compared to CP- and MC-CDMA incorporating the MIMO architectures. This paper presents an in-depth analysis of two MIMO architectures proposed for BS-CDMA. The practical challenges facing MIMO BS-CDMA are highlighted and discussed in detail. Extensive simulation study is conducted to investigate the performance of MIMO BS-CDMA under various mobile environments. Based on these analyses, a new criteria is proposed to determine the performance of MIMO BS-CDMA systems. The rest of this paper is organized as follows. Section II presents an overview of the basic block processing concept. Section III presents the details of two MIMO implementations of BS-CDMA, namely Layered Space-Time (LST) and Space-Time Coded (STC) BS-CDMA. Section IV discusses practical challenges facing the two proposed architectures. Section V discusses simulation excercise and presents results from simulated model. Section VI concludes the paper. Notation: Bold lower case denote column vector; bold upper case denote matrix; [.]T and [.]+ denote transpose and matrix psuedo-inverse; denotes circular convolution; Im denotes identity matrix of size m × m; [a]i denotes ith row entry of column vector a; [A]ij denotes ith row and j th column of matrix A;
c 2008 IEEE 1536-1276/08$25.00
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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 6, JUNE 2008
II. BS-CDMA: A R EVIEW To overcome the limitation of CP- and MC-CDMA due to MUI during uplink transmission, chip-interleaving DS-CDMA was proposed in [8]. A simplified BS-CDMA scheme was later proposed in [3] which employed FDE. In [3], the information bits dk (n) belonging to the k th user are first grouped into T blocks of size M , dk (i) = dk (iM ) · · · dk (iM + M − 1) , where n is related to i by n = iM + m, m ∈ 0, M − 1 (note that this in all subsequent discussions). relation applies T be the k th user’s spreading code Let ck = ck,1 · · · ck,G and G be the spreading factor. Block spreading operation is performed on dk (i) which is a Kronecker product with ck to produce the chip matrix Xk (i) = ck ⊗ dTk (i). The chips are transmitted row-by-row and each row mades up one chipblock. The g th chip-block is denoted by xgk (i) = ck,g dTk (i) in which CP is appended before transmission. After CP th removal, the received signal K during the g g block interval g g is given by r (i) = k=1 hk (i, g) xk (i, τk ) + n (i), th where hk (i, g) corresponds to k user’s channel during g th chip-block interval, τk denotes the delay for user k T and dk (i, τk ) = dk (iM − τk ) · · · dk (iM + M − 1 − τk ) . When channel variation across G chip-blocks is small, hk (i, 1) ≈ · · · ≈ hk (i, G) ≈ hk (i). Assume that user one is the desired user, i.e. τ1 = 0 and τk ≥ 0 f ork = 1. The output of the block despreading operation is given by: G 2 c1,g r(i) = h(i) d1 (i) g=1
+
K k=2
hk (i) dk (i, τk )
G g=1
c1,g ck,g
+
G
c1,g ng (i)
g=1
(1) It can easily be verified that if τk is less than the length of CP, BS-CDMA maintains perfect code orthogonality during both synchronous and asynchronous transmission. The result of the block despreading operation is simply the cyclic convolution between the transmitted symbols and the user’s channel parameters, with MUI being completely removed. In addition, subsequent processings will occur symbol-wise which translates to a reduction of processing complexity by the spreading factor, G. III. MIMO A RCHITECTURES FOR BS-CDMA S YSTEMS Two basic MIMO BS-CDMA architectures, namely layered space-time BS-CDMA (LST BS-CDMA) and space-time coded BS-CDMA (STC BS-CDMA) will be elaborated in the following subsections. A. Layered Space-Time BS-CDMA (LST BS-CDMA) In LST BS-CDMA [7], information bits dk (n) belonging to the k th user are fed into a VBLAST mapper. The mapper first groups these bits into blocks T dk (iM ) · · · dk (iM + M − 1) . of size M , dk (i) = After grouping, NT consecutive blocks are multiplexed into NT substreams (layers) at the output. Output ¯ k,p (i) = of the pth substream is given by d T dk (NT i + (p − 1)M ) · · · dk (NT i + pM − 1) .
The output of spreading operation on the pth layer is a ¯T (i). The g th chip-block G × M matrix, Xk,p (i) = ck d k,p ¯ xk,p (i, g) = ck,g dk,p (NT i) is appended by CP before transmission. At the q th receive antenna, CP is first removed and the chips are arranged back into G × M matrix and is given as: Rq (i) =
NT K k hk,qp (i) xτk,p (i, 1) · · · k=1 p=1
T k (i, G) + nq (i) hk,qp (i) xτk,p
(2)
where hk,qp (i, g) is the channel between the q th receive antenna and k th user’s pth transmit antenna and nq (i) = T nq (i, 1) · · · nq (i, G) where nq (i, g) is the M × 1 additive white gaussian noise (AWGN) during g th interval. Assume that signal detection is intended for user one and the channel remains invariant during M chip-blocks period. The result of block despreading operation is yq (i) = NT ¯ p=1 H1,qp (i)dk,p (i) + νq (i) where H1,qp (i) is circular Toeplitz matrix having h1,qp (i) as its first column and νq = G g=1 c1,g nq (i, g) can be thought of as the "average" of the additive noise. Performing FFT on yq (i) results in: y ¯q = FM yq =
NT
˘ 1,p + ν¯q ¯ 1,qp d H
(3)
p=1 −j2πab
N where FM is M × M FFT matrix with [F , M ]ab = e ¯ 1,qp (M − 1) is user 1’s di¯ 1,qp = diag ¯h1,qp (0) · · · h H ˘ 1,p = agonal channel frequency response matrix and d T ˘ ˘ d1,p (0) · · · d1,p (M − 1) is the frequency response of the ¯1,p (NT i) and ν¯q (i) is the frequency transmitted symbols d response of the "average" noise. Without loss of generality, ˘1,p , H ¯ 1,qp and nq the index i has been dropped from yq , d in Eqn. (3) and from further discussions. By arranging the lth subcarrier from the NR receive antennae, per-tone zero forcing (ZF) or minimum mean square error (MMSE) equalization as given in [7] can be used. After equalization, the equalized signal response is converted back to time-domain through an FFT operation.
B. Space-Time Coded BS-CDMA (STC BS-CDMA) SC CDMA System employing conventional spreading approach such as in [2], requires chip-wise processing. For such a system to exploit transmit diversity (NT ≥ 2), ST encoding would have to be performed at chip-level or after symbols are spread into chips. The proposed system, however, employing block spreading, allows the design in [9] to be easily adopted to the proposed STC BS-CDMA since encoding is performed on symbols instead of chips. To begin with, generalized real orthogonal design (GROD), Gr and generalized complex orthogonal design (GCOD), Gc are given in [9] as: T Definition1 : Define x = x1 , · · · , xNS and let Gr (x) be an ND × NT matrix with entries 0, ±x1 , · · · , ±xNS . If GrT (x)Gr (x) = α(x21 + · · · + x2NS )INT with α positive, then Gr (x) is termed a GROD in variables x1 , · · · , xNS of size ND × NT and rate R = NS /ND .
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T x1 , · · · , xNS Definition2 : Define x = and let Gc (x) be an ND × NT matrix with entries 0, ±x1 , ±x∗1 , · · · , ±xNS , ±x∗NS . If GcH (x)Gc (x) = α(|x1 |2 + · · · + |xNS |2 )INT with α positive, then Gc (x) is termed as GCOD in variables x1 , · · · , xNS of size ND × NT and rate R = NS /ND . When NT = 2, a complex orthogonal matrix with rate R = 1(NS = ND = NT ) can be easily constructed by applying simple manipulation to Gr (x). However, such matrix does not exist for NT > 2. General GCOD with rate R = 12 for NT > 2 can be constructed as follows: 1. Construct GROD Gr (x) of size NS × NT with R=1 2. Replace the symbols x1 , · · · , xNS by their conjugates x∗1 , · · · , x∗NS to arrive at Gr (x∗ ) T 3. Form Gc (x) = GrT (x), GrT (x∗ ) . The ST encoder takes in NS M × 1 symbols T dk (iNS M ) · · · dk ((i + 1)NS M − 1) = dk (i) and divides them into NS blocks of size M × 1 each, with the pth block represented as dk,p (i) = T dk (iNS M + (p − 1)M ) · · · dk (iNS M + pM − 1) , p ∈ [1, NS ]. The output of the ST encoder is: ⎡
¯k,1 (iND ) d ⎢ .. ¯ D(i) =⎣ . ¯ k,NT (iND ) d
··· .. . ···
⎤ ¯k,1 (iND + ND − 1) d ⎥ .. ⎦ . ¯k,NT (iND + ND − 1) d
¯k,p (i) refers to the block of symbols to be transmitted where d from the pth antenna during ith interval. Block spreading on each M × 1 block results in G × M spread matrix, Xk,p (i) = ¯T (i). Chips from the spread matrix are then read row-wise ck d k and G rows are transmitted one-by-one after CP insertion. At the receiver, CP is first removed and the received chips are then stacked row-by-row as:
2 K k=1
p=1 2
hk,1p (i, 1) xk,p (i, 1) · · · (6)
T hk,1p (i, G) xk,p (i, G)
TABLE I C OHERENCE R ATIO TABLE FOR MIMO BS-CDMA S YSTEMS (C HIP R ATE - 4M CPS )
M
G =8
G = 16
G = 32
G = 8
FD = 16.67Hz 128 256 512
G = 16
G = 32
FD = 40Hz
0.029
0.058
0.116
0.069
0.140
0.279
(0.058)
(0.116)
(0.233)
(0.140)
(0.279)
(0.559)
0.058
0.116
0.233
0.140
0.279
0.559
(0.116)
(0.233)
(0.467)
(0.279)
(0.559)
(1.117)
0.116
0.233
0.467
0.279
0.559
1.117
(0.233)
(0.467)
(0.931)
(0.559)
(1.117)
(2.235)
M
G = 8
G = 16
G = 32
FD = 200Hz 128 256 512
0.349
0.698
1.397
(0.698)
(1.397)
(2.794)
0.698
1.397
2.794
(1.397)
(2.794)
(5.587)
1.400
2.794
5.587
(2.794)
(5.587)
(11.175)
(2i)th and (2i + 1)th block periods results in: y ¯(2i) = FM y(2i) ˘k,1 (2i) + H ˘k,2 (2i) + ν¯1 (2i) ¯ 1,12 (2i)d ¯ 1,11 (2i)d =H ˘∗k,2 (2i) ¯ 1,11 (2i + 1)d y ¯(2i + 1) = −H ¯ 1,12 (2i + 1)d ˘∗k,1 (2i) + ν¯1 (2i + 1) +H
(4) ¯ where D(i) has been constructed by replacing x1 , · · · , xNS in Gc (x) that was constructed using step one to three by √12 dk,1 (i), · · · , √12 dk,NS (i) and x∗1 , · · · , x∗NS by P1M d∗k,1 (i), · · · , P1M dk,NS (i). Here, P1M is a M × M permutation matrix [9] which effectively performs timereversal operation on d∗k,p (i). For discussion, assume the case when NT = 2. The encoder output is simply: ¯ (2i) d ¯k,1 (2i + 1) d ¯ D(i) = ¯k,1 ¯k,2 (2i + 1) dk,2 (2i) d (5) dk (2i) −P1M d∗k (2i + 1) = P1M d∗k (2i) dk (2i + 1)
R(i) =
1989
+ n(i)
p=1
¯k (i). Performing block dewhere xk,p (i, g) = ck,g d spreading operation (for user 1) results in y(i) = 2 ¯ p=1 H1,1p (i)d1,p (i) + ν(i). Performing FFT during the
(7) where Eqn.(7) makes use of the time-reversal property of DFT which states that conjugate time-reversal corresponds to conjugate of individual frequency tones, i.e. FM P1M d∗k (2i) ≡ ˘∗ (2i). Similarly, Orthogonal Restore Combining (ORC) [6] d k or MMSE techniques can then be performed on individual tones, followed by IFFT operation to recover the time-domain symbols for detection. IV. C HALLENGES OF MIMO BS-CDMA IN FAST FADING C HANNELS Up to this point, a very important assumption made is that the channel remains invariant throughout one spreading module (see Section II). While this assumption is valid for high-rate system under low mobility condition, it may not be so under the presence high Doppler spread. The following sections discuss the factors limiting this assumption and its impact on MIMO BS-CDMA systems.
A. LST BS-CDMA For analysis purpose, consider a system with chip rate of 4Mcps, where chip duration is TC = 0.25μsec. The total duration of a single spreading module is given as TSM = G(M + LCP )TC , which means that the minimum time length for earlier assumption to hold depends on G, M , and LCP . ) for a different value Comparison of TSM against TCO ( TTSM CO of G and M is given in Table I. The numbers given in the table without bracket correspond to LST BS-CDMA system. L is assumed to be one-quarter of the block size (L = 14 M ). Now, if TCO < TSM , the output of the block despreading
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operation becomes:
yq =
NT
block is now
G
H1,qp +
˜ 1,qp (g)c21,g H
NT K G
+
(8)
˜k,qp (g) = hk,qp (g)−hk,qp (1) is referred to as residual where h ˜ 1,qp (g) is a toeplitz matrix with channel parameter and H ˜k,qp (g) as the first column. After FFT operation, Eqn. (3) h now becomes
y ¯q =
¯ 1,qp + H
p=1
+
NT K G
G
˘ k,qp (g)c2 H 1,g
˘1,p d
g=2
2 K
βk,qp (2i, l)d˘k (2i + p − 1, l) + ν¯q (2i, l)
y¯q (2i + 1, l) = (−1)p α1,qp (2i + 1, l)d˘∗1 (2i + p NT ), l) +
α1,qp (2i, l)d˘1 (2i + p − 1, l)
k=2 p=1
¯k,qp c1,g ck,g + νq ˜ k,qp (g)d H
k=2 p=1 g=2
NT
2 p=1
¯ 1,p d
g=2
p=1
+
y¯q (2i, l) =
(9)
˘ k,qp (g)d ˘k,p c1,g ck,g + ν¯q H
k=2 p=1 g=2
˘ k,qp (g, 0) · · · ˘ ˘ k,qp (g) = diag(h hk,qp (g, M − 1)) is where H the frequency response of the channel variation during g th ˜ k,qp (g). As can be seen from Eqn. (8), block interval, H despreading operation no longer removes MUI completely and this component is referred to as residual MUI. The lth tone of the FFT ouput from the NR antennae can be ˘ 1 (l) + ¯ 1 (l) + G H ˘ 1 (g, l)c21,g d arranged as y ¯(l) = H g=2 K G ˘ ˘ ¯ 1 (l) is ¯(l), where H k=2 g=2 c1,g ck,g Hk (g,l)dk (l) + ν ¯ 1,qp (l), d ˘k (l) = ¯ 1 (l) = h of size NR × NT with H qp T ˘ k (g, l) is the residual channel pad˘k,1 (l) · · · d˘k,NT (l) , H ˘ hk,qp (g, l) and ν¯(l) = rameter with [Hk (g, l)]qp = ˘ T ν¯1 (l) · · · ν¯NR (l) . The MMSE equalizer can then be easily derived from here.
B. STC BS-CDMA As highlighted earlier, two problems arise when channel variation occurs (TSM > TCO ). Firstly, channel response that is multiplied with the data is no longer a single fixed value, rather, it depends on the degree of variation within a block. Secondly, residual MUI causes performance degradation to STC BS-CDMA. Comparison of TSM against TCO for STC BS-CDMA system with two transmit antennae and different values of G and M is given by the number in brackets in Table I. As the ), smaller values translate to number represents the ratio ( TTSM CO lower degree of variation within a single spreading module. Continuing from III-B, assume that NT = 2. If CCT is larger than the total duration of G chip-blocks, the lth subcarrier or the lth tap of the FFT output during (2i)th and (2i + 1)th
2 K (−1)p βk,qp (2i + p NT , l) k=2 p=1 d˘∗k (2i
+ p NT , l) + ν¯q (2i + 1, l)
(10) ¯ k,qp (i, l) + G h ˘ k,qp (i, g, l) and where αk,qp (i, l) = h g=2 G ˘ βk,qp (i, l) = c1,g ck,g g=2 h k,qp (i, g, l). These tap outputs can now be arranged row-by-row as: T y ˘(2i, l) = y˘1 (2i, l) y˘2 (2i, l) y˘1∗ (2i + 1, l) y˘2∗ (2i + 1, l) ˘1 (l) + ¯ 1 (l)d =H
K
˘k (l) + ν¯(l) ˘ k (l)d H
k=2
(11) ˘ k (l) are given as: ¯ k (l) and H where H ⎡ ⎤ α1,12 (2i, l) α1,11 (2i, l) ⎢ α1,22 (2i, l) ⎥ ⎥ ¯ k (l) = ⎢ α1,21 (2i, l) H (12) ⎣−α1,11 (2i + 1, l) α1,12 (2i + 1, l)⎦ −α1,21 (2i + 1, l) α1,22 (2i + 1, l) ⎡ ⎤ βk,12 (2i, l) βk,11 (2i, l) ⎢ βk,22 (2i, l) ⎥ ⎥ ˘ k (l, g) = ⎢ βk,21 (2i, l) (13) H ⎣−βk,11 (2i + 1, l) βk,12 (2i + 1, l)⎦ −βk,21 (2i + 1, l) βk,22 (2i + 1, l) T and ν¯(l) = ν¯1 (2i, l) ν¯2 (2i, l) ν¯1∗ (2i + 1, l) ν¯2∗ (2i + 1, l) . In [6], ORC equalizer matrix is given as GORC (l) = 1 ¯H γ(l) H1 (l) where γ(l) is the normalization factor. Applying ORC to Eqn. (11) results in: 1 ¯H ¯ ˘1 (l) H (l)H1 (l)d γ(l) 1 K 1 ¯H ˘ ¯ H (l)¯ ˘k (l) + 1 H + ν (l) H1 (l)Hk (l)d γ(l) γ(l) 1 k=2 (14) ¯ 1,qp (2i + 1, l) In an ideal scenario, h = G ˘ ¯ h1,qp (2i, l) and ≈ g=2 hk,qp (2i + 1, g, l)c1,g ck,g G ˘ (2i, g, l)c c ≈ 0. This means that h k,qp 1,g k,g g=2 ˘1 (l) + noise, Eqn. (14) simply becomes ¯ s(2i, l) = d 1 ¯H ¯ where γ(l) H1 (l)H1 (l) = I2 . When this is not true, ORC ¯ 1,qp (2i+1, l) = h ¯ 1,qp (2i, l). technique performs poorly since h ¯ s(2i, l) =
V. S IMULATION S TUDIES Extensive simulation studies were conducted on both LST and STC BS-CDMA systems. The chip rate used is 4Mcps. The length of CP (LCP ) is fixed as one-quarter of the block size. The channel between a pair of receive and transmit antenna is assumed to be independent and identically distributed from the others. Jake’s Rayleigh fading channel model is used. The number of path L, is assumed as 20 with a maximum
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10
0
-1
10
-2
BER
10
Fd=16.67Hz-2Tx2Rx Fd=40Hz-2Tx2Rx Fd=200Hz-2Tx2Rx Fd=16.67Hz-4Tx4Rx Fd=40Hz-4Tx4Rx Fd=200Hz-4Tx4Rx
10-3
8
16 Number of Active Users
24
(a) LST BS-CDMA (M=512,G=32,SNR=10dB) 100
10
-1
10-2
10
-3
10
-4
10
-5
Solid Line - 2Tx2Rx Dotted Line - 2Tx1Rx
BER
delay spread of less than LCP . Uniform delay profile is assumed for the channel. Four test cases were devised. The aims and results of each investigation are elaborated below. Test Case 1: Impact of Doppler Spread on Residual MUI. This test case aims to investigate how the proposed system performs under the different channel conditions. Performance for three different Doppler Frequency values are simulated: (1) Fd = 16.67Hz; (2) 40Hz; and (3) 200Hz. The received signal-to-noise ratio (SNR) for each user is fixed as 10dB. The spreading factor is set as 32 and the number of active users is varied to simulate different load conditions. Block size is assumed to be 512. The BER performance of LST BS-CDMA and STC BS-CDMA systems are shown in Fig. 1(a) and 1(b) respectively. The results show that the system performance of LST and STC BS-CDMA is influenced by two factors: 1. Channel condition; and 2. Channel variation acros G chipblocks. The performance degradation due to channel condition can be analyzed based on single-user performance, where it can be seen that performance for low mobility condition (Fd = 16 and 40Hz) are close to each other and they are superior than that during high mobility condition (Fd = 200Hz). When channel varies between the different chip-blocks, block despreading does not remove MUI perfectly. The degree of degradation due to MUI is reflected from the gradient of the performance curves. It can seen that the slopes are steeper during high mobility condition. Test Case 2: Impact of Block Size under fixed Channel Coherence Ratio (CCR). This test case aims to investigate how performance of the proposed system is influenced by block size. As invariant channel assumption is not always true, a good criterion is to fix the ratio between duration of a single spreading module and channel coherence time, referred to as Channel Coherence Ratio (CCR). The Doppler frequency is set as 40Hz, while the block size and spreading factor configuration is set as: (1)M = 128, G = 32; (2)M = 256, G = 16 and (3)M = 512, G = 8. From Table I, it can be seen that this corresponds to a common CCR value of 0.279 and 0.559 for LST and STC BS-CDMA systems respectively. Half-load performance for LST and STC BSCDMA are depicted in Fig. 5. The results show that given a fixed CCR value, system performance is not affected by the block size used. Similar results are also obtained under single-user and full-load conditions. Test Case 3: Impact of Block Size under Non-Fixed Channel Coherence Ratio (CCR). This test case aims to analyse how MIMO BS-CDMA systems perform with respect to the CCR values. The spreading factor is set as 32. The block size is varied as 256 and 512 for the three different frequencies. For abrevity, these are referred as I and II respectively. Performance of 2 × 2 LST and STC BS-CDMA are shown in Fig. 3 and 4 respectively. For LST BS-CDMA, I performs only about 1dB better than II at Fd = 16.67Hz. This gap grows to about 2dB at Fd = 40Hz while both systems exhibit error floor for Fd = 200Hz. For STC BS-CDMA, the effectiveness of ORC equalizer diminishes for high mobility condition and error floor greater than 10% is exhibited when Fd = 200Hz. With MMSE equalizer, the performance gap is insignificant for Fd = 16.67Hz. This gap grows to 1dB and 3dB for Fd = 40 and 200Hz repsectively.
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Test Case 4: Performance Criteria for MIMO BS-CDMA Channel Coherence Ratio (CCR). So far, results have shown that performance degradation due to MUI occurs in both LST and STC BS-CDMA systems when Doppler spread is large. In addition, CCR value (instead of block size) determines the performance of both systems. Based on these observations, this section proposes CCR as the quantifying criteria to determine the performance of MIMO BS-CDMA systems. The performance of LST and STC BS-CDMA systems under different CCR values is shown in Fig. 5. The CCR values used for LST BS-CDMA systems are 0.058, 0.116, 0.466, 0.698, 1.117, 1.400 and 2.794, while those used for STC BS-CDMA are 0.058, 0.116, 0.233, 0.698, 1.117 and 2.235. Based on these results, two parameters determine the system performance: (1) Single-user threshold CCR value (T CCRsingle ); and (2) MUI threshold CCR value (T CCRMUI ). T CCRsingle indicates the point where singleuser performance starts to degrade, while T CCRMUI indicates the point where MUI effect starts to occur. For LST BS-CDMA, single-user threshold is found to be around 1.4(T CCRsingle ≈ 1.4), while the MUI threshold is around 0.55(T CCRMUI ≈ 0.55). In the case of STC BSCDMA, the values differ for ORC and MMSE equalizer. For ORC, the single-user and MUI threshold are found to be
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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 6, JUNE 2008
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T CCRsingle|ORC ≈ 0.25 and T CCRMUI|ORC ≈ 0.55. In the case of MMSE, the values are 1.1 and 0.55 respectively VI. C ONCLUSION In this paper, two MIMO architectures employing singlecarrier block-spread transmission are presented. A novel receiver arrangement in BS-CDMA system leads to symbol-wise processing and thus reduction in the processing complexity. As an effective indicator on the amount of channel variation during the transmssion of a block of symbols, Channel Coherence Ratio (CCR) was proposed as the key parameter in determining the performance of MIMO BS-CDMA system. Single-user and MUI threshold CCR values determine the point where performance degradation due to poor channel condition and residual MUI starts. R EFERENCES [1] D. Falconer, S. L. Ariyavisitakul, A. Benyamin-Seeyar, and B. Eidson, “Frequency domain equalization for single-carrier broadband wireless systems,” IEEE Trans. Commun., vol. 43, no. 2/3/4, pp. 191–193, Feb. 1995.
Fig. 5.
Impact of coherence ratio.
[2] A. S. Madhukumar, F. Chin, Y. C. Liang, and K. Yang, “Singlecarrier cyclic prefix assisted CDMA system with frequency domain equalization for high data rate transmission,” EURASIP J. Wireless Commun. Networking, vol. 1, pp. 149–160, 2004. [3] X. Peng, F. Chin, T. T. Tjhung, and A. S. Madhukumar, “A simplified transceiver structure for cyclic extended CDMA system with frequency domain equalization,” in Proc. IEEE 61st Veh. Technol. Conf.-Spring, May 2005, vol. 3, pp. 1753–1757. [4] S. M. Alamouti, “A simple transmit diversity technique for wireless communication,” IEEE J. Select. Areas Commun., vol. 16, no. 8, pp. 1451–1458, Oct. 1998. [5] P. W. Wolniansky, G. J. Foschini, G. D. Golden, and R. A. Valenzuela, “V-BLAST: An architecture for realizing very high data rates over richscattering wireless channel,” in Proc. Int. Symp. Signals, Syst., Electron., 1998, pp. 295–300. [6] S. D. Tio, A. S. Madhukumar, A. B. Premkumar, and Z. Lei, “Performance analysis of space-time coded block spread systems for CDMA downlink,” in Proc. IEEE Global Telecommun. Conf. (Globecomm), Nov. 2005, vol. 4, pp. 2292–2296. [7] S. D. Tio, A. S. Madhukumar, and A. B. Premkumar, “Layered spacetime architecture for MIMO block spread CDMA systems,” IEEE Commun. Lett., vol. 10, no. 2, pp. 70–72, Feb. 2006. [8] S. Zhou, G. B. Giannakis, and C. L. Martret, “Chip-interleaved blockspread code division multiple access,” IEEE Trans. Commun., vol. 50, no. 2, pp. 235–248, Feb. 2002. [9] S. Zhou and G. B. Giannakis, “Single-carrier space-time block coded transmissions over frequency-selective fading channels,” IEEE Trans. Inform. Theory, vol. 49, no. 1, pp. 164–179, Jan. 2003.
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