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INVITED PAPER

Special Section on Recent Progress in Antennas and Propagation Researches

Applications of Space Division Multiplexing and Those Performance in a MIMO Channel∗ Takeo OHGANE†a) , Toshihiko NISHIMURA† , and Yasutaka OGAWA† , Members

SUMMARY Currently, space division multiplexing (SDM), where individual data streams are transmitted from different antennas simultaneously, is expected to be a promising technology for achieving a high data rate within a limited frequency band in a multiple-input multiple-output channel. In this paper, transmitter and receiver architectures of SDM applications are described, and performance improvement with the increase of data streams is shown referring to results of computer simulations. In addition, channel coded systems are also evaluated. key words: MIMO, spatial multiplexing, BLAST

1.

Introduction

Recently, much research on signal transmission through a multiple-input multiple-output (MIMO) channel have been presented [1]. Among them, Bell Laboratories layered space-time (BLAST) architecture [2], [3], appearing as the first MIMO application, demonstrated that MIMO systems can achieve very high capacity. MIMO systems are categorized into (1) a high-quality transmission of a single data stream as space-time codes (STC) [4]–[6] and a transmit and receive diversity [7], [8] or (2) a high-data-rate transmission of multiple data substreams such as BLAST. Both are well studied and many papers have been published in a period of a couple of years∗∗ . Specifically, MIMO systems for a high-rate wireless local area network (WLAN) has become the hottest topic due to the growth of broad band internet services. At present, the MIMO transmission is standardized in the WLAN standard IEEE 802.11, and several worldwide chip venders and manufacturers have demonstrated its prototype [9]. A MIMO system such as BLAST multiplexes data into several substreams and achieves a high data rate by transmitting multiple substreams simultaneously. This multiplexing is done in the spatial domain. Here, it is called space division multiplexing (SDM). Due to inter-substream interference at receivers in SDM, we need signal processing technologies for substream detection, such as spatial filtering∗∗∗ and maximum likelihood detection (MLD). BLAST, which repeats spatial filtering and replica cancelling, is also a well-known detector in Manuscript received December 7, 2004. Manuscript revised January 26, 2005. † The authors are with the Graduate School of Engineering, Hokkaido University, Sapporo-shi, 060-8628 Japan. ∗ This article was originally published in the IEICE Transactions on Communications (Japanese Edition), vol.J87-B, no.9, pp.1162–1173, Sept. 2004. a) E-mail: [email protected] DOI: 10.1093/ietcom/e88–b.5.1843

addition to those above. Since we assume that the MIMO channel information is unknown at the transmitter in SDM, all the substreams have the same information rate and transmit power. However, it is known that higher capacity is achievable when the MIMO channel information is available at the transmitter [11], [12]. Specifically, by forming multiple transmit beams with the eigenvectors given from the singular value decomposition (SVD) of a MIMO channel matrix, a MIMO channel is transformed into spatially orthogonal channels (eigenchannels). Since each eigenchannel has a different quality, we can increase the total channel capacity by optimum assignment of resources (data rate and transmit power) [13]– [16]. In this paper, we call this spatial multiplexing using eigenchannels eigenbeam space division multiple access (ESDM). Control of the data rate and transmit power of each substream is also applicable to SDM. Several groups have reported that capacity was improved through the resource control to almost the same as that of E-SDM [17]–[20]. Here, we call this multiplexing with resource control weighted SDM (W-SDM). In this paper, we consider SDM, W-SDM, and E-SDM and describe their concepts. In addition, several multistream detection methods and performance comparisons for both uncoded and coded cases are discussed. The paper organization is as follows. First, the MIMO channel model used in the work is defined. After describing spatial multiplexing methods and signal processing at the receiver, we compare the bit error rate (BER) performance with the number of antennas from 2 to 4 by computer simulations. Finally, we present conclusions and show a perspective for the future. 2.

Channel Model

Hereafter, consider a MIMO channel (in equivalent lowpass system) constructed by N transmit-antennas and L receiveantennas (see Fig. 1), where each channel is flat (frequencyunselective)-faded due to the excess delay of each path being discarded∗∗∗∗ . Defining the N-dimensional transmit-signal vector as x(t) consisting of signals transmitted from transmit an∗∗ See the following special issues: IEEE J. Selected Areas Commun. (in April and June, 2003), IEEE Trans. Inform. Theory (in October 2003), IEEE Trans. Signal Processing (in November 2002). ∗∗∗ An adaptive array [10] may be a more familiar name.

c 2005 The Institute of Electronics, Information and Communication Engineers Copyright 

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Fig. 1

Fig. 2

A MIMO channel model.

tennas, an L-dimensional receive-signal vector through a MIMO channel is written as r(t) = Hx(t) + n(t), where an L × N  h11 H = . . . hL1

channel matrix H is expanded as  . . . h1N   hi j . . .  .  . . . hLN

(1)

number of substreams is definitely identical to the number of transmit antennas N †† . Defining an N-dimensional signal vector consisting of each data substream as s(t), we have s(t) = x(t). Then, the receive-signal vector given by Eq. (1) is rewritten as r(t) = Hs(t) + n(t).

(2)

In the above equation, hi j denotes the channel response from the jth transmit antenna to the ith receive antenna. n(t) is an L-dimensional noise vector of which each element denotes the noise component included in the received signal and follows an independent Gaussian process of zero mean and variance of σ2 . Thus, we have   (3) E n(t)nH (t) = σ2 I L , where I L is the L-dimensional identity matrix and H denotes the Hermitian transpose. When many paths exist between transmit and receive antennas, each element of the channel matrix H generally follows a mutually correlated complex Gaussian process. The correlation is affected by the angular spread of paths; a larger angular spread provides lower correlation. Specifically, the correlation between elements in the same row/column in H becomes low when the angular spread from the transmitter/receiver, respectively, is large. In later discussion, we consider the case where both angular spreads are large enough to satisfy the condition that each element of H should become an independent complex Gaussian process† . 3.

A transmitter architecture of SDM.

Spatial Multiplexing

3.1 Space Division Multiplexing In SDM, a data stream is divided into multiple substreams equally and these are transmitted with equal power from transmit antennas, as shown in Fig. 2, since the quality of each substream is mutually equal on average. Thus, the ∗∗∗∗ Therefore, the following discussions are not applicable to the frequency-selective fading channels. In those cases, we must introduce a multicarrier system such as orthogonal frequency division multiplexing (OFDM) or apply other beamforming methods [14], [15] and equalization at the receiver [21]. Since these are beyond the scope of this paper, we ignore the detailed description.

(4)

Considering the ith element of the above equation, we have ri (t) =

N

hi j s j (t) + ni (t).

(5)

j=1

This equation shows that each received signal is corrupted by inter-substream interference. Therefore, the substream detector with a function to suppress interference is required. Specific methods are discussed later. Since SDM systems transmit multiple substreams, the number of which equals that of transmit antennas, the total data rate can be increased easily. However, the signal quality of each substream would be degraded due to intersubstream interference. Shannon capacity of a Gaussian channel, where the signal-to-noise-power ratio (SNR) is γ, is given by [24] C = log2 (1 + γ) bps/Hz.

(6)

When we use a MIMO channel for single-stream transmission (such as transmit-receive diversity), the channel SNR is highly improved. However, for example, a twofold better SNR provides only 1 bps/Hz increase in capacity. In contrast, there are multiple substreams in SDM and total capacity is given by the sum of the capacity of each substream. Therefore, even if the SNR of each substream degrades, we obtain higher capacity compared to that of single-stream transmission. It can be said that SDM suppresses SNR degradation through the use of multiple receive antennas and improves capacity through the use of multiple transmit antennas. † On increasing the correlation between each pair of elements, the performance degrades in all spatial multiplexing methods. Here, we ignore the description of this characteristic due to space limitation [22], [23]. †† In general, the number of transmit antennas is assumed to not exceed the number of receive antennas (N ≤ L), since this condition must be satisfied for the spatial filtering to function properly as described later. When using MLD, such a requirement is not needed. However, in order to obtain a receive diversity gain, the receiver must have multiple antennas (N ≤ L in general). In contrast, W-SDM and E-SDM, shown later, may be applicable when N > L.

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where h j is the jth column vector of H. Rewriting Eq. (9) to a vector-matrix form yields

3.2 Maximum Likelihood Detection The optimum multi-substream detection for spatial multiplexing is MLD [24]. The number of possible signal constellations of each substream is defined by the modulation scheme employed. Assuming the number of modulated signal constellations as to be M, we have M N possible combinations of each substream constellation. Let us define one of them as ˆs(t). Then, the conditional probability density of r(t) when sˆ (t) is transmitted is p(r(t)|ˆs(t)) =

1 2 e−µ/2σ , (2πσ2 )L

(7)

where µ = ||r(t) − Hˆs(t)||2 .

(8)

Here || · || denotes the Euclidean vector norm. MLD chooses the most likely (or the least µ) combination. MLD provides the receive diversity gain where the diversity order is equal to the number of receive antennas. However, it needs M N calculations of µ so that the system complexity increases exponentially with transmit antennas and constellations. In order to reduce the complexity, the range of search must be narrowed. For this purpose, several methods have been proposed. Specifically, most methods, for example, sphere decoding, which limits the range of search to within a certain distance, and the M-algorithm [25]–[30] apply a layered approach using QR decomposition. 3.3 Spatial Filtering Whereas MLD is the most complicated method, spatial filtering (or an adaptive array) [10], shown in Fig. 3, may be said to be the easiest. Here, it should be noted that the number of receive antennas must not be less than the number of transmit antennas (L ≥ N) to achieve sufficient reduction of inter-substream interference. Using L-dimensional weight vector w j for detecting the jth substream, we have the spatial filtering output y j (t) = wTj r(t)

(9)

= wTj h j s j (t) +

N

wTj hn sn (t)

n=1,n
j

+

wTj n(t),

(10)

y(t) = W T r(t)

(11)

= W Hs(t) + W n(t), T

T

where y(t) is the N-dimensional filter-output vector and W is the L × N weight matrix expanded to W = [w1 , w2 , . . . , wN ].

An architecture of spacial-filtering.

(13)

In general, the weight matrix is given by zero-forcing (ZF) or minimum mean square error (MMSE) algorithms. The ZF algorithm forces the interference component included in Eq. (10) to be zero. The weight matrix is given by W zf = H∗ (HT H∗ )−1 .

(14)

W Tzf is the Moore-Penrose generalized inverse matrix of H and it satisfies W Tzf H = I N where I N is the Ndimensional identity matrix. Substituting the above equation into Eq. (12), we obtain y(t) = s(t) + W Tzf n(t).

(15)

This equation indicates complete interference suppression. Thus, we can represent each substream’s quality with SNR. SNR of the jth substream is γ j =< |s j (t)|2 > /||wzf, j ||2 σ2 ,

(16)

where < · > denotes an ensemble average. Without loss of generality, we assume that < |s j (t)|2 > is the same for any j. Hereafter, we use < |s j (t)|2 >= P s . Although the ZF algorithm removes the interference component completely, as in Eq. (15), noise effects are not considered at all. Therefore, in some cases, the ZF weight emphasizes the noise component in compensation for interference suppression. The MMSE algorithm avoids this problem to determine the optimum weight for minimizing both interference and noise power in the spatial filtering output. The weight matrix in MMSE is given by W mmse = (H∗ HT + σ2 I L /P s )−1 H∗ .

(17)

Since the filtering output in MMSE includes interference components, we cannot derive a simple equation such as Eq. (15) in the ZF case. The quality of each substream is represented by SINR calculated from signal, interference, and noise power. The output SINR is obtained from γ˜ j =< |y j (t)|2 > /(P s − < |y j (t)|2 >),

Fig. 3

(12)

(18)

where < |y j (t)|2 > is the power of the filter output signal for the jth substream detection [31]. The denominator of the above equation corresponds to the power of the error signal between the desired and the filter output. Using the jth column vector of the weight matrix, we have

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< |y j (t)|2 > = P s wTmmse, j h j .

(19)

This spatial filtering requires L2 th-order processing per symbol, except the weight matrix calculation. Although solving the weight matrix requires L3 th-order processing, it may be required only once per burst. Thus, the complexity of spatial filtering is reduced significantly compared to MLD. However, the obtained diversity order is (L + 1 − N) (no diversity gain when L = N). 3.4 Ordered Successive Detection The spatial filter bank outputs multiple substreams simultaneously. Since the quality (SNR or SINR) of each substream is not the same, ordered successive detection (OSD) detects the substream with the best quality, first [3]. Here, we assume that spatial filtering by the ZF or MMSE algorithm is used for substream detection. Consider that the jth substream was detected first. Since it is reasonably expected that the decision yˆ j (t) of the filter output y j (t) is correct, we regenerate the receive-signal vector by subtracting the component including yˆ j (t) from the original receive-signal vector r(t). Thus, we have r (t) = r(t) − h j yˆ j (t).

(20)

Using this new receive-signal vector, the next-best substream is detected under the condition that the jth substream no longer exists† . If there are no decision errors for the jth filter output, the number of substreams is one less. Thus, due to additional diversity gain, the performance of the next stage will be improved. After several iterations of the above process, all substreams can be detected, as shown in Fig. 4. The average performance of all substreams in OSD is better than that in spatial filtering due to diversity gain in the low-SNR region, as described later. Actually, the decision results include errors. Thus, the obtained diversity gain is reduced in the high-SNR region. However, the use of channel coding decreases decision errors and improves the performance of cancelling replicas generated by re-encoding. Since the complexity of OSD is almost the same as that of spatial filtering, there are many studies on it. This method was named BLAST by Bell Laboratories. It can be said that BLAST is the most important contribution for implementing the MIMO application.

trix is unknown at the transmitter. Under this condition, we found that each substream quality is different in spatial filtering. Here, let us consider that the detected substream quality is fedback to the transmitter. Then, the total bit error rate is expected to be improved by rate adaptation (assigning a higher rate to a substream with better quality and vice versa). In addition, transmit power adaptation is also possible. W-SDM incorporates antenna selection in addition to this resource adaptation. The number of transmit substreams K (K ≤ N) corresponds to the number of selected antenna elements. A mapping pattern between transmit antennas and substreams (see Fig. 5) is defined by the N × K transmit switch matrix T w as x(t) = T w As(t),

(21)

where T w has K ones and (N − 1)K zeros, and there are no columns and rows that have multiple ones. Thus, the transmit-signal vector s(t) is K-dimensional. The transmit power is controlled by



(22) A = diag( P1 , P2 , . . . , PK ), where Pk denotes the transmit power assigned to the kth substream. There are several ways to select K antennas from N antennas and to assign the transmit power and data rate to each substream. The most important thing is to apply a fair criterion, such as average BER or throughput, to select the best combination for providing good quality or satisfying the required quality. When there is no antenna selection in W-SDM, resource control is relatively easy since the optimum assignment of transmit power and data rate can be defined by each substream quality fedback from the MIMO receiver. However, the antenna selection requires a quality check of all possible combinations. In such a case, the MIMO transmitter must know all information on the MIMO channel or the MIMO receiver must feedback the optimum combination (antenna selection and resource adaptation) after making the selection by itself. For example, the case of 2-tx 2-rx has three combinations of the transmit switch matrix. A larger number of transmit antennas, however, increases the number of combinations dramatically.

3.5 Weighted SDM In the above discussion, it is assumed that the channel ma-

Fig. 5

Fig. 4

An architecture of OSD.

A transmit architecture of W-SDM.

† We regenerate the channel matrix by subtracting the jth column vector from the original channel matrix.

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3.6 Eigenbeam SDM As described above, W-SDM selects the K antennas of N antennas by using the transmit switch matrix. Extending this idea to forming K-individual beams using N antennas provides a new multiplexing method of mapping each substream to each beam. Here, let us consider the eigenvalue decomposition (EVD) of G = H H H. G is the N-dimensional nonnegative Hermitian matrix and we have N eigenvectors en (n = 1, . . . , N) that satisfy

Fig. 6

A transmit architecture of E-SDM.

eHj Ge j = λ j (λ1 ≥ · · · ≥ λR > λR+1 = · · · = λN = 0) eiH Ge j

= 0 (i
j),

(23) (24)

where λ j is the jth eigenvalue. R larger eigenvalues of N eigenvalues (R = rank(H) ≤ min{N, L}) are nonnegative real numbers. Let the number of substreams be K (K ≤ R). Defining N × K transmit weight matrix as T e = [e1 e2 · · · eK ]

(25)

and the corresponding L × K receive weight matrix as W e = (HT e )∗ ,

(26)

we have the received signal r(t) =Hx(t) + n(t) =HT e As(t) + n(t).

(27)

Multiplying the receive weight matrix with the received signal, we have the spatial filtered output y(t) = W Te r(t) = T eH H H HT e As(t) + W Te n(t) = Λ As(t) + W Te n(t),

(28)

where Λ = diag(λ1 , λ2 , . . . , λK ).

SNR of the jth detected substream is given by

An equivalent model of E-SDM.

γe, j = λP j P s /σ2 .

(31)

Using this equation, we obtain the equivalent system model of the E-SDM transmitter, as shown in Fig. 7. It is thought that E-SDM transforms the MIMO channel into Korthogonal channels. Since each substream quality is given by SNR in Eq. (31) in E-SDM, resource (transmit power and data rate) control can be accomplished using this SNR. The number of substreams selected is R at most. The order of the quality of the orthogonal channels is uniquely determined by the eigenvalues. Thus, the selectable combinations are not so numerous as those in W-SDM. For 2-tx 2-rx, we have just two cases (two beams of all eigenvalues and one beam of the largest eigenvalue). In addition, due to a simple rule of assigning a higher data rate to a substream of higher quality, rate adaptation is easy. However, the resource adaptation requires all information of MIMO channels at the transmitter. It should be noted that the optimum receive weight can also be obtained by ZF or MMSE spatial filtering. 4.

Numerical Analysis

(29) 4.1 Simulation Parameters

This equation indicates that the transmit and receive-weight pair (T e , W e ) accomplishes interference-free detection. The above spatial multiplexing using the eigenbeams is called E-SDM (see Fig. 6). In E-SDM, the receive weight matrix is the complex conjugate of multiplying the transmit weight matrix and the channel matrix. Thus, it can be said that the weight matrix satisfies the maximum ratio combining (MRC) condition that maximizes the SNR of each received substream† . Since the noise component in Eq. (28) satisfies < (W Te n(t))∗ (W Te n(t))T >= σ2 Λ,

Fig. 7

(30)

We carried out numerical analysis on the above three spatial multiplexing methods. Here, we assumed the total data rate to be 2 bps/Hz (2 bits per symbol duration) per antenna, proportional to the number of transmit antennas. For example, in the 4-tx case, SDM has 4 substreams of QPSK. Thus, the total rate is 8 bps/Hz (8 bits per symbol duration). In W-SDM and E-SDM, the number of substreams depends on the resource adaptation. Thus, we have 5 selections: 256QAM × 1, 64QAM × 1 + QPSK × 1, 16QAM × 2, 16QAM × 1 + QPSK × 2, and QPSK × 4. † This property indicates that the receive weight in E-SDM is optimum and provides the same performance as the MLD.

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Here also in W-SDM, we must take care with the antenna selection. For receiver processing, we considered MLD, ZF, MMSE, and OSD (two types with ZF and MMSE: OSD-ZF and OSD-MMSE hereafter) as discussed above. In E-SDM, since all methods have the same performance, we used the simple ZF algorithm. Also in W-SDM, only the ZF algorithm was applied since there is no significant difference in performance† . For the sake of convenience, we assumed that the number of transmit antennas is equal to the number of receive antennas. It varied from 2 to 4. The MIMO channel was modeled as flat (frequency non-selective) uncorrelated quasistatic fading. We assumed that channel information is completely known at both the transmitter and receiver. The packet length was 48 SDM symbols. In the 4-tx case, total transmitted data were 384 bits per packet. In ESDM and W-SDM, resource adaptation is needed. Here, the minimum total BER criterion was applied [13], [16]. When channel coding is employed, each substream is individually coded (a convolutional code of a constraint length of three and coding rate of 1/2) for the sake of convenience†† . The data rate per antenna is 1/2 that in the uncoded case, 1 bps/Hz. The packet length is equal to that in the uncoded case, i.e., 48 SDM symbols after coding. The channel interleave size is the same as the packet size. Soft-decision Viterbi decoding was applied. W-SDM and E-SDM occasionally use multilevel modulation as 16QAM. In such a case, a soft decision such as that described in [33] is carried out. Since E-SDM forms transmit beams, the received power per antenna is different from those in SDM and WSDM even if the total transmit power is identical. Therefore, the total transmit power was used as the BER measure. Hereafter, the total transmit power normalized by the power yielding E s /N0 = 0 dB in the case of single omniantenna transmission. This measure can be used as the average E s /N0 per antenna in SDM and W-SDM. 4.2 Performance Comparison in Different Receiver Structures The BER performance is shown in Figs. 8(a)–(c) with the number of antennas from 2 to 4. First, let us discuss receiver structures in SDM. In all cases, MLD shows the best performance. The obtained diversity order is 2 in Fig. 8(a) and 4 in Fig. 8(c). Thus, MLD provides the same diversity order as the number of receive antennas regardless of the number of interference signals. It should be noted that the BER at the same transmit power is improved with increasing of number of transmit/receive antennas. This indicates that a larger number of transmit/receive antennas gives higher channel capacity in SDM. In contrast, simple spatial filtering with ZF and MMSE have no diversity gain regardless of the number of receive antennas. However, ZF exhibits worse performance than

Fig. 8

BER performance of uncoded SDM applications.

† In SDM, high correlation between a certain pair of substreams degrades the performance of spatial filtering compared with MLD [32]. In W-SDM, however, we do not select the combinations having a highly correlated pair. Thus, the degradation of ZF is not significant. Actually, it is about 1 dB in the 4-tx 4-rx case. †† Space-time coding over the substreams is very effective. Here, because we applied OSD, only per substream coding was used.

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MMSE since ZF suppresses all inter-substream interference whereas MMSE tries to maintain the gain towards the target substream by not suppressing weak interference such as noise. This degradation becomes worse with the number of antenna elements. The BER performance at the same transmit power also degrades. In SDM, therefore, the receiver structure affects the channel capacity. In OSD cases, the performance difference between ZF and MMSE is more significant. OSD-ZF exhibits diversity gain in the low-power region (up to 15 dB in the 2-tx 2-rx case and 20 dB in the 4-tx 4-rx case). Unfortunately, this gain disappears in the high-power region due to decision error propagation. In contrast, OSD-MMSE exhibits the diversity gain over a wide range [34]. Specifically, the diversity order of more than 2 is obtained up to a normalized transmit power of 20 dB in the 4-tx 4-rx case. OSD-MMSE selects the least interfered substream as the first-detected one. Here, due to the property of maintaining the gain towards the target in MMSE, selective diversity gain is expected. Although the detailed description is omitted, the BER of the first-selected substream is the best when observing the BER performance per ordered substream. It can be said as that this high detection performance leads to a total performance improvement. Considering its simplicity and near-MLD performance, we expect OSD-MMSE to be an easily implemented method. The BER performances of W-SDM and E-SDM outperform that of SDM. The superiority is significant in the 2tx 2-rx case. The obtained gain against SDM at BER= 10−4 is about 5 dB in W-SDM and 6 dB in E-SDM. Although the gain is reduced with the number of antenna elements, ESDM still has about 3 dB gain in the 4-tx 4-rx case. These multiplexing methods are more effective when there is a larger quality difference. Therefore, with an increase in the number of receive antennas, the quality difference becomes small and the effect of resource adaptation is lost. Actually, greater improvement is observed in the case of fewer receive antennas in E-SDM. In addition, W-SDM and E-SDM have the advantage of high performance by only simple spatial filtering, making it possible to reduce the receiver complexity. If the transmitter has MIMO channel information and the ability of resource adaptation, W-SDM and E-SDM are very effective. It should be noted that the performance of W-SDM is worse than that of SDM in the low-SNR region when 4-tx 4-rx. Here, we employed the minimum BER criterion for resource adaptation. This is because there is adaptation error due to BER approximation using the Chernoff bound. Fig. 9

BER performance of convolutional-coded SDM applications.

4.3 Performance Comparison in Channel Coded Cases As a more realistic situation, the performance in the coded case was evaluated, as shown in Figs. 9(a)–(c), where only OSD-MMSE was applied to the receiver structure for SDM. In W-SDM and E-SDM, the resource adaptation was carried out based on the upper bounded BER of the convolutional code.

The figure indicates an improvement on BER (or channel capacity) with increasing number of transmit antennas in all systems. In comparison, at BER of 10−4 , the obtained gains of E-SDM and W-SDM against SDM are about 9 dB and 8 dB in the 2-tx 2-rx case and about 4 dB and 2 dB in the 4-tx 4-rx case, respectively. Although these gains decrease

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in the 4-tx 4-rx case as in the uncoded case, it can be said that W-SDM and E-SDM are still effective. It should be noted that the coded BER performance in SDM with OSD-MMSE is highly improved considering the uncoded case since the error propagation in replica cancelling is reduced by using error-corrected decisions. 5.

Conclusions

In the paper, the MIMO systems widely investigated for application to higher data rate transmission, SDM, W-SDM, and E-SDM, were described. W-SDM and E-SDM require not only MIMO channel information but also the adaptation capability for data rate and transmit power. However, a significant improvement in the BER performance is obtained by these multiplexing methods. Thus, W-SDM and E-SDM would be very attractive if those implementations were possible. Fortunately, with increasing number of transmit/receive antennas, the degradation of SDM decreases. Specifically, the coded BER performance of SDM approaches those of W-SDM and E-SDM. Such a system is a candidate for a more realistic structure. At present, studies on MIMO transmission are extended to space-time channel coding to obtain near-Shannon capacity or multi-user MIMO systems [35]–[38]. The basic characteristics of MIMO systems is defined by the MIMO channel itself, and it is known that correlations between channels degrade the channel capacity and BER performance. However, it has also been reported that the line-of-sight situation with high correlation and high SNR provides better BER performance compared to the non-line-of-sight situation with low correlation and low SNR [39]. Thus, it is very important to study MIMOchannel modeling and MIMO-transmission systems taking actual propagation situations into consideration [40], [41]. Basic characteristics of the antenna element, i.e., input/output port of a MIMO channel, is another important factor that affects the MIMO capacity. Evaluations of mutual coupling between elements and of MIMO channel capacity formed by differently polarized antennas [42]–[44], particularly experimental evaluations, are expected in the future studies. Acknowledgments The authors would like to thank Mr. Takahiko Tsutsumi for assistance with computer simulations. References [1] G.J. Foschini and M.J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wirel. Pers. Commun., pp.311–335, March 1998. URL: http://www1.belllabs.com/project/blast/ [2] G.J. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multiple antennas,” Bell Labs Tech. J., vol.1, no.2, pp.41–59, 1996.

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Takeo Ohgane received the B.E., M.E., and Ph.D. degrees in electronics engineering from Hokkaido University, Sapporo, Japan, in 1984, 1986, and 1994, respectively. From 1986 to 1992, he was with Communications Research Laboratory, Ministry of Posts and Telecommunications. From 1992 to 1995, he was on assignment at ATR Optical and Radio Communications Research Laboratory. Since 1995, he has been with Hokkaido University, where he is an Associate Professor. His interests are in multipath propagation and adaptive arrays in digital land mobile communications. He received the IEEE AP-S Tokyo Chapter Young Engineer Award in 1993. Dr. Ohgane is a member of the IEEE.

Toshihiko Nishimura received the B.S. and M.S. degrees in physics and Ph.D. degree in electronics engineering from Hokkaido University, Sapporo, Japan, in 1992, 1994, and 1997, respectively. In 1998, he joined the Graduate School of Engineering (reorganized to Graduate School of Information Science and Technology at present) at Hokkaido University, where he is currently a Research Associate of Electronics and Information Engineering Division. His current research interests are in the MIMO system using smart antenna. Dr. Nishimura is a member of the IEEE and the Physical Society of Japan.

Yasutaka Ogawa was born in Sapporo, Japan, on March 22, 1950. He received the B.E., M.E., and Ph.D. degrees from Hokkaido University, Sapporo, Japan, in 1973, 1975, and 1978, respectively. Since 1979, he has been with Hokkaido University, where he is currently a Professor of the Graduate School of Information Science and Technology. During 1992–1993, he was with ElectroScience Laboratory, the Ohio State University, U.S.A. as a Visiting Scholar, on leave from Hokkaido University. His interests are in adaptive antennas, mobile communications, super-resolution techniques, and MIMO systems. Dr. Ogawa is a member of the IEEE.