An orthogonal ulti-bea based IO schee for ulti-user wireless systes Dong-chan Oh o and Yong-Hwan Lee School of Electrical Engineering and IC, Seoul ational University Kwana P.O. Box 34, Seoul, 151-600, Korea, Tel.: +8--880-8413, Fax.: +8--880-813 E-ail: ac81@trans.snu.ac.r and ylee@snu.ac.r Abstract In this paper, we propose a ultiple-access transission schee that can siultaneously achieve both diversity and ultiplexing gain in the ulti-user ulti-input ulti-output (IO) doain, by using orthogonal ultiple rando beas. Orthogonal ultiple beas are generated so that the users encounter ultiple channels at the sae tie, enabling the use of ulti-user diversity through each channel. Although the signal-to-noise power ratio (SR) of each channel is reduced in proportion to the nuber of beas, ultiple beas are utilized so that the ultiplexing gain is larger than the decrease of SR, increasing the overall syste capacity. The proposed schee can generate spatial channels as any as the nuber of transit antennas regardless of the nuber of receiver antennas, while requiring partial channel inforation at the transitter. Thus, the proposed schee is applicable to ulti-input single-output (ISO) schees as well as IO schees, enabling the use of flexible antenna structures in the receiver. I. Introduction 1 The next generation transission syste should be able to provide high data rate ultiedia services to users in obile, noadic and fixed wireless environent in a sealess anner. The deand for high data rate signaling has led to the developent of various advanced transceiver techniques for provision of near channel capacity. In recent years, the capacity of wireless systes has been increased significantly with the developent of two advanced technologies; ulti-antenna technique nown as ultiinput and ulti-output (IO) [1-4] and pacet scheduling nown as opportunistic scheduling or ultiuser diversity (UD) [6,7]. The IO syste can iprove the capacity by increasing the diversity or spatial ultiplexing gain using This wor was (in part) supported by the Sasung Electronics Research (Sypass4G). ulti-antenna channels. Thus, the syste capacity can be increased in proportion to the nuber of antennas in rich scattering channel environent. Space-tie coding (STC) is a typical IO diversity schee [3], and diagonal Bell laboratories layered space-tie (D-BLAST), vertical BLAST (V-BLAST) and IO with singular value decoposition (SVD) are typical IO ultiplexing schees [1,,4]. However, it is not easy to get both full diversity and ultiplexing gain siultaneously due to the trade-off issue between the diversity and ultiplexing gain. In addition, the diversity and ultiplexing gain can substantially be reduced depending on the channel condition [5]. For exaple, the STC cannot provide the diversity gain if all the eleents of the channel atrix experience a fading null [3]. The spatial ultiplexing lie the BLAST cannot provide the ultiplexing gain if the ran of the channel atrix is equal to one [].
otivated by the inforation theoretic results in [1], we can use the UD to tae advantage of independent fading statistics of each user [8]. Allowing a user in the best channel condition to send the signal, we can achieve a syste capacity even larger than in additive white Gaussian noise (AWG) channel with the sae signal-tonoise power ratio (SR) [7]. However, when the channel gain has a sall fluctuation and/or varies slowly as in fixed wireless or noadic channels, the UD ay not significantly contribute the iproveent of capacity. To overcoe this proble, the base station generates beas using ultiple antennas with rando weights, nown as opportunistic beaforing [7]. It was reported that the opportunistic beaforing can provide a diversity gain larger than the STC. oreover, the opportunistic beaforing in a ISO schee can achieve a throughput siilar to the coherent beaforing when the nuber of users is large [7]. It was briefly entioned that the opportunistic beaforing can be extended to the use of ultiple beas in a ulti-antenna schee [7]. However, no further result has been reported on the design of ulti-bea-based IO structure, particularly with the use of ultiantennas in the receiver. In this paper, we propose a IO schee that can siultaneously achieve the diversity and ultiplexing gain in the ulti-user IO doain, with the use of SE detection at the receiver. The SE criterion is applied to axiize the SIR, which is equivalent to axiizing the syste perforance [1]. The SR of each channel is reduced in proportion to the nuber of beas. However, the proposed schee generates ultiple beas orthogonal to each other and utilizes the so that the ultiplexing gain is larger than the decrease of SR. oreover the use of an efficient antenna technique at the receiver can substantially suppress the interference fro other beas. As a result, the overall syste capacity of the proposed schee is larger than that of the opportunistic beaforing schee [7]. Spatial ultiplexing gain can be obtained by cobining the transission beaforing and dirty paper pre-coding in [9]. However, the previous schees require perfect channel state inforation (CSI) of all users. In practical applications, it ay not be feasible for the transitter to use accurate CSI with liited bandwidth for feedbac signaling. Thus, it ay be desirable to use a schee that can perfor with partial CSI without significant perforance degradation. The proposed schee needs only the signal-to-interference-and-noise power ratio (SIR) fro each user, significantly reducing the feedbac signaling burden for the CSI. This paper is organized as follows. In Section II, we describe the proposed orthogonal ulti-bea (OB) based OFD syste, including the generation of OBs. The proposed IO syste is verified by coputer siulation in Section III. Finally, we suarize the conclusion in Section IV. II. Proposed OB based OFD syste We consider the downlin transission of ulti-user data signal in a pacet-based cellular syste. We assue that each user has perfect inforation on the channel between the base station and obile user. On the other hand, the base station has partial inforation on the channel (e.g., only instantaneous SIR) due to liited bandwidth for the feedbac signaling. We consider the use of a pacet scheduling schee that allocates the resource to the user based on the channel condition. The base station assigns the channel to a user in the best quality (e.g., highest short-ter SIR), exploiting the UD. As the dynaic range of the channel fluctuations increases, the UD gain increases. However, this UD gain can be liited in the presence of a line-of-sight (LOS) path or little scattering environent [7]. To increase the UD gain, we consider the use of orthogonal rando beas. Fig.1 depicts the proposed OB based IO syste, where the base station transits ultiple user signals siultaneously over parallel channels generated by antennas and each user receives the signal using
The SE weight vector th bea is given by [10] w of the -th user for the i - H H σ w i, ( Hpi) He H e+ I (4) P where P is the received signal power, σ is the noise power of each receiver antenna and I is an ( ) identity atrix. The data signal can be estiated by cobining r with weight vector w i, -1 Fig. 1. The proposed OB based IO syste antennas. The received signal of the -th user can be represented as r HPd+n, 1,,, K (1) where d is the -diensional (di.) signal vector, is the -di. noise vector whose eleents are zero ean coplex circular-syetric Gaussian rando variables with the sae unit variance, H is the ( )-di channel atrix of the -th user, and P [ p p p ],,..., 1 denotes a unitary atrix whose j-th colun represents the beaforing weight for the j-th bea. We assue that each user experiences independent fading. Satisfying the orthogonality condition, the weight vector pi can randoly be generated as [7] jθ () t n p ( t) α ( t) e 1,,..., () where α () t and θ () t are rando processes in the range of 0 α ( t ) 1 and 0 θ ( t) < π. We assue as noralized transit power, i.e., α () 1 1 t. Then, the effective channel of the -th user is given by H H P (3) e Each user adjusts the receiver weight atrix to axiize the SIR using a iniu ean squared error (SE) ethod. The SE criterion is applied to axiize the SIR, which is equivalent to axiizing the utual inforation (i.e., axiizing the entropy) [1]. ( ) d w r w H d+n (5) ˆi, i, i e The short ter SIR of the i -th bea of the -th user after controlling the interference can be estiated as γ i, σ PR WH e ii, [ W ] + P i, R WH e i, 1 1, i Based on this SIR inforation, the base station allocates each spatial channel to a user with the highest SIR. It is nown that the use of receiver antennas can control the interference fro (-1) beas. In case of (6) <, the receiver ay not sufficiently suppress the interference fro other beas. However, this proble can be alleviated by cobining an opportunistic scheduler that chooses a user with high power, while being less interfered. The total syste capacity can be represented as C OB n 1 ( + η γ ) log 1 (7) where γ n is the SIR of the scheduled user through the n-th bea and η is a syste loss factor representing the SIR loss due to syste realization. Fig. suarizes the operation of the proposed OB based IO syste. First, the transitter generates orthogonal ultiple beas equal to the nuber of transit antennas. Then, each user reports the SIR of each bea to the base station. ote that the SIR is calculated assuing the use of ultiple antennas with the optiu cobining coefficient in a SE sense. Based on the reported SIR of each user, the base station selects n
Table 1. Syste paraeters in siulation Iteration 1000 uber of users 1,, 4 18 Avg. user SR 10dB, 0dB Antenna configuration (Tx-by-Rx) 4-by-4, 4-by-, 4-by-1 Channel Rayleigh ~ C(0,1) Rician (K factor : 5) Syste loss factor η : -4dB Spectral Efficiency (bps/hz) 1 10 8 6 4 0 0 0 40 60 80 100 10 140 Users OB 4Tx 4Rx OB 4Tx Rx OB 4Tx 1Rx Single user IO upper bound 4Tx 4Rx 4Tx Rx 4Tx 1Rx (a) When the average SR is 10dB 3.5 Spectral Efficiency (bps/hz) 3.0.5.0 1.5 1.0 0.5 OB 4Tx 4Rx OB 4Tx Rx OB 4Tx 1Rx Single user IO upper bound 4Tx 4Rx 4Tx Rx 4Tx 1Rx 0.0 0 0 40 60 80 100 10 140 Users (b) When the average SR is 0dB Fig.. Flow chart of the proposed OB syste users who have the highest SIR through one of ulti-beas. Finally, the base station sends out ultiple user pacets (data) in parallel. III. Perforance evaluation The perforance of the proposed OB based IO syste is verified by coputer siulation. We assue the transission of pacet signal over flat Rayleigh or Rician fading channel with a Rician factor of 5. The siulation paraeters are suarized in Table 1. We assue that the users experience utually independent channel with the sae average SR. Fig. 3 depicts the syste capacity of the proposed OB-based IO syste in Rayleigh fading channel in ter of the spectral efficiency. The upper bound of the single user IO represents an upper bound achievable in a single user syste (i.e., without the UD). It can be Fig. 3. The spectral efficiency of the proposed OB syste seen that the perforance of the proposed OB-based IO syste increases as the nuber of users increases, ainly due the UD gain. Thus, unless the nuber of users is too sall, the proposed schee outperfors the single-user IO schee. It can also be seen that, as the nuber of receiver antennas increases, the receiver antennas can effectively suppress the interference effect, significantly iproving the spectral efficiency. In high SR environent, the syste perforance is ainly liited by the interference for other beas. Thus, the use of ultiple receiver antennas is quite effective for iproveent of the SIR. Fig. 4 copares the spectral efficiency of the proposed OB and opportunistic beaforing with a (4X) IO schee when the average SR is 10dB. It can be seen that the proposed OB schee outperfors the opportunistic
Siulation results also show that the proposed OB schee outperfors the opportunistic beaforing schee in both Rayleigh and Rician channel. References Fig. 4. Throughput of (4X) OB and Opportunistic beaforing IO schees syste beaforing schee in both Rayleigh and Rician channel. This can be explained as follows. Although the transit power for each bea is changed inversely proportional to the nuber of beas in the OB schee, ultiple beas are utilized so that the ultiplexing gain is larger than the decrease of the SR. In addition, the receiver antenna technique can effectively suppress the interference fro other beas. IV. Conclusion We have considered the use of orthogonal ultiple rando beas in a IO schee for ultiple access wireless systes. Utilizing ultiple rando beas orthogonal to each other, the proposed OB IO schee can provide both the ulti-user diversity and ultiplexing gain siultaneously. Although the SR of each channel is reduced in proportion to the nuber of beas, ultiple beas are utilized so that the UD and ultiplexing effect is larger than the decrease of SR, increasing the overall syste capacity. In addition, we have proposed an SE-based detection schee applicable to ultiple receiver antenna structures with flexibility. The perforance of the proposed OB-based IO schee has been verified by coputer siulation. Siulation results show that the perforance of the proposed schee even can be better than that of the single user IO, when the nuber of users is oderately large. [1] G. J. Foschini and. J. Gans, On liits of wireless counications in a fading environent when using ultiple antennas, Wireless Personal Coun., Vol. 6, o. 3, pp. 311 335, June 1998. [] G. D. Golden, G. J. Foschini, V. A. Valenzuela and P. W. Wolniansy, Detection algorith and initial laboratory results using V-BLAST space-tie counication architecture, Electron. Lett, Vol. 35, pp. 14 16, Jan. 1999. [3] S.. Alaouti, A siple transit diversity technique for wireless counications, IEEE J. Select. Areas Coun., Vol. 16, o. 8, pp. 1451 1458, Oct. 1998. [4] G. Lebrun, T. Ying and. Faulner, IO transission over a tie-varying TDD channel using SVD, Electron. Lett., Vol. 37, o., pp.1363 1364, Oct. 001. [5] Z. Lizhong and D..C. Tse, Diversity and ultiplexing: a fundaental tradeoff in ultipleantenna channels, IEEE Trans. Infor. Theory, Vol. 49, o. 5, pp. 1073 1096, ay 003. [6] R.W. Heath Jr.,. Airy and A. J. Paulraj, ultiuser diversity for IO wireless systes with linear receivers, in Proc. Asiloar Conf. Signals, Systes and Coputers, Vol., pp. 1194 1199, ov. 001. [7] P. Viswanath, D.. C. Tse and R. Laroia, Opportunistic beaforing using dub antennas, IEEE Trans. Infor. Theory, Vol. 48, o. 6, pp. 177 194, June 00. [8] V. Taroh,. Seshadri, and A. R. Calderban, Spacetie codes for high data rate wireless counication: Perforance criterion and code construction, IEEE Trans. Infor. Theory, vol. 44, pp. 744-765. ar. 1988. [9]. Shubert and H. Boche, Joint 'dirty paper' precoding and downlin beaforing, IEEE Int. Syp. Spread-Spectru Technol., pp. 536 540, Sept. 00. [10] R. W. Heath Jr.,. Airy and A. J. Paulaj, ultiuser diversity for IO wireless systes with linear receivers. in Proc. Asiloar Conf. Signals, Syste and Coputers, Vol., pp.1194-1199, ov.001.