efficiencies for users who are farther from the base

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1 NLYSIS ND RESULTS FOR H-MIMO - HYBRID OF SPTIL MULTIPLEXING ND DPTIVE BEMFORMING Gu Bong Lim and Leonard J. Cimini, Jr. Larry J. Greenstein University of Delaware Dept. of Elec. and Comp. Eng. Newark, DE cimini(ece.udel.edu WINL Rutgers University Piscataway, NJ lj ggwinlab.rutgers.edu STRCT The use of multiple antennas at both ends of a wireless link can provide substantial increases in capacity. In MIMO systems, the multiple antennas could be utilized in different ways to maximize performance in a particular environment. In [1], a spatial multiplexing system was compared with a system that uses multiple antennas to perform adaptive beamforming. In this paper, we evaluate the performance of a hybrid MIMO (H-MIMO) system where the antennas are used in a combination of these two modes. Through simulations, we show that, over a wide range of target outages and Ricean Kfactors, the hybrid systems can achieve higher efficiencies for users who are farther from the base station or, alternatively, can provide higher capacities to a larger percentage of users in a cell. I. INTRODUCTION Because of the ever-increasing demand for higher data rates, maximizing the spectral efficiency is of paramount importance in next-generation wireless systems. n effective step in this direction is the use of multiple antennas at the transmitter, at the receiver, or at both ends, that is, so-called multiple-input-multiple-output (MIMO) systems (e.g., see [2]-[5]). In recent years, it has been shown that MIMO systems can be used for spatial multiplexing, providing the potential for a linear increase in capacity with the number of antennas (e.g., see [6]-[7]). Substantial gains have been verified through analysis and simulation in single-cell environments [8]- [9] as well as in multi-cell applications []-[13]. In MIMO systems, the multiple antennas could be utilized in different ways to maximize performance in a particular environment. In [1], using a comprehensive simulation in a real-world cellular environment, a spatial multiplexing () system was compared with a system that uses multiple antennas to perform adaptive beamforming (). lthough is shown to be surprisingly robust, the results in [1] also demonstrate different sensitivities to the degree of scattering in the environment and the target outage for the two schemes. n interesting possibility is to employ a hybrid MIMO (H-MIMO) system, where the antennas are used in a combination of the and modes. In this paper, we evaluate the performance of H-MIMO systems in a cellular environment. In Section II, the link and channel models used in the simulations are presented. In Section III, the interference model is described along with a discussion of the receiver processing. Simulation results are presented in Section IV and the paper is summarized in Section V. Throughout the paper, we will use the following notation: x, x,and X denote a scalar, a vector, and a matrix, respectively. II. LINK ND CHNNEL MODELS. Link Model In a system, the data stream is divided into N substreams, and each substream is transmitted over a different antenna using the same frequency band. t the receiver, the composite signal is received by M antennas, and the resulting M-dimensional signal vector is r Hx + n (1) Here, x represents the N-dimensional transmitted signal vector, H is the MxN channel gain matrix, and n is the M-dimensional noise vector with individual components modelled as zero-mean, unit-variance, complex Gaussian random variables. In the system, a single data stream is transmitted over the N antennas, with a transmit beamforming weight vector w. The M-dimensional signal vector at the receiver for this mode is given by r Hwx + n (2)

2 Orgn Data stream CO SdLbsfLetr_ Ir O-r-1g)r3;al (Subsystem 1) line-of-sight (LOS) and non-line-of-sight (NLOS) components. Using this model, we can control the richness of the scattering environment, which strongly influences the performance of each system [1]. More specifically, the channel response is represented as 7 LJL::,trearnlL X H (Subs:ysl:em dbttltrn9 3 K+1 HLOS + +1 HNLOS (5) where HLOS and HNLOS are the MxN channel matrices for the LOS (or specular) and scattering components, respectively, and where K is the ratio of the LOS and NLOS powers (called the Ricean K factor). The respective channel matrices are given by HNLOS HLOS (6) GZa(Ot)a(Or) G cd-7s where the elements of the MxN matrix Z are statistically independent, unit-variance, complex Gaussian random variables. The quantities a(ot) and a(or) are the specular array response vectors at the transmitter and receiver, respectively. The gain G is determined by the distance between the base station and a mobile (d), the path-loss exponent (a), and the shadow fading (s), a lognormal random variable. The constant c is a function of the carrier frequency and does not effect the comparison which follows. We also assume that the fading is flat over the bandwidth of interest. For wider bandwidths, OFDM can be used in conjunction with MIMO to counteract the frequency-selective fading. Fig. 1. Transmit antenna configurations for the Hybrid IS3 (three independent substreams) and Hybrid IS2 (two independent substreams) systems. To guarantee a fair comparison, the total transmitted power is constrained to P in all cases. The transmit beamforming vector, w, is determined using eigenbeamforming. In this method, the signal is transmitted through the channel with the largest path gain (largest eigenvalue). Thus, w is simply the eigenvector corresponding to the largest eigenvalue of HtH, with the norm set to unity [ 1 ]. The two hybrid systems considered in this paper are shown in Figure 1. We focus here on a system with N4 transmit antennas and M4 receive antennas; the extension to more general system configurations is straightforward. For the Hybrid IS2 (two independent substreams) system, the received signal vector is the combination of two signals and is given by r1 ris2 H1wlxl, r2 ri + r2 + n H2w2X2 III. SYSTEM MODEL ND RECEIVER PROCESSING We consider downlink transmission in a multi-cell environment. We limit consideration to the nearest six co-channel cells, which usually dominate the system performance. We assume that sectorized antennas, with a half-power beamwidth of 900, are used at the base stations, which are located at the centers of each cell. The base stations in the co-channel cells are assumed to transmit the maximum number of independent substreams, that is, they operate in the mode. Using this model, the received interference-plus-noise vector at the desired mobile unit is given by (3) Here, the subscript i is used for indexing the subsystems. For the Hybrid IS3 (three independent substreams) system, the received signal vector is a combination of and signals and is given by ri Hlwlxl, r2 ris3 ri +r2+ n H2x2 /Gz (4) rint 1 HkXk + n (7) and the corresponding covariance matrix is B. Channel Model In the simulations in Section IV, we use a Ricean fading channel model which takes into account both Rint E{Hrint rit I kl 2 Hk(pklk +nlni (8)

3 where Hk is the channel gain matrix from the kth cochannel cell to the desired mobile, (Pk E{XkXt }, and s7 1n E{nnt}. MMSE combining is used to recover the transmitted signals. So, the receiver weighting in the mode is Wr (HHt + Rint )-Ht (9) The corresponding weighting in the mode is Wr (Rd + Rin)1Hw () Rd HwwtHt Similarly, for the Hybrid IS2 and IS3 systems, the receiver weights are as follows: Hybrid IS2: Wri ((Rdl + Rd2 + Rint))Hiwi Rdi Hiwiwi Hi i 1, 2 Hybrid IS3: Wrl (Rdl + Rd2 + Rint) Hlwl Wr2,3 (Rdl + Rd2 + Rint) 1H2 (12) Rdl HlwlwtHt, Rd2 H2Ht In all cases, we assume that the channel matrix can be perfectly estimated at the receiver. IV. SIMULTION RESULTS ND DISCUSSION In this section, we present results that show the performance of each of the systems described above. We focus on a 4x4 system and use the following parameters: path-loss exponent 3.5, lognormal shadowing with standard deviation 8 db, and a median received SNR 25 db at the cell boundary. First, we present the spectral efficiency (in bps/hz) that a given percentage of users can achieve or exceed as a function of the distance from the base station. We then provide the complementary cumulative distribution function (CCDF) of the spectral efficiency, which is a good measure of the system-level performance of each approach. The spectral efficiency is computed for the four systems using the Shannon capacity. First, a channel matrix is generated and then the SINR (Signal-to- Interference+Noise Ratio) is determined from SINRi W11RdiWri/W11RuWrin (13) where i indicates the independent substream and Ru is the received interference-plus-noise covariance matrix. The capacity for each substream is calculated using the well-known formula, Ci 92(1 + SINRj) (14) and the net capacity is derived as the sum of the capacities of the individual substreams.. Capacity Versus Distance In this simulation, mobiles are uniformly distributed in a hexagonal cell. We consider ten base-to-user distance regions for the cell, namely, [- +0.l k]dmaxc < d < [ k]dmax with k 1 to and where dmax is the maximum distance in each cell. In each of these regions, we find the capacity that is achieved or exceeded for a fraction (1 -po) of all users, where po is the target outage probability. We use po in our calculations (% outage), and we call the capacity for this outage the outage capacity. Results are shown in Figure 2 for a reuse factor of 7, a target outage of %, and two values of K: 0 (Rayleigh fading) and. When the mobile unit is close to the base, the SINR is usually quite high, and, the mode (transmitting the maximum number of independent substreams) will be the most efficient. However, the capacity using degrades rapidly as the mobiles move away from the base. Thus, if we introduce some power gain at the expense of maximum capacity, such as in the Hybrid IS2 and IS3 systems, then this variation over the cell can be reduced and, in turn, the outage capacity improved. This is illustrated in Figure 2a where the hybrid systems provide a higher capacity than over a large part of the cell. The K factor in this figure is 0, giving the maximum scattering and the most advantageous conditions for. In the extreme case where only one substream is transmitted (the mode), the variation over the cell is small but the capacity is also much lower than for the other approaches. We have also performed the simulation with different reuse factors. Results for a reuse factor of 1 are shown in Figure 3. s the reuse factor is decreased, and the distance between the co-channel cells is thus decreased, the performance of all the systems, as expected, degrades. In this case, the system has slightly better performance as the mobile moves farther from the base station due to the larger power gain. In reading these and subsequent results, some important factors to keep in mind are the following: (1) Whereas per-user capacity increases with reuse factor, the overall system capacity will be highest for reuse 1 (see [13]). (2) The capacity results shown in the figures will be lower for smaller values of median SNR at the cell boundary. (3) In reduction to practice, the signal constellation size required for a given capacity will relate inversely to the number of independent signal streams, which militates in favor of using. 3

4 K0, Reuse7, % outage 45F 45 I N zir 35- I'- - - IS2 - IS3 - Ir 35- K, Reuse7, % outage - - IS2 - IS3 -.) 25 C-) ).) 25 ~~~~~~~~~~~~~~~~~~~~~~~~~~1. C-) ) ) 15 ) 15 QL Fig >.2. Capacity versus distance from the base station for reuse factor 7. I Normalized distance (a) K0, Reuse1, % outage C _ Normalized distance 7,and two values of Ricean K factor (outage K, Reuse1, % outage IS E3 I%) z I O 0n CL ~~ ~ omaie distanc..a0) O~~~~~~~~~~~~~~~~S Fig fDctor ~ ~ ~ K0 Reue Normalized distance 1, and two of Ricean K factor (outage %) K, Reuse7 (-) 0.8 8' IS2 IS3 - (-) 0.8 8' IS2 IS3 cj. CL) U.5 cj. ) 'n 0.3 'n O _ 0 O _ (a) Fig. 4. CCDF of the capacity for reuse factor 7, and two values of Ricean K factor 4

5 K, Reuse7 K, Reuse o 0.8 IS2 o 074 a a) a, 0L ~ 2n j 00 1IS3 o 0.8 U, (L) ---- (i) 0.8- IS3 8'0.7-c IS2... Fig. 5. CCDF of the capacity for a reuse factor 0 7 and K 0. Fig. 6. CCDF of the capacity when co-channel base stations transmit only one substream for reuse factor 7 and K B. Capacity Distribution Here, the goal is to determine what fraction of users in a cell can achieve or exceed a target capacity. In this simulation, mobiles are uniformly distributed in a cell, the capacity of each user is evaluated, and the CCDF is computed. Results are shown in Figure 4 for a reuse factor of 7 and two values of the Ricean K factor: 0 and. The results illustrate that hybrid systems can provide higher spectral efficiencies to more users in a cell. However, the highest capacities are still achieved using the mode. For example, from Figure 4a, with a K factor of 0, a capacity of bps/hz can be achieved by 70% of the users in a cell if the Hybrid IS3 system is used, but only 65% using the mode and 60% using the Hybrid IS2 system. To attain a higher capacity, say bps/hz, more independent substreams ( or Hybrid IS3) are required. For very low outages, say IO% or less (90% CCDF), both hybrid systems outperform the system. s the K factor increases from 0 to (Figure 4b), the degree of scattering richness decreases, and, as discussed previously, the performance of all of the systems which use more than one independent substream degrades. The hybrid systems are now better than the system over a larger percentage of the cell. If we increase the Ricean K factor to (Figure 5), we see that the performance of degrades the most, and the hybrid systems are much better. In particular, the Hybrid IS3 system is better than the mode over 85% of the cell and the Hybrid IS2 is better than over almost 70% of the cell. For all of the results presented so far, we have assumed that all of the co-channel base stations operate in the mode and transmit the maximum number of independent substreams (L4). We can also reduce the number of independent substreams that the interfering base stations use and observe the effect on performance. Results are shown in Figure 6 for the case where the co-channel base stations transmit only one independent substream with a reuse factor of 7 and K. It is clear from the figures that as the number of interfering streams decreases, the performance of the, Hybrid IS2, and Hybrid IS3 systems tend to improve. On the other hand, as expected, the performance in the mode does not change. In particular, the Hybrid IS3 system is better than the mode over 75% of the cell and the Hybrid IS2 is better over % of the cell. C. No Transmitter Beamforming In the previous results, it was assumed that eigenbeamforming was used at the transmitter. This requires that accurate channel state information be available (based on feedback from the mobile). Here, we consider the case when there is no transmitter beamforming (i.e., w 1). Results are shown in Figure 7 for a reuse factor of 7 with K0 (a) and K. In comparing these results with those in Figure 4, we see that, as expected, the capacity of the and hybrid systems degrades. Nevertheless, the degradation is minimal and the benefit of not requiring feedback from the mobiles is significant. V. CONCLUSION In this paper, we introduce and evaluate the performance of a hybrid MIMO system that combines spatial multiplexing and adaptive beamforming. In particular, 5

6 KO, Reuse7 1.. K, Reuse7 Div-lS (o) 0.8 o 0.7 au c 06 a) 0.5- Div-lS2 (o) 0.8 o 0.7 au c 06 (L) U.5 Div-lS ~ IV \. I Div-lS3 J.- 'i...i L) 0.43 QL 0~ 0.2 (a) Fig. 7. Div-lS Div-lS2 afu 2) a) 'n N CCDF of the capacity without transmitter beamforming for a reuse factor 7, and two values of the Ricean K factor [3] S. lamouti, " simple transmit diversity technique for wireless communications," IEEE J Sel. reas in Commun., vol. 16, pp , Oct [4] B. Friedlander and S. Scherzer, "Beamforming versus transmit diversity in the downlink of a cellular communication system," IEEE Trans. on Veh. Technol., vol. 53, pp , July 04. [5] D. Gesbert, M. Shafi, D. Shiu, and P. Smith, "From theory to practice: n overview of MIMO space-time coded wireless systems," IEEE J Sel. reas in Commun., vol. 21, pp. 2812, pril 03. [6] G. J. Foschini and M. J. Gans, "On limits of wireless communications in a fading environment when using multiple antennas," Wireless Pers. Commun., vol. 6, pp , [7] I. E. Telatar, "Capacity of multi-antenna gaussian channels," Eur. Trans. Telecommun., vol., pp , Nov [8] S. Catreux, P. F. Driessen, and L. J. Greenstein, "Data throughputs using multiple-input multiple-out (MIMO) techniques in a noise-limited cellular environment," IEEE Trans. on Commun., vol. 1, pp , pril 02. [9] S. Catreux, L. J. Greenstein, and V. Erceg, "Some results and insights on the performance gains of MIMO systems," IEEE J Sel. reas in Commun., vol. 21, pp , June 03. [] R. S. Blum, "MIMO capacity with interference," IEEE J Sel. reas in Commun., vol. 21, pp , June 03. [11] R. S. Blum, J. H. Winters, and N. R. Sollenberger, "On the capacity of cellular systems with MIMO," IEEE Commun. Letts., vol. 6, pp , June 02. [12] S. Catreux, L. J. Greenstein, and P. F. Driessen, "Simulation results for an interference-limited multiple-input multiple-output cellular system," IEEE Commun. Letts., vol. 4, pp , May [13] S. Catreux, P. F. Driessen, and L. J. Greenstein, "ttainable throughput of an interference-limited multiple-input multipleoutput cellular system," IEEE Trans. on Commun., vol. 49, pp , ug. 01. we considered the case of 4 transmit and 4 receive antennas in a multi-cell environment. We transmitted from 1 (adaptive beamforming) to 4 (spatial multiplexing) independent substreams and evaluated the resulting capacity. lthough the mode is quite robust (as found in [1]), the hybrid systems can provide improved performance in a multi-cell environment. Through simulations, we showed that the hybrid systems can achieve higher efficiencies for users who are farther from the base station or, alternatively, can provide higher capacities to a larger percentage of the cell. These conclusions apply over a wide range of target outages as well as Ricean K factors. Some challenges for the future include developing realistic algorithms for implementing these hybrid systems and possibly developing a method for adaptation within a cell to use the most advantageous mode for that part of the cell. It would be instructive to obtain results for other combinations of M and N, and for lower values of median SNR at the cell boundary. VI. CKNOWLEDGMENT The authors thank Severine Catreux-Erceg for her generous technical support and the Korean government for funding GuBong Lim during his graduate studies. REFERENCES [1] F. R. Farrokhi,. Lozano, G. J. Foschini, and R.. Valenzuela, "Spectral efficiency of FDM/TDM wireless systems with transmit and receive antenna arrays," IEEE Trans. on Wireless Commun., vol. 1, pp , Oct. 02. [2] J. H. Winters, "Optimum combining in digital mobile radio with cochannel interference," IEEE J Sel. reas in Commun., vol. SC-2, pp , July