TDMA wireless systems with transmit and

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 1, NO. 4, OCTOBER 2002

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Spectral Efficiency of FDMA/TDMA Wireless Systems With Transmit and Receive Antenna Arrays Farrokh R. Farrokhi, Member, IEEE, Angel Lozano, Senior Member, G. J. Foschini, Fellow, IEEE, and Reinaldo A. Valenzuela, Fellow, IEEE

Abstract—In recent years, the ever growing need for higher capacity in wireless systems has fueled the interest in exploiting the spatial dimension—through the use of antennas arrays—to improve the utilization of the available radio spectrum. As a result, a large number of space–time techniques have been proposed wherein arrays are used to mitigate interference and enhance signal levels. More recently, information theory has shown that, with spatial data multiplexing, very large spectral efficiencies can be attained in multipath channels using transmit and receive antenna arrays. In this paper, the system benefit of using transmit and receive arrays in multicell scenarios is evaluated as a function of both the propagation environment and the number of antennas. Our results confirm the potential for very large system spectral efficiencies associated with the use of transmit and receive arrays, in particular in interference-limited rich-multipath conditions wherein the ability to perform interference mitigation—leading to tighter spectral reuse—and spatial data multiplexing grows with the number of antennas. In environments free of multipath, the potential is smaller but still very significant, associated with interference mitigation and signal enhancement only, since spatial data multiplexing is no longer possible. Index Terms—Adaptive arrays, antenna diversity, fading channels, multiple-antenna communication theory, spectral efficiency.

I. INTRODUCTION

T

HE EVER GROWING need for higher levels of capacity in wireless communication systems has fueled the interest in exploiting the spatial dimension, through the use of antennas arrays, to improve the utilization of the available radio spectrum. As a result, a large number of space–time techniques have been proposed wherein arrays are used to mitigate interference and enhance signal levels [1]. More recently, advances in information theory have proved the enormous capacity potential associated with the simultaneous use of multiple-transmit and multiple-receive (MTMR) antennas for spatial data multiplexing, in particular when the channel is such that the transfer functions between different transmit and receive antenna pairs are largely independent [2]–[6]. To exploit this potential, a number of layered space–time architectures have been formulated [7]–[9]. In these schemes, multiple parallel data streams are transmitted Manuscript received April 5, 2000; accepted March 10, 2002. The editor coordinating the review of this paper and approving it for publication is D. L. Goeckel. F. R. Farrokhi was with Lucent Technologies, Bell Laboratories, Holmdel, NJ 07733-0400 USA. He is now with Centillium Communications, Fremont, CA 94538 USA (e-mail: [email protected]). A. Lozano, G. J. Foschini, and R. A. Valenzuela are with Lucent Technologies, Bell Laboratories, Holmdel, NJ 07733-0400 USA (e-mail: [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TWC.2002.804078

simultaneously and in the same frequency band. With sufficient multipath in the channel, these different streams can be separated at the receiver because of their distinct spatial signatures. Remarkably, in its original form, MTMR techniques do not require the transmitter to possess any channel information; only the receiver is required to estimate the channel. Nonetheless, provided that the scattering richness is sufficiently high, the spectral efficiency attainable—in this open-loop configuration—is very close to the maximum spectral efficiency supported by the channel. Closed-loop MTMR schemes, where information on the channel is available at the transmitter, have also been reported [4], [10], [11]. While extremely promising, most MTMR analyses presented to date were restricted—with few exceptions [12], [13]—to the context of a single-user link or, at most, of an isolated cell [14]. Thus, the impact of these techniques on the overall spectral efficiency of a multicell system had not been assessed. Furthermore, the system-level benefit of using spatial multiplexing over other array processing techniques was still not quantified. On the other hand, the spectral efficiency of single-antenna wireless systems has been extensively studied in the past, mostly with the assumption—determined by the interest in providing voice services—of constant and identical data rates for all users and minimal tolerance to delay [15]–[17]. In that case, there is a clear tradeoff between the link spectral efficiency and the system spectral efficiency [18]. Since every user is exposed to interference from all other co-channel users, the highest system spectral efficiency is not attained when every individual user is independently attempting to maximize its own link spectral efficiency, but rather when every user selflessly reduces its transmit power to the lowest possible level that can sustain the target data rate [19]. Such a strategy requires the use of power control, which can be implemented in a distributed fashion with no loss of optimality [20], [21]. If the traffic is dominated by delay-resilient data—as might be the case in emerging systems—and the data rates are variable and heterogeneous, rate adaptation becomes, not only an attractive complement, but even an alternative to power control [22]–[25]. The system spectral efficiency with fixed-power and rate adaptation has been recently studied in [26]. Also, the impact of antenna diversity was investigated in [27]. Similar analyses with adaptive-array techniques were presented in [28] and [29]. In this paper, we evaluate how the system spectral efficiency using MTMR scales with the number of antennas depending on how those antennas are utilized. These comparative evaluations are performed in a frequency-flat Ricean environment with different degrees of scattering richness. Since the emphasis of the

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paper is not on comparing different multiple access options, but rather on how to use a given set of antenna resources most effectively, only combinations of frequency-division multiple access (FDMA) and time-division multiple access (TDMA) are considered. The use of capacity-approaching codes is presumed in order to abstract the results from the choice of a specific code or modulation format. Frequency selectivity, on the other hand, can be dealt with at the cost of additional complexity [4], [30]. Given the exploding interest on data traffic, we restrict ourselves to the case where the total transmit power per user and per base station are held constant while the data rate is being adapted. The paper is organized as follows. First, the link and channel models are introduced in Section II. In Section III, the different space–time techniques are presented and their spectral efficiencies formulated. The system model is described in Section IV along with the simulation environment. Finally, the performance evaluations of the algorithms are performed in Section V and the results are summarized in Section VI.

In the limit of a purely scattering environment, the deterministic component vanishes. On the other hand, in the limit of a purely specular or line-of-sight (LOS) environment, the deterministic component constitutes the entire channel response. Hence, the Ricean model comprises the rich-scattering and specular as particular (extreme) cases. Notice also that our spatial model implicitly assumes that the only source of correlation among the array elements is the deterministic component. This simplistic approach enables modeling a variety of propagation conditions without introducing an excessive number of parameters (such as angle spread, antenna separation, etc.) [36]–[38]. Despite its simplicity, the model is valid as long as the user terminal is buried in the clutter—so that its angle spread is large enough to render a small antenna separation sufficient—and the antenna separation at the base station is large enough [39]–[41]. With the -factor defined as the ratio of deterministic-toscattered power, the channel response is given by [42]

II. LINK AND CHANNEL MODELS where

A. Link Model Every user link consists of a transmitter and a receiver with and antennas, respectively. The channel responses from every transmit antenna to every receive antenna are assembled into a channel matrix . With that, the -dimensional received signal vector depends on the -dimensional transmit signal vector via

where is an -dimensional interference-plus-noise vector with spatial covariance matrix

with the variance of the entries of representing the largescale (local average) path gain encompassing distance-dependent decay as well as shadow fading. The gain of the individual antennas is also absorbed into . The elements of the norare statistically independent malized scattering component unit-variance complex Gaussian random variables. The channel specular component, in turn, is given by

where which includes a thermal-noise term matrix of the transmit signal is

. The spatial covariance

with the total transmit power limited to irrespective of the . The covarinumber of transmit antennas, that is, ance of the desired signal at the receiver is

We assume that [31]–[33].

has been perfectly estimated at the receiver

B. Channel Model In order to simulate a wireless channel with different degrees of scattering richness, we use a vector extension of the wellknown Ricean model [34]. Accordingly, the channel matrix has two distinct components. 1) A specular component that illuminates the arrays uniformly and is, thus, spatially deterministic from antenna to antenna. 2) A scattered complex Gaussian component that varies randomly and independently from antenna pair to antenna pair [35].

with and the specular array responses at the transmitter and receiver, respectively. The array response corresponding to an -element linear array, for instance, is where is the given by angle of arrival or departure of the specular component with respect to the array and is the antenna spacing in wavelengths. III. MTMR TECHNIQUES A. Closed-Loop MTMR Let us assume, for now, that the interference has a Gaussian distribution. The optimal choice for the signal distribution is then Gaussian (see, for example, [43]). The mutual information is given by [44]

(1) The highest mutual information determines the maximum link spectral efficiency, achieved when the channel matrix and the interference covariance are known at the transmitter and

FARROKHI et al.: SPECTRAL EFFICIENCY OF FDMA/TDMA WIRELESS SYSTEMS

the covariance of the transmit signal is adjusted appropriately [10], [11], given by (2) is the power assigned to each channel eigenmode, where which is found by a water-fill process as

with and with the constant chosen such that the total transmit power . The function is zero when the argument is is equal to negative indicating that the corresponding mode is too weak and should be allocated no power. The goal of this decomposition process is to find the channel eigenmodes in the presence of the interference in order to send multiple independent data streams through those eigenmodes. The transmit covariance matrix that achieves (2) is given by Notice that this MTMR scheme requires an explicit feedback link relaying the channel and the interference covariance measured at the receiver back to the transmitter. While optimal—in the sense of maximum link spectral efficiency—the use of this algorithm within the context of a multicell environment poses some challenges. Since the spatial signature of every user has an impact on all other co-channel users, there is some arrangement of spatial signatures which would maximize the system capacity, but such a solution could only be computed and enforced by a centralized entity with instantaneous information on the state of the system. A practical approach, distributed and based only on local cell information, would have to be iterative. Hence, every user would adjust the spatial characteristics of its output signal based on the structure of its interference, which would—in turn—trigger new adjustments by all other co-channel users and so forth. To the best of our knowledge, the convergence of this process has not been conclusively proved, although we have observed—in stationary environments—convergence to a fixed point in every one of our computer experiments. As an alternative, it is possible to formulate a form of MTMR wherein the transmitter is supplied with information about the channel, but not about the interference. This class of MTMR is attractive because it may be implemented without the need for an explicit feedback link in time-division duplexed (TDD) systems and also because—with fixed per-user power—it eliminates the need to iterate and thus the need to ensure proper convergence of the spatial signatures.1 Therefore, in the remainder of the paper we will concentrate on such form of closed-loop MTMR. With no information about the spatial characteristics of the interference, the default signaling is that for which the interference is spatially white and thus the link spectral efficiency values computed using . reduces to (2) with the 1In

a dynamic environment, it would still be necessary to ensure that the transmit covariance adjustment rate is fast enough with respect to the coherence time of the channel, but that is beyond the scope of this paper.

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The values, however, are still as before because—although unknown to the transmitter—the interference may be colored at the receiver. B. Open-Loop MTMR When the transmitter is deprived of any channel or interference information, the most reasonable transmit covariance ma, indicating that the available power trix is should simply be equally distributed among all modes [5]. Consequently, the link spectral efficiency is given by (3) In open-loop MTMR, every transmit antenna radiates a separate data stream. Although these streams must be uncorrelated for the transmit covariance to be diagonal, from a coding perspective they can be threaded together. C. Adaptive Array Processing (Beamforming) In a closed-loop adaptive array (AA) or beamformer, a single data stream is transmitted simultaneously from multiple antennas with proper weight coefficients [45]. The coefficients for transmit antennas are assembled into an -dimensional the vector . Therefore, the received signal can be expressed as where is here a scalar. The transmit covariance matrix is given and the spectral efficiency is by (4) with optimal combining at the receiver [46]–[49]. The optimal is the one that maximizes (4) with the constraint that the total ) be limited to transmit power (specified by the norm of , which is simply the principal eigenvector of with norm set to unity. As in optimal MTMR with channel state and interference information, iterative optimization approaches are necessary in order for the algorithm to operate in a distributed fashion within a multicell environment. In contrast with MTMR, though, convergence of this scheme to a fixed point has been proved [28]. Nonetheless, here too we choose to implement a sub-optimal version of the algorithm wherein the interference is unknown at the transmitter and hence—with fixed per-user power—there is no need to iterate. With that restriction, the optimal is now the with norm set to and the specprincipal eigenvector of tral efficiency can be obtained simply by plugging that value into (4). Note that, within the context of an individual link, the spectral efficiency of closed-loop MTMR always exceeds that of AA.2 In the context of an multicell scenario, however, interference mitigation becomes very relevant and, as a result, link efficiency results do not necessarily extrapolate. Having fewer spatial degrees of freedom tied up into spatial data multiplexing, AA receivers may be able to mitigate co-channel interference more

K!1

2In closed-loop MTMR, the power is optimally distributed across all modes whereas, in AA, only the principal mode is excited. Only as and all modes but the principal one vanish do their spectral efficiencies become identical.

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effectively while AA transmitters may spill less interference onto other co-channel users. The overall effect on the system spectral efficiency is, therefore, not obvious.

on a set of co-channel sectors, the signal at the receiver in sector is given by

D. Directive Array (DA) Processing Implementing MTMR or AA techniques requires a radio-frequency (RF) chain per antenna at both transmitter and receiver. In order to simplify the RF requirements, the antennas can be arranged as a DA. In such configuration, the transmitter can steer a beam toward the receiver if only its directional location is known. That is

where is the matrix channel response from the transmitter is the transmit vector in sector to the receiver in sector , and intended for user with covariance is the noise vector at receiver . The summation extends to all co-channel sectors. The total covariance matrix at receiver is given by

where defines the directional location of the receiver.3 When the receiver uses a DA as well, the combining vector at the re, where is the angle to the desired ceiver is given by transmitter. The received signal is given by

The desired-signal covariance matrix is

and the capacity can now be evaluated as in architectures with a single antenna at both transmitter and receiver. The (scalar) desired signal variance is given by

and the (scalar) interference-plus-noise variance is given by

with the link spectral efficiency being (5) Again, although the link spectral efficiency with DA is always inferior to that of either MTMR or AA, we want to quantify the system impact of using either scheme. E. Single-Antenna Techniques Finally, we will also use, as a reference, a system with singleantenna transmitters and receivers. Notice that, in such conditions, all spatial processing schemes reduce to the same solution. IV. SYSTEM MODEL AND SIMULATION ENVIRONMENT We consider a multicell system layout with three sectors per cell, where some combination of FDMA and TDMA is employed with each user regarded as noise by the other co-channel users and with no interchannel interference. Users are uniformly distributed throughout the system and connected to the sector from which they receive the strongest local-average signal. In the remainder, we concentrate on the downlink only, which has the most stringent capacity demands for data applications. However, a similar analysis could be applied to the uplink. Focusing 3The formulation we present herein corresponds specifically to linear arrays. The analysis can be generalized to any arbitrary array geometry by replacing a with the corresponding array response.

(6) and the interference-plus-noise covariance matrix is

It is known that, in an interference channel, joint Gaussian signaling falls short of maximizing the total system capacity [50]. In fact, the optimal signaling in that general case is an unsolved information-theory problem. However, if the temporal structure of the interference from other cells is not exploited, Gaussian signaling is optimal. Thus, we assume Gaussian signaling throughout our system, which makes the interference also Gaussian. Furthermore, in our search for general results and relative performance levels, we also postulate the use of codes tending toward achieving capacity [44], [51]. With that, we avoid invoking specific modulation formats or code structures. No temporal variation of the fading process is assumed within the coding horizon and thus the spectral efficiency is a random variable for every channel realization. Through Monte–Carlo simulations over a very large number of user locations and channel realizations, it is possible to obtain a statistical distribution of spectral efficiency. We conduct such simulations on a wrapped-around universe with 100 perfectly sectorized hexagonal cells arranged in a 10 10 grid. The terminal antennas are omnidirectional. The propagation exponent is set to 3.5 and the shadow fading is log-normally distributed with an 8-dB standard deviation. The cell size, transmit power, and noise floor are scaled to ensure that the system is mostly interference-limited, with the signal-to-noise ratio (SNR) with respect to the underlying thermal noise higher than 25 dB in 90% of the locations. All these parameters are summarized, for convenience, in Table I. We consider three different reuse factors, which cover a wide range of system arrangements. In order of increasing tightness, we consider: 1) Reuse 3/9. Every unit of bandwidth is used in one sector of every third cell. 2) Reuse 1/3. Every unit of bandwidth is used in one sector of every cell. 3) Reuse 1/1. Universal Reuse. Every unit of bandwidth is used in every sector of every cell. For every scheme, the system spectral efficiency in bps/Hz/sector is computed as the corresponding link spectral efficiency normalized by the denominator of the reuse factor.


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TABLE I SYSTEM PARAMETERS

Fig. 2. Cumulative distribution of system spectral efficiency in rich-scattering = = 16 as a function of the reuse factor. conditions ( = 0) with

K

Fig. 1. 90% system spectral efficiency as a function of the Ricean with reuse 3/9 and 12, = 16.

M=

N

K -factor

M N

• The AA and DA techniques improve monotonically with and, in the limit of , the AA efficiency becomes identical to that of closed-loop MTMR, clearly indicating that beaming a single data stream is the most adequate solution in such conditions. • The spectral efficiency advantage is very large in all cases with respect to the baseline single-antenna system. When using MTMR with sufficient scattering, the advantage is particularly strong. Since rich-scattering channels hold the most potential for large spectral efficiencies, in the remainder we will concentrate . Nonetheless, for mostly on the limiting case of completeness, we will also show results for the other limiting . case, B. Impact of the Frequency Reuse Factor

V. SYSTEM PERFORMANCE EVALUATION Given the large dimensionality of the parameter space that we intend to investigate, we proceed to study the impact of the different parameters separately. A. Impact of Scattering Richness First, we evaluate how the various techniques behave as a function of the scattering richness. Shown in Fig. 1 is the spectral efficiency attained in 90% of every cell as a function of the -factor with reuse 3/9. To emphasize the differences, the anal, ysis is performed using a large number of antennas ( ). We can make the following observations. • MTMR clearly outperforms all other techniques in highly scattering scenarios, although its advantage diminishes with decreasing scattering. Nonetheless, its robustness is remarkable for its spectral efficiency does not drop , significantly with Ricean factors as large as which covers most cases of practical interest [52]. • Closed-loop MTMR is never inferior to any of the other schemes at this outage level.

Next, we consider the impact of the reuse factor. Presented in Fig. 2 are the system spectral efficiency cumulative distributions . Again, in order to emphasize for all reuse factors with ). the behaviors, the number of antennas is large ( We observe the following. • With single-antenna transmitters and receivers, a tighter reuse factor yields a higher spectral efficiency in the upper tail of the cumulative—favorable locations—but a shrinking efficiency in the poor locations represented by the lower tail. , array directive gains are effectively lost and • With thus the performance of a DA system is identical to that of a single-antenna system. • With AA, the spectral efficiencies—for every reuse factor—show a relatively small variance. Clearly, the AA processing effectively mitigates and controls co-channel interference. In fact, as long as the number of dominant interferers is smaller than the number of receive antennas, the receiver can push the interference level down to the noise floor [27]. Therefore, the lower tail of the cumulative distribution, corresponding to the worst locations

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Fig. 3. Cumulative distribution of system spectral efficiency in specular ) with 16 as a function of the reuse factor. conditions (

Fig. 4. 50%, 90%, and 99% system spectral efficiency as a function of the number of antennas = with reuse 3/9 and = 0.

within each cell, is very well behaved.4 However, AA is unable to provide further efficiency increases in those locations within every cell—corresponding to the upper tail—where conditions are favorable. In those locations, additional antennas only contribute array gain, which results in a slow—asymptotically logarithmic—efficiency improvement. • With MTMR, on the other hand, the spectral efficiency growth is much faster—asymptotically linear—with the number of antennas [2]. Thus, users in favorable locations can utilize their antennas to attain much larger efficiencies and, as a result, the spectral efficiency spread is much larger and its peak is almost an order of magnitude higher. Nonetheless, since the interference caused by a MTMR transmitter has components in multiple spatial dimensions, it also requires multiple spatial degrees of freedom for proper mitigation. As a result, interference . control is much more difficult except possibly if Thus, in our example with , the lower tail of the open-loop MTMR cumulative does not improve with tightening reuse. Furthermore, the lower tail of the open-loop MTMR cumulative is always behind the corresponding AA cumulative, with the cross point increasing as reuse tightens and interference levels increase. With closed-loop MTMR, that effect is almost completely eliminated as users in detrimental locations signal in fewer spatial dimensions and thus better operating points are found. is depicted in Fig. 3. A similar analysis for • In this case, closed-loop MTMR behaves exactly as AA and—therefore—their spectral efficiencies coincide. • Since the channel only supports a single spatial signaling dimension, interference control is effective in all cases as long as the number of receive antennas exceeds the number of significant interferers. Hence, spectral efficien-

cies increase—as the reuse tightens—monotonically for all algorithms and outage levels. Given the distinct behavior of the algorithms at different points in their cumulatives, in the remainder we will concentrate on three representative outage levels: 50%, 90%, and 99% service.

K!1

M =N =

4This particular behavior may be different in a code-division multiple access (CDMA) system, wherein the number of interferers tends to be large. Nonetheless, the tendency in data-oriented CDMA systems is to reduce as much as possible the number of simultaneous transmissions [53]–[56], in which case our observation would hold.

M N

K

C. Impact of the Number of Antennas In Fig. 4, the spectral efficiency growth as a function of the and reuse 3/9. To number of antennas is shown with and are scaled reduce the number of parameters, both simultaneously. It can be observed that: • With AA, the efficiency growth is roughly logarithmic. • With MTMR, even in open-loop fashion, the growth is basically linear. The slope is very steep at the 50% level, but less so at 10% and even less at 1%. In every case, the slope changes as the number of antennas exceeds that of the number of significant interferers. This effect is more noticeable at the 90% and 99% levels, where the effects of interference are more pronounced. Results in Fig. 4, however, are particular to reuse 3/9. It appears clear from the previous section that the reuse that yields the highest spectral efficiency is different at 50%, 90% or 99%. In addition, the optimal reuse also varies with the number of antennas. Hence, since an advanced TDMA system would most likely adapt its reuse dynamically [57], [58] based on whichever operating point is chosen, a true measure of the spectral efficiency growth with the number of antennas should be calculated with the most adequate reuse at every point. This is, therefore, how the next set of results was generated. For every number of antennas and outage level, the efficiency was evaluated for the various reuse factors that we consider and the best one was selected. The resulting set of curves, presented in Fig. 5, indicates that: • The slopes oscillate because of the reuse factor granularity. They increase every time enough antennas are added for the reuse factor to go up a notch and they diminish while


M =N

Fig. 5. 50%, 90%, and 99% system spectral efficiency as a function of the with optimized reuse and 0. number of antennas

K=

additional antennas are added within a given reuse. With dynamic channel assignment, the granularity would disappear [57]. • At 99%, AA outperforms both open-loop and closed-loop MTMR. • At 90%, AA is still superior to open-loop MTMR, but inferior to the closed-loop. • At 50%, MTMR is vastly superior In every case, it must be taken into account that absolute system spectral efficiencies are very sensitive to propagation parameters. Therefore, it is the relative scaling rather than the absolute numbers themselves that is relevant. Finally, let us use the results obtained thus far to illustrate what the ultimate capacity limits would be—for a TDMA system with favorable scattering conditions—as a function of the number of antennas. For this example, we choose as our service requirement that 90% of users be served at some minimum rate with 5 MHz of available bandwidth, a typical figure for upcoming third-generation systems [59]–[61]. The algorithm of choice is open-loop MTMR, which would probably constitute the most attractive option for mobile systems. The corresponding data rates as a function of the number of time-multiplexed users per sector and the number of antennas are displayed in Fig. 6. With single-antenna transmitters and receivers, the data rate that can be provided to 90% of users—under highly idealized conditions—is only on the order of 650 Kb/s. Furthermore, attaining such a rate with 90% probability requires that every user consume the capacity of an entire sector. That falls very short of the 2 Mb/s that were initially specified for third-generation services, which—with a single antenna—could only be supported within a small portion of every cell [62]. However, with only four antennas, the single-user 90% rate jumps to over 6 Mb/s. In that case, three simultaneous users per sector could be supported at 2 Mb/s. Thus, the use of transmit and receive antenna arrays would facilitate providing the type of data rates that will be needed for third-generation and beyond.

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Fig. 6. Data rate achievable by 90% of users versus number of users per sector as a function of the number of transmit and receive antennas with open-loop MTMR and = 0.

K

Notice also that, for this exercise, we have assumed roundrobin time multiplexing so that each user is given an equal share of the sector capacity. That is not necessarily the most appropriate policy in all circumstances and one can envision scheduling strategies with distinct objectives such as maximizing total throughput (more capacity allocated to spectrally efficient users in favorable locations), increasing fairness (more capacity given to low-efficiency users in detrimental locations), etc. If, in addition to rate adaptation, power control is also implemented, then scheduling and power control would have to be jointly optimized [63].

VI. CONCLUSION We have evaluated, through computer simulation, the systemlevel benefit of using transmit and receive antenna arrays with fixed power in multicell scenarios as a function of the propagation environment and the number of antennas. From the analysis and results presented within the paper, we can conclude the following. • The use of transmit and receive antenna arrays offers the potential for very large system spectral efficiency increases, in particular in interference-limited rich-scattering environments wherein the ability to perform interference mitigation—leading to tighter frequency reuse—and spatial data multiplexing grows with the number of antennas. In specular or LOS environments, the potential is smaller—associated with interference mitigation and signal enhancement only, since data multiplexing is no longer possible—but still very significant. • The use of MTMR—open-loop if sufficient scattering is present, closed-loop in all cases—yields average and peak spectral efficiencies that are much higher and scale much faster with the number of antennas than with any other array processing technique. • The use of adaptive-array techniques (transmit beamforming and receive optimal combining), wherein the

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available degrees of freedom are not used for spatial multiplexing, yields the highest spectral efficiency when the tolerated outage level is small and the ability to control and mitigate interference is essential.5 This is particularly true with respect to open-loop MTMR, which cannot support the same level of frequency reuse tightness at small outage levels. Closed-loop MTMR does a much better job at achieving a compromise between data multiplexing and interference control and thus it has superior performance except at very small outage levels. • As the scattering richness decreases, closed-loop MTMR and AA processing become equivalent. • Although closed-loop MTMR is always more efficient than open-loop, the latter remains a very attractive option because it eliminates the need for either fast feedback links or TDD structures while still providing extremely large average and peak efficiencies. Finally, it is necessary to point out that the above results were derived under no complexity constrains. This is, therefore, only a first step toward understanding the system potential offered by practical schemes employing transmit and receive arrays in wireless communications. REFERENCES [1] A. J. Paulraj and C. Papadias, “Space–time processing for wireless communications,” IEEE Signal Process. Mag., pp. 49–83, Nov. 1997. [2] G. J. Foschini and M. J. Gans, “On the limits of wireless communications in a fading environment when using multiple antennas,” Wireless Pers. Commun., pp. 315–335, 1998. [3] V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space–time codes for high data rate wireless communications: Performance criterion and code construction,” IEEE Trans. Inform. Theory, vol. 44, pp. 744–765, Mar. 1998. [4] G. Raleigh and J. M. Cioffi, “Spatio-temporal coding for wireless communications,” IEEE Trans. Commun., vol. 46, no. 3, 1998. [5] I. E. Telatar, “Capacity of multi-antenna Gaussian channels,” Eur. Trans. Telecommun., vol. 10, pp. 585–595, Nov. 1999. [6] S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Select. Areas Commun., vol. 16, Oct. 1998. [7] G. J. Foschini, “Layered space–time architecture for wireless communications in a fading environment when using multi-element antennas,” Bell Labs Tech. J., pp. 41–59, 1996. [8] G. J. Foschini, G. D. Golden, R. A. Valenzuela, and P. W. Wolnianski, “Simplified processing for high spectral efficiency wireless communication employing multi-element arrays,” IEEE J. Select. Areas Commun., vol. 17, no. 11, pp. 1841–1852, Nov. 1999. [9] G. D. Golden, G. J. Foschini, R. A. Valenzuela, and P. W. Wolniansky, “Detection algorithm and initial laboratory results using V-BLAST space–time communications architecture,” Electron. Lett., vol. 35, pp. 14–16, Nov. 1998. [10] F. R. Farrokhi, G. J. Foschini, A. Lozano, and R. A. Valenzuela, “Linkoptimal BLAST processing with multiple-access interference,” in Proc. IEEE Vehicular Technology Conf. (VTC’2000), Boston, MA, Sept 2000. [11] F. Rashid-Farrokhi, G. J. Foschini, A. Lozano, and R. A. Valenzuela, “Link-optimal space–time processing with multiple transmit and receive antennas,” IEEE Commun. Lett., vol. 5, pp. 85–87, Mar. 2001. [12] G. J. Foschini, H. C. Huang, and H. Viswanathan, “Multiple antennas in random code CDMA systems: Transmission, detection and spectral efficiency,” in Proc. WCNC’99, New Orleans, LA, Sept. 1999. [13] S. Catreux, P. F. Driessen, and L. J. Greenstein, “Simulation results for an interference-limited multiple-input multiple-output cellular system,” IEEE Commun. Lett., vol. 4, pp. 334–336, Nov. 2000. [14] S. Diggavi, “On Achievable Performance of Spatial Diversity Fading Channels,” Trans. Inform. Theory, vol. 47, pp. 308–325, Jan. 2001.

5AA receivers are extremely effective at mitigating interference as long as the number of receive antennas exceeds the number of dominant interferers, which in TDMA tends to be small. If MTMR users were to coexist with AA users, this advantage may vanish because of the multiple dimensions on which MTMR users signal.

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Farrokh R. Farrokhi (S’88–M’97) received the B.S. and M.S. degree (highest honors) in electrical engineering from Sharif University of Technology, Tehran, Iran, in 1988 and 1992, respectively, and the Ph.D. degree in electrical engineering from the University of Maryland, College Park, in 1997. From 1998 to 2000, he was a Member of Technical Staff in the Wireless Research Department, Bell Labs, Lucent Technologies, Holmdel, NJ. Since 2000, he has been with the Advanced Research and Development Department, Centillium Communications, Fremont, CA, as a Senior Staff Engineer. His research interests include array and statistical signal processing, wireless communications, and networking. Dr. Farrokhi received the 1996–97 George Harhalakis Outstanding Systems Engineering Graduate Student Award in recognition of outstanding contributions in cross-disciplinary research, from the University of Maryland.

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Angel Lozano (S’90–M’99–SM’02) was born in Manresa, Spain, in 1968. He received the engineering degree in telecommunications (with honors) from the Polytechnical University of Catalonia, Barcelona, Spain, in 1992, and the M.S. and Ph.D. degrees in electrical engineering from Stanford University, Stanford, CA, in 1994 and 1998, respectively. Between 1996 and 1998, he worked for Pacific Communication Sciences Inc. (PCSI), San Diego, CA. In January 1999, he joined Bell Laboratories (Lucent Technologies), Holmdel, NJ, where he is currently a Member of the Technical Staff. His research interests include resource allocation in wireless systems, multiple access schemes, adaptive antennas, space–time processing, and a variety of topics related to communication theory and wireless system design. He holds six patents. He also participated in the technical program committee for the International Conference on Communications (ICC’02) held in New York City, in May 2002. Dr. Lozano, has served as Associate Editor for IEEE TRANSACTIONS ON COMMUNICATIONS in the area of Wireless Network Access and Performance, since October 1999.

G. J. Foschini (S’60–M’72–SM’83–F’86) received the B.S.E.E. degree from New Jersey Institute of Technology (NJIT), Newark, NJ, the M.E.E. from New York University, New York, and the Ph.D. degree in mathematics from Stevens Institute, Hoboken, NJ. He has been involved with data communications research on many kinds of systems including wireless communications and optical communications systems. He has done research on point-to-point systems as well as on networks. He has taught at Princeton University, Princeton, NJ, and Rutgers University, Piscataway, NJ. Dr. Foschini won the 2001, Bell Labs Inventor’s Award.

Reinaldo A. Valenzuela (M’85–SM’89–F’99) received the B.S. degree from the University of Chile, Santiago, and the Ph.D. degree from the Imperial College of Science and Technology of the University of London, U.K. At Bell Laboratories, Holmdel, NJ, he studied indoor microwave propagation and modeling, packet reservation multiple access for wireless systems and optical wavelength division multiplexing (WDM) networks. He became Manager of the Voice Research Department at Motorola Codex, Boston, MA, where he was involved in the implementation integrated voice and data packet systems. On returning to Bell Laboratories, he led a multidisciplinary team to create a software tool for wireless system engineering (WiSE), now in widespread use in Lucent Technologies. He received the Distinguished Member of Technical Staff award and is Director of the Wireless Communications Research Department. He is interested in microwave propagation measurements and models, intelligent antennas, third-generation wireless system, and space–time systems achieving high capacities using transmit and receive antenna arrays. He has published over 80 papers and has 12 patents. Dr. Valenzuela is the Editor for the IEEE TRANSACTIONS ON COMMUNICATIONS and the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS.