Introduction
The explosive growth of both the wireless industry and the Internet is creating a huge market opportunity for wireless data access. Limited Internet access at low speeds (a few tens of kilobits per second at most) is already available as an enhancement to some second-generation (2G) cellular systems. However, those systems were originally designed with the sole purpose of providing voice services and, at most, short messaging, but not fast data transfers. Third-generation (3G) mobile wireless systems, currently under development, will offer true packet access at significantly higher speeds [1]. Theoretically, user data rates as high as 2 Mb/s will be supported in certain environments, although recent studies have shown that approaching those rates might only be feasible under extremely favorable conditions -- in the vicinity of a base station and with no other users competing for bandwidth [2]. In fact, as will be argued in this article, traditional wireless technologies are not particularly well suited to meet the extremely demanding requirements of providing the very high data rates and low cost associated with wired access, and the ubiquity, mobility, and portability characteristic of cellular systems. Some fundamental barriers, related to the nature of the radio channel as well as to limited bandwidth availability at the frequencies of interest, stand in the way. As a result, the cost per bit in wireless is still high and not diminishing fast enough. In contrast, the wired world is already providing basically free bits, which has accustomed an entire generation of Internet users to accessing huge volumes of information at very high speeds and negligible cost. In this article we establish practical limits on the data rates that can be supported by a wireless data access system with a typical range of parameters, and we show how those limits can be lifted by using a combination of transmit and receive antenna arrays with powerful space-time processing techniques.
Fundamental Limitations in Wireless Data Access
A Brief History of Capacity
Ever since the dawn of the information age, capacity has been the principal metric used to assess the value of a communication system. However, several definitions of capacity exist. We refer to link capacity or user capacity to signify the highest data rate at which reliable communication is possible between a transmitter and a receiver. At the same time, we use system capacity to indicate the total throughput -- sum of user data rates -- within a cell or sector. System capacity can be converted into area capacity simply via normalizing by the cell size. Since existing cellular systems were devised almost exclusively for telephony, user data rates were low1 and had minimal variability. In fact, source rates were purposefully reduced to the minimum level necessary to support a highly compressed voice call and implicitly traded for additional users [3]. Therefore, systems were designed to accomodate a large number of low-data-rate users. With the emergence of wireless data services, many of these concepts are becoming obsolete. User data rates are increasingly variable and heterogeneous. The value of a system is no longer defined only by how many users it can support, but also by its ability to provide high peak rates to individual users as needed; in other words, by its ability to concentrate large amounts of capacity at very localized spots. Thus, in the age of wireless data, user data rate surges again as an important metric.
Due to the logarithmic relationship between the capacity of a wireless link and the signal-to-interference-and-noise ratio (SINR) at the receiver [4], trying to increase the data rate by simply transmitting more power is extremely costly. Furthermore, it is futile in the context of a dense interference-limited cellular system, wherein an increase in everybody's transmit power scales up both the desired signals as well as their mutual interference, yielding no net benefit. Therefore, power increases are useless once a system has become limited in essence by its own interference. Furthermore, since mature systems designed for high capacity tend to be interference-limited [3], it is power itself -- in the form of interference -- that ultimately limits their performance. As a result, power must be carefully controlled and allocated to enable the coexistence of multiple geographically dispersed users operating in various conditions. Hence, power control has been a topic of very active research for many years.
Increasing the signal bandwidth -- along with the power -- is a more effective way of augmenting the data rate. However, radio spectrum is a scarce and very expensive resource at the frequencies of interest, where propagation conditions are favorable.2 Moreover, increasing the signal width beyond the coherence bandwidth of the wireless channel results in frequency selectivity. Although well-established techniques such as equalization and orthogonal frequency-division multiplexing can address this issue, their complexity grows rapidly with the signal bandwidth.3 Altogether, it is imperative that every unit of bandwidth be utilized as efficiently as possible. Consequently, spectral efficiency -- defined as the capacity per unit bandwidth -- has become another key metric by which wireless systems are measured. In order to improve it, multiple access methods -- originally rather conservative in their design -- have evolved toward much more sophisticated schemes. In the context of frequency-division multiple access (FDMA) and time-division multiple access (TDMA), this evolutionary path has led to advanced forms of dynamic channel assignment that enable adaptive and much more aggressive frequency reuse [3]. In the context of code-division multiple access (CDMA), it has led to a variety of multiuser detection and interference cancellation techniques (see [5] and the references therein for a compilation of the vast literature on these topics).
Space: The Last Frontier
As a key ingredient in the design of more spectrally efficient systems, in recent years space has become the last frontier. Nonetheless, the use of the spatial dimension in wireless is hardly new. In fact, one could argue that the entire concept of frequency reuse on which cellular systems are based constitutes a simple way to exploit the spatial dimension. Cell sectorization, a widespread procedure that reduces interference, can also be regarded as a form of spatial processing. Moreover, even though the system capacity is ultimately bounded, the area capacity can be increased almost indefinitely4 by shrinking the cells and deploying additional base stations [3]. This idea has been the cornerstone of several low-tier microcellular system proposals. However, the cost and difficulty of deploying the vast infrastructure required to provide ubiquitous coverage using only microcells has proven prohibitive in the past; it remains to be seen whether that will change with the advent of wireless data. In light of these developments, the use of the spatial dimension is now geared mostly toward maximizing the system capacity on a per-base-station basis.5 Here, base station antenna arrays are the enabling tools for a wide range of spatial processing techniques devised to enhance desired signals and mitigate interference [6]. Coverage can be extended and tighter user packing becomes possible, enabling, in turn, larger cell sizes and higher capacities. With sufficiently large arrays, capacity can be extended even beyond the point at which every unit of bandwidth is effectively used in every sector through space-division multiple access (SDMA), which enables the reuse of the same bandwidth by multiple users within a given sector as long as they can be spatially discriminated.
Lifting the Limits with Transmit and Receive Arrays
Until recently, the deployment of antenna arrays in mobile systems was contemplated -- because of size and cost considerations -- exclusively at base station sites. The principal role of those arrays, long before interference suppression and other signal processing advances were conceived, was to provide spatial diversity against fading [3]. Signal fading, arising from multipath propagation caused by scattering, has always been regarded as an impairment that had to be mitigated. However, recent advances in information theory have shown that, with the simultaneous use of antenna arrays at both base station and terminal, multipath interference can be not only mitigated, but actually exploited to establish multiple parallel channels that operate simultaneously and in the same frequency band [7–9]. Based on this fundamental idea, a class of layered space-time architectures was proposed and labeled BLAST [10]. In BLAST, multiple data streams are simultaneously radiated using different antennas within a transmit array. With sufficient multipath, a receiver also equipped with an array can separate and successfully decode all those data streams using sophisticated signal processing that bridges the gap between array processing and multiuser detection. A critical feature of BLAST is that the total radiated power is held constant irrespective of the number of transmit antennas. Hence, extraordinary levels of spectral efficiency can be achieved without any increase in the amount of interference caused to other users. In that sense, BLAST can be seen as an evolved form of SDMA wherein a number of single-antenna user terminals have been collocated into a BLAST terminal that handles their multiple signals simultaneously. Intuitively, this requires the base station to be able to resolve the individual antennas within the terminal array, which in turn would require synthesizing an impossibly narrow beam. With BLAST, the scattering environment around the terminal is used as an aperture through which those antennas become effectively resolvable. Furthermore, since the multiple terminal antennas are collocated, the transmit data streams can be threaded into powerful space-time codes [11]. Notice that by reusing the same bandwidth multiple times, BLAST enables large increases in user data rate without increasing the user bandwidth.
Models and Assumptions
Our analyses are conducted in the 2 GHz frequency range, which is where 3G systems will initially be deployed. This is a favorable band from a propagation standpoint [3]. Also, and again in line with the 3G framework, the available bandwidth is assumed to be B = 5 MHz. However, for simplicity we ignore frequency selectivity with the argument that it can be dealt with using the techniques mentioned earlier and their extension to the realm of antenna arrays and BLAST [6].
We concentrate on the downlink only, which has the most stringent demands for data applications. However, a similar analysis could be applied to the uplink, although with much tighter transmit power constraints. A cellular system with fairly large cells is assumed, with every cell partitioned into 120° sectors.
The propagation scenario we consider, portrayed in Fig. 1, is based on the existence of an area of local scattering around each terminal. Little or no local scattering is presumed around the base stations.6 From the perspective of a base station, the angular distribution of power that gets scattered to every terminal is characterized by its root-mean-square width, commonly referred to as angle spread. Typical values for the angle spread at a base station are in the range of 1–10°, depending on the environment and range [3]. The antennas composing a base station array can be operated coherently if they are closely spaced, or decorrelated by spacing them sufficiently apart [12]. At a terminal buried in clutter, on the other hand, angle spreads tend to be very large -- possibly as large as 360° -- and thus, large uncorrelation among its antennas is basically guaranteed.
We use M to denote the number of antennas within every base station sector and N to indicate the number of antennas at every terminal. The channel responses from every sector antenna to every terminal antenna are assembled into an N 
M channel matrix H = {hnm}. Ignoring frequency selectivity, the entries of H are complex Gaussian scalars (Rayleigh-distributed in amplitude) whose local-average path gain has a range-dependent component and a shadow fading component. We choose to model the range-dependent component using the well-established COST231 model, which is based on Hata's fit to Okumura's measurements [3]. In suburban environments at 2 GHz, the local-average power path gain corresponds to7
L= 4 · 10–14 d–3.5 G
= –134 – 35 log10(d) + 10 log10 (G) dB,(1)
with d the range in kilometers and G the total (combined transmit and receive) antenna gain. The shadow fading is taken to be log-normally distributed with an 8 dB standard deviation [3]. The correlation among the entries of H is determined by the antenna spacing and angle spread. Antennas within a terminal are assumed fully uncorrelated, whereas those within a base station sector are assumed either also uncorrelated (for sufficiently large spacing) or fully correlated (for close spacing and coherent operation). Therefore, the rows of H are always independent, whereas the columns can be either linearly dependent or also independent.
While power control proved to be an essential ingredient in voice systems, where source rate variability was minimal, in wireless data systems rate adaptation becomes not only an attractive complement, but even a full alternative to power control. Hence, in this study we restrict ourselves to the case where the total power per user is held constant while the data rate is being adapted.
Furthermore, we concentrate on open-loop architectures wherein transmitters do not have access to the instantaneous state of the channel. Only long-term information (i.e., information that varies slowly with respect to the fading rate) is available to the transmitters.8 In its original form, BLAST has no need for instantaneous channel information at the transmitter. However, more elaborate closed-loop forms of BLAST have been devised in order to exploit that information in those cases when it may be available, such as when a fast feedback link is available or when time-division duplexing is employed [8, 9, 13].9 It is assumed -- in all cases -- that the channel matrix H is known perfectly at the receiver. Notice that this may require training overhead or, alternatively, blind acquisition algorithms.
The in-band noise power is 
2 = N0BF, where N0 is the one-sided noise spectral density, B is the signal bandwidth, and F is the receiver noise figure. We set the noise figure to an optimistic value of F = 3 dB and use the noise spectral density corresponding to a standard temperature of 300 K. The local-average SNR, excluding fading oscillations, can be expressed as
(2)
with PT the total radiated power.
In order to abstract our conclusions from the choice of specific codes or modulation formats, the use of capacity-approaching signals is presumed [4].
Single-User Data Rate Limits
Single-User Data Rate Bounds
Let us first consider an isolated single-user link limited only by thermal noise. Within the context of a real system, this would correspond to an extreme case wherein the entire system bandwidth is allocated to an individual user. Furthermore, it would require that no other users be active anywhere in the system or that their interference be perfectly suppressed. Clearly, these are unrealistic conditions; thus, the single-user analysis provides simply an upper bound, only a fraction of which is attainable. Also, since for a system to be interference-limited it is necessary that the signal-to-noise ratio (SNR) be large enough that the noise level is much lower than the interference, this analysis also determines what cell sizes can be supported in interference-limited conditions.
With a single transmit antenna and a single receive antenna, the single-user data rate bound can be expressed using Shannon's universal equation as
(3)
where |h|2 is the (instantaneous) channel power gain. When instantaneous information about h is not available at the transmitter, this bound is achieved by transmitting a Gaussian signal with average power PT [4]. Since the channel h is time-varying in nature, the bound fluctuates with it. With sufficiently deep interleaving and/or sufficient bandwidth, it is possible to average out the small-scale fading fluctuations. The shadow fading, however, cannot be similarly averaged out without imposing an unacceptable degree of latency. Thus, we prefer to resort to the idea of outage rate, which is the value of C supported with certain (high) probability. For most of our results, we choose 90 percent as the probability of support, which implies that 10 percent of the bursts or coding blocks may contain errors. This appears to be a reasonable operating point for many applications, although other operating points are certainly possible.
When multiple antennas are used at the transmitter and/or receiver, Shannon's equation -- with no instantaneous channel information at the transmitter -- can be generalized [7] to
(4)
with IN the identity matrix and |h|2 replaced by HH†. As a reminder, the entries of the matrix H represent the independent hnm channels between the M transmit and N receive antennas. As the number of antennas -- both M and N equally -- gets large, Eq. 4 converges to
(5)
where 
is the local-average SNR as defined in Eq. 2. Notice that the achievable data rate grows linearly with the number of uncorrelated antennas, which is a key result that contrasts with conventional diversity systems -- using an array at either transmitter or receiver only --wherein the growth is only logarithmic [7].
Steered Directive Array
We first consider the use of an array at the base station only, with M closely spaced antennas operating coherently. Since an estimate of the directional location of the terminal can be usually derived from the uplink, the use of directive array algorithms has been regarded as an attractive option for enhancing the performance of existing 2G systems.
Each individual base station antenna has a gain of 15 dBi. The terminal is equipped with a single omnidirectional antenna. Under these conditions, and assuming the beam synthesized at the base is properly steered toward the terminal, the single-user data rate bound can be expressed as
(6)
As M grows, the array becomes more directive; thus, more precise information about the directional location of the terminal is needed in order to fully illuminate its local scattering area. Also, since no further directional gain can be realized beyond the point at which the beamwidth becomes smaller than the angle spread, the size of a directive array has a fundamental bound imposed by the environment. We set M = 8, at which point the beamwidth falls below 10°, as the maximum number of 15 dBi antennas that can be aggregated.10
The 90 percent single-user capacities corresponding to this scenario are presented in Fig. 2 with the transmit power set to PT = 10 W. Because of the logarithmic relationship between rate and power, the use of a base station directive array offers very limited improvement in terms of single-user data rate.
Transmit Diversity
An alternative strategy, also based on the deployment of base station arrays only, which has already been incorporated into the 3G roadmap, is that of transmit diversity. In this case, the base station antennas must be spaced sufficiently far apart so that their signals are basically uncorrelated.11 The single-user data rate bound with transmit diversity can easily be derived from Eq. 4 to be
(7)
with hm the channel response from each of the uncorrelated array antennas to the terminal. Notice that, in this case, the base station needs no information on the directional location of the terminal, which is a very attractive feature that eliminates the calibration burden associated with directive arrays. The corresponding single-user results, shown in Fig. 3, are nonetheless similar to their directive array counterparts. Although in this case there is no fundamental bound to the size of the array, there is little advantage in increasing it beyond M ≈ 3–4 because of the diminishing returns associated with adding additional diversity branches to an already diverse link. Furthermore, in a true wideband system, frequency diversity would further reduce the benefits of transmit diversity.
Multiple-Transmit Multiple-Receive Antenna Architectures
We finally turn our attention to architectures with both transmit and receive arrays. As in the transmit diversity case, base station antennas must be spaced apart for proper decorrelation [12]. In addition, the terminal must be equipped with its own array. Also as in the diversity case, no information about the directional location of the terminal is required. In order to avoid cluttering our results with an excessive number of parameters, we scale the size of both the base station and the terminal arrays simultaneously; that is, we set M = N. The capacities, obtained directly from Eq. 4, are depicted in Fig. 4. For completeness, the transmit diversity curves of Fig. 3 are also shown. Notice the extraordinary growth in attainable data rates unleashed by the additional signaling dimensions provided by the combined use of transmit and receive arrays. With only M = N = 8 antennas, the single-user data rate can be increased by an order of magnitude. Furthermore, the growth does not saturate as long as additional uncorrelated antennas can be incorporated into the arrays.
Data Rate Limits Within a Cellular System
In this section we extend our analysis in order to reevaluate the user data rate limits in much more realistic conditions. To that end, we incorporate an entire cellular system into the study.
Most emerging data-oriented systems feature time-multiplexed downlink channels, certainly those evolving from TDMA, but also those evolving from CDMA [14, 15]. With that, same-cell users are ensured to be mutually orthogonal; thus, the interference arises exclusively from other cells. Accordingly, we consider a time-multiplexed multicell system with base stations placed on a hexagonal grid. Users are uniformly distributed and connected to the sector from which they receive the strongest signal. To further mimic actual 3G data systems, rate adaptation with no power control is assumed. Transmit signals are assumed Gaussian, which maximizes capacity as long as no multiuser detection across cells is attempted [4]. Altogether, the results presented in this section can be considered upper bounds for a 5 MHz data-oriented 3G system.
The results correspond to Monte Carlo simulations conducted on a 19-cell universe: a central cell, wherein statistics are collected, surrounded by two rings of interfering cells. The cell size is scaled to ensure that the system is basically interference-limited.12 The simulation parameters are summarized, for convenience, in Table 1.
Figure 5 displays cumulative distributions of system capacity (in megabits per second per sector) over all locations with transmit arrays only as well as with transmit and receive arrays. These curves can also be interpreted as user peak rates, that is, user data rates (in megabits per second) when the entire capacity of every sector is allocated to an individual user. With transmit arrays only, the benefit appears significant only in the lower tail of the distribution, corresponding to users in the most detrimental locations. The improvements in average and peak system capacities are negligible. Moreover, the gains saturate rapidly as additional transmit antennas are added. With frequency diversity taken into account, those gains would be reduced even further. The combined use of transmit and receive arrays, on the other hand, dramatically shifts the curves offering multifold improvements in data rate at all levels. Notice that, without receive arrays, the peak data rate that can be supported in 90 percent of the system locations -- with a single user per sector -- is only on the order of 500 kb/s with no transmit diversity and just over 1 Mb/s therewith. Moreover, these figures correspond to absolute upper bounds. With modulation excess bandwidth, training overhead, imperfect channel estimation, realistic coding schemes, and other impairments, only a fraction of these bounds can be actually realized. Without receive arrays, user rates on the order of several megabits per second can only be supported within a restricted portion of the coverage area and when no other users compete for bandwidth within the same sector.
Conclusions
Traditional wireless technologies are not very well suited to meet the demanding requirements of providing very high data rates with the ubiquity, mobility, and portability characteristic of cellular systems. Given the scarcity and exorbitant cost of radio spectrum, such data rates dictate the need for extremely high spectral efficiencies, which cannot be achieved with classical schemes in systems that are inherently self-interfering. Increased processing across the spatial dimension thus appears to be the only means of enabling the types of capacities and data rates needed for ubiquitous wireless Internet and exciting multimedia services. While the most natural way of utilizing the space dimension may be to deploy additional base stations in order to allow for more frequent spectral reuse with smaller cells, economical and environmental considerations require that performance be enhanced on a per-base-station basis. That, in turn, calls for the use of antenna arrays. While the deployment of base station antenna arrays is becoming universal, it is really the simultaneous deployment of base station and terminal arrays that unleashes vast increases in capacity and data rates by opening up multiple signaling dimensions. Space-time processing techniques can exploit this dimensionality to concentrate large amounts of capacity in localized spots. Recognizing this potential, the 3G Partnership Project (3GPP) recently approved the use of transmit and receive arrays as a working item for the high-speed downlink packet access mode currently under development [14].
In this article, we have quantified the benefits of using antenna arrays -- in the context of emerging mobile wireless data systems -- as a function of the number of available antennas. Although absolute capacity and data rate levels are very sensitive to the specifics of the propagation environment, the improvement factors are not. Hence, the relative scaling, rather than the absolute numbers themselves, is relevant.
Needless to say, a number of hurdles must be overcome before these new concepts can be widely implemented. First of all, it is necessary to assess the antenna arrangement and spacings that are required as well as the scattering richness of the environments of interest. In this respect, the BLAST prototype, operational for some time at our Crawford Hill facility, has yielded extremely encouraging results [10]. Additional -- and equally encouraging -- results from other sources are also surfacing. Second, the historical opposition to installing multiple antennas on a terminal must be conquered. While the shrinking size of cellular phones was a powerful argument sustaining that thesis, terminals requiring higher data rates tend to naturally be larger in size, so they can take full advantage of the increased throughput. As a result, they also offer additional room for multiple closely spaced antennas. In fact, it is the cost of multiple separate radio chains that poses a limitation which might prove to be more stringent than the antennas themselves. Hence, the development of low-cost integrated multiple-chain radio solutions has become a research topic of the utmost importance.
Acknowledgments
The authors would like to acknowledge many fruitful discussions with D. Chizhik, G. J. Foschini, M. Gans, H. C. Huang, C, Papadias, and H. Viswanathan at Bell Laboratories, as well as with Prof. S. Verdú at Princeton University.
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Biographies
Angel Lozano received his Engineer degree in telecommunications from the Polytechnical University of Catalonia, Barcelona, Spain, in 1992, and M.S. and Ph.D. degrees in electrical engineering from Stanford University, California, in 1994 and 1998, respectively. In January 1999 he joined the Wireless Communications Department at Bell Laboratories Lucent Technologies. His research interests include resource allocation in wireless systems, adaptive antennas, multiple access, and a variety of other topics related to communication theory. He is currently Associate Editor of IEEE Transactions on Communications. He has published over 20 papers and holds four patents.
Farrokh R. Farrokhi [S'88, M'97] received B.S. and M.S. degrees (highest honors) in electrical engineering from Sharif University of Technology, Tehran, Iran, in 1988 and 1992, respectively, and a Ph.D. degree in electrical engineering from the University of Maryland at College Park in 1997. In 1998 he joined the Wireless Research Department, Lucent Technologies as a member of technical staff. His research interests include array and statistical signal processing, wireless communications, and networking.
Reinaldo A. Valenzuela [F] obtained his B.S. from the University of Chile and his Ph.D. from the Imperial College of Science and Technology, United Kingdom. He is director of the Wireless Communications Department at Bell Laboratories. His areas of interest are propagation measurements and models, 3G wireless systems, and achieving high capacities employing transmit and receive antenna arrays. He has published over 60 papers and holds 10 patents.
