1740
`
`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 42, NO. 2/3/4, FEBRUARY/MARCH/APRIL 1994
`
`The Impact of Antenna Diversity on the
`
`Capacity of Wireless Communication Systems
`
`Jack H. Winters, Senior Member, IEEE, Jack Salz, Member, IEEE, and Richard D. Gitlin, Fellow, IEEE
`
`significantly increased by exploiting the other dimension,
`space, that is available to the system designer. To capitalize
`on the spatial dimension, multiple antennas, spaced at least a
`half of a wavelength apart, are used to adaptively cancel the
`interference produced by users who are occupying the same
`frequency band and time slots. The interfering users can be in
`the same cell as
`the target user, and thus
`interference
`cancellation allows multiple users in the same bandwidth - in
`practice the number of users is limited by the number of
`antennas and the accuracy of the digital signal processors used
`at the receiver. The interferers can also be users in other cells
`
`(for frequency reuse in every cell), users in other radio
`systems, or even other types of radiating devices, and thus
`interference cancellation also allows radio systems to operate
`in high interference environments.
`Optimum combining and signal processing with multiple
`antennas,
`is not a new idea [2-5]. But spurred on by new
`theoretical results, described in the sequel,
`it may be one
`whose time has come. Spatial diversity can be thought of as
`an overlay technique that can be applied to many wireless
`transmission systems, and it is known that with M antennas,
`M —1 interferers can be nulled out [3—5]. Consequently it can
`be used, perhaps in a proprietary manner,
`to increase the
`capacity of installed systems. Or, spatial diversity can be
`thought of as an alternative to the use of microcells to increase
`capacity. Microcells, while quite attractive, do create control
`(handoft) problems, require more base stations, and require
`sophisticated location planning for the new base stations. So,
`the
`added complexity of more
`antennas
`for optimum
`combining may be offset by the reduced complexity of the
`network controller, along with the reduction in the number of
`base stations, and the need for frequency planning (with
`frequency reuse in every cell). Furthermore, nulling of
`interferers can allow for low power transmitters to coexist with
`.high power transmitters without a substantial decrease in
`performance and could lead to overlaid systems. Moreover, in
`some cases time-division retransmission [6] can be used to
`concentrate the complexity in the centralized base station (in
`this case the optimum combiner is used both as a receiver and
`transmitter array), so that
`the increased cost
`is amortized
`among all the users.
`Use of spatial diversity is certainly made more compelling
`by the continued decrease in the cost of digital
`signal
`processing hardware,
`the
`advances
`in
`adaptive
`signal
`processing, and the above system benefits. Our continuous
`interest in this subject has recently yielded a new analytical
`result that is proven in the body of this paper: for a system
`with N users in a flat Rayleigh fading environment, optimum
`0090-6778/94$04.00 © 1994 IEEE
`
`interference-dominated
`Abstract—For a broad class of
`wireless systems including mobile, personal communications, and
`wireless PBX/LAN networks, we show that a significant increase
`in system capacity can be achieved by the use of spatial diversity
`(multiple antennas), and optimum combining. This is explained
`by the following observation:
`for
`independent
`flat-Rayleigh
`fading wireless systems with N mutually interfering users, we
`demonstrate that with K +N antennas, N ——l interferers can be
`nulled out and K+1 path diversity improvement can be achieved
`by each of the N users. Monte Carlo evaluations show that these
`results also hold with frequency-selective fading when optimum
`equalization is used at the receiver. Thus an N-fold increase in
`user capacity can be achieved, allowing for modular growth and
`improved performance by increasing the number of antennas.
`The interferers can also be users in other cells, users in other
`radio systems, or even other types of radiating devices, and thus
`interference cancellation also allows radio systems to operate in
`high interference environments. As an example of the potential
`system gain, we show that with 2 or 3 antennas the capacity of
`the mobile radio system IS-54 can be doubled, and with 5
`antennas a 7-fold capacity increase (frequency reuse in every
`cell) can be achieved.
`
`I.
`
`INTRODUCTION
`
`The chief aim of this paper is to demonstrate theoretically
`that
`antenna diversity (with optimum combining)
`can
`substantially increase the capacity of most interference-limited
`wireless
`communication
`systems. We
`also
`study
`implementation techniques and issues for achieving these
`increases in operating systems. Increasing the number of users
`in a given bandwidth is the dominant goal of much of today’s
`intense research in mobile radio, personal communication, and
`wireless PBX/LAN systems [1—6].
`Currently, there is a great debate between the proponents of
`digital Time Division Multiple Access (TDMA) and Code
`Division Multiple Access (CDMA) (i.e., spread spectrum) as
`to which system provides maximum system capacity, without
`adding undue complexity, beyond that of today’s analog
`systems. While it is clear that both TDMA and CDMA are
`very attractive relative to today’s analog systems, we believe it
`may well be possible to realize a substantial additional gain in
`system capacity by the use of spatial diversity.
`Towards this end, it is the purpose of this paper to set on
`sound theoretical
`footing some old ideas and proposals
`claiming that the capacity of most wireless systems can be
`
`Paper approved by Justin Chuang, the Editor for Wireless Networks of the
`IEEE Communications Society. Manuscript received February 18, 1993;
`revised September 28, 1993. This paper was presented at the lst International
`Conference
`on Universal Personal Communications, Dallas, Texas,
`September 29 — October 2, 1992.
`The authors are with AT&T Bell Laboratories, Holmdel, NJ 07733.
`IEEE Log Number 9401575.
`
`CLEARWIRE 1014
`
`

`

`WINTERS at 111.: THE IMPACT OF ANTENNA DIVERSITY
`
`1741
`
`
`
`
`Receiver
`Processor
`
`. Outputs
`
`N
`
`VM
`
`Fig. l. Multiuser communication block diagram.
`
`B. Flat Rayleigh Fading
`
`the channel matrix C(w) is
`With flat Rayleigh fading,
`independent of frequency and all the elements of C can be
`regarded as
`independent,
`zero—mean, complex Gaussian
`random variables with variance 0,2 for the 1"” user, provided
`the
`antenna
`elements
`are
`sufficiently
`separated.
`This
`separation is typically about half a wavelength at the mobile
`because of local multipath and several wavelengths at the base
`station (because in many cases there is a line-of-sight from the
`base station to the vicinity of the mobile). Let us consider the
`high signal-to-noise case (which results in the "zero—forcing"
`optimum combiner solution). Under these assumptions (2)
`reduces to
`-
`
`(MSE)011 = (CfCHi N0 -
`
`(3)
`
`Since the minimum MSE for any signal-to—noise is always less
`than or equal to the MSE of the zero-forcing combiner (3), the
`zero-forcing solution serves as an upper bound on the MSE
`solution. For these reasons and the fact that it is easier to
`
`analyze the zero-forcing structure, we proceed in this paper
`with this approach. Using the MSE given by (3), we find that
`an exponentially tight upper bound on the conditional
`probability of error is given by [8, Eq. (16)]
`l
`
`P 1(C) S exp {—J‘l- -—-_} ,
`
`”
`
`oz (C’Chl
`
`(4)
`
`the signal-to-noise ratio for user
`
`"1“,
`
`where p is
`
`0202a 1
`
`p " No
`In order to analyze the performance of the general set-up,
`we must be able to determine the statistical properties of the
`random variable a = i/(Cfcm. From the definition of the
`inverse of a matrix we express this quantity as follows,
`
`i.e.,
`
`combining provided by a base station with K +N antennas can
`null out N —l
`interferers as well as achieve K +1 diversity
`improvement against multipath fading. Computer simulation
`shows that these results also hold with frequency-selective
`fading when optimum equalization is used at the receiver. In
`addition, the average error rate, or outage probability, behaves
`as if each user were either spatially or frequency isolated from
`the other users and derives the full benefit of the shared
`
`antennas for diversity improvement. These results provide a
`solid basis for assessing the improvement that can be achieved
`by antenna diversity with optimum combining.
`In Section 2, we present theoretical results for flat fading
`and computer simulation results for frequency-selective fading
`with optimum combining. Experimental verification of
`interference suppression with flat
`fading is described in
`Section 3. In Sections 4 and 5, we discuss the application of
`optimum combining to the proposed North American standard
`for
`digital mobile
`radio,
`18-54,
`and
`other
`systems,
`respectively. A summary is presented in Section 6.
`
`II. PERFORMANCE ANALYSIS
`
`A. System Description
`
`Figure 1 shows a wireless system with N users, each with
`one antenna, communicating with a base station with M
`antennas. The channel
`transmission characteristics matrix
`
`C (to) can be expressed as
`C<w) = [€1th C2(09)
`
`Circe)
`
`(1)
`
`where u) is the frequency in radians per second and the N
`column
`vectors
`(each
`with M—elements)
`C1((o),
`C2(m),...,CN(w) denote the transfer characteristics from the i’h
`user,i = 1,2,...,N to the j’h,j = 1,2,...,M receiver or antenna.
`Now consider the Hermitian matrix CT(w)C(w), where the
`dagger sign stands for "conjugate transpose." If the vectors in
`(1) are linearly independent, for each to, then the N><N matrix
`inverse,
`(C TC)‘1
`exists. This
`is a mild mathematical
`requirement and will most often be satisfied in practice since it
`is assumed that users will be spatially separated.
`At the receiver, the M receive signals are linearly combined
`to generate the output signals. We are interested in the
`performance of this system with the optimum linear combiner,
`which combines the received signals to minimize the mean-
`square error (MSE) in the output. An explicit expression was
`provided for the least obtainable total (for all N users) MSE in
`[7 , Eq. (17)]. The formula for the minimum MSE for user "1"
`only, without loss of generality, is given by
`71/1~
`
`(MSE)011 = a: __
`
`T
`21:
`
`-1|:/T
`
`-I
`
`f
`
`N0
`:|11
`[I + C (w)C(m) 02
`
`a
`
`13% stands for the "1 1" component
`where 02 = E l a5,” l 2, [
`of a matrix, T is the symbol duration, No is the noise density,
`and 51$,” are the l” user’s complex data symbols.
`
`dco (2)
`
`a _ det (CfC) _ A~(Ct,-...Civ)
`— -———
`A11
`AN—1(CZv"'7CN)
`
`5
`
`(
`
`)
`
`where det(-) stands for determinant, A 11 is the "11" cofactor,
`AN(C1,...,CN) = det (CIC),
`and AN_1(C2,...,CN)
`is
`the
`determinant resulting from striking out the first row and first
`column of C 7‘C. From the definition of the determinant
`
`

`

`1742
`
`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 42, NO. 2/3/4, FEBRUARY/MARCH/APRIL 1994
`
`P, =EC Pe(C) SEC exp 4—9; +1 =Eae “3
`,
`~
`Ga
`(C7011
`M—N+1
`
`AN<61.CZ.....CN)= E :thipicawctci, ,(6>
`
`where the sum is extended over all N! permutations of
`l, 2,..., N, the “+" sign is assigned for an even permutation and
`"-“ for an odd permutation, it can be seen that it is possible to
`factor out Cf on the left and C1 on the right in each term.
`This factorization makes it possible to express AN in the
`following form
`
`AN(C1,C2,...,CN) = C{F(C2,C3,...,CN)C1
`
`(7)
`
`where F is an MXM matrix independent of ~C1. By
`normalizing F by AN_1(C2...CN) so that F /AN_1 = M, we can
`express the quantity of interest as a positive quadratic form
`
`u=ct1frcl
`
`(8)
`
`where M is Herrnitian and non—negative. Diagonalizing M by
`a unitary transformation (1), we write for at
`
`0t=Cf¢TA¢C1=z7LAz
`M
`
`= E k,-
`
`i=1
`
`izil2
`
`(9)
`
`- AM), ki’s being the eigenvalues of M,
`-
`where A is diagOtl -
`z=¢C1,andzi=(¢C1),-,i=1,...,M.
`'
`Since C1 is a complex Gaussian vector, so is z conditioned
`on (p. Also, the vectors C1 and z possess identical statistics
`since (1) is unitary. Therefore, conditioned on the eigenvalues,
`the random variable 0t
`is a weighted sum—of—squares of
`Gaussian random variables and therefore has a known
`
`probability distribution.
`One would expect the actual distribution of Ct to be rather
`complicated since for example the characteristic function of 0t,
`conditioned on the eigenvalues,
`is readily evaluated in the
`form
`
`E {eidm
`
`
`
`x,,i=1,...,M} = I
`
`M
`
`I
`
`i=1
`
`(1 — map—1 .
`
`(10)
`
`But since the eigenvalues are complicated nonlinear functions
`of the remaining N —1 vectors, (C2,C3,...,CN),
`the actual
`characteristic function of at, the average of (10) with respect to
`the eigenvalues, appears to be intractable. However, as shown
`in Appendix A, the eigenvalues of M are equal to either 1 or
`zero, with M —N +1 eigenvalues equal to 1, and thus (X is Chi—
`square distributed.
`in (4), we evaluate explicitly the
`Applying this result
`average probability of error1 , i.e.,
`
`1 A more detailed derivation of the results in this section is presented in [9].
`
`
`:Ezexp -LZE izil2 =1+L2]
`
`Ga
`
`,
`
`i=1
`
`—(M—N+l)
`
`,(11)
`
`Ga
`
`average probability of error with optimum
`the
`Thus,
`combining, M antennas, and N interferers is the same as
`maximal ratio combining with M —N +1 antennas and no
`interferers.
`
`The physical implications of this result are as follows. The
`error rate of a particular user is unaffected by all other users.
`It only depends on the user’s own SNR, p. Of course, the
`price paid is in the diminished diversity benefits obtained for
`each user. For, when the number of antennas M equals the
`number of users N, the average error rate is as if there was
`only one antenna per user. But remarkably,
`the resulting
`performance is as if all the other users or interferers did not
`exist. The nulling-out of other users results only in reduced
`diversity benefits. But even when M =N +1, all users enjoy
`dual diversity, i.e., the addition of each antenna adds diversity
`to every user.
`
`Furthermore, as stated previously, the above result is error
`rate performance with zero—forcing weights, whereby the
`interference is completely cancelled.
`In most practical
`systems, though, we don’t need to cancel the interference, but
`only suppress it into the noise, and thus the minimum MSE
`combiner can achieve even better results than shown above.
`
`Note also that in most systems, the number of interferers is
`much greater than the number of antennas. However, these
`interferers are usually much weaker than the desired signal
`(rather than equal to it, as we have considered), and optimum
`combining can still achieve gains over maximal
`ratio
`combining (see, e.g., [11]), although our theoretical results
`(11) no longer apply.
`
`C. Frequency—Selective Fading
`
`With frequency—selective fading, unfortunately, no closed
`form analytical results exist as for the flat fading case. The
`problem is complicated since in this case the variances of the
`output noise samples are complicated functionals of the matrix
`channel characteristics, C(m). The performance of optimum
`(MSE)
`combining
`and
`optimum equalization
`(linear
`equalization with an infinite length tapped delay line) has been
`previously studied by computer
`simulation in [17]
`for
`cochannel interference and frequency—selective fading. These
`results
`showed
`that
`the
`performance
`improves with
`frequency-selective fading and optimum equalization. Here
`we want to verify that for the zero—forcing combiner and
`optimum equalization, the capacity and performance gains we
`obtained with flat fading still hold or are even improved.
`With frequency-selective fading and optimum equalization,
`the MSE is given by (2). For the zero—forcing combiner, with
`sufficiently high signal-to-noise ratio, in (2) the I matrix is
`7,
`negligible as compared to Lia—”£0202 and is dropped.
`0
`
`

`

`WINTERS et al.: THE IMPACT OF ANTENNA DIVERSITY
`
`Using the probability of error bound for given MSE of [8, Eq.
`(16)] (as in Section 2.2), we obtain an exponentially tight
`bound on the conditional probability of error given by
`
`P C
`
`e(
`
`((0))
`
`1
`p
`s ——_—
`
`6XP{ 63 02(0}
`
`where
`
`—1
`T 1%
`02(C(w)) = E; I [Cl(w)C(oo)]udoo .
`«:—
`
`(12)
`
`(13)
`
`The outage probability as well as the average probability of
`error depends
`in a complicated way on the statistical
`characterization of the matrix C (0)).
`If we assume that the propagation mode is by uniformly
`distributed scatterers and delay spread cannot be neglected,
`then a reasonable statistical model for C(00) is the following.
`For each frequency 0.), every entry in C(01))
`is complex
`Gaussian, but
`at different
`frequencies
`the
`entries
`are
`correlated.
`Specifying the multidimensional
`correlation
`function provides a complete statistical characterization of the
`matrix medium. For this model, which is often referred to as
`the "frequency-selective fading" Rayleigh medium, we can
`derive an upper bound on the average probability of error.
`Also, for a two ray model of the frequency-selective Rayleigh
`process for each entry of the matrix C, we have carried out
`Monte Carlo evaluations. We will discuss these results later,
`
`but first we provide an outline of our bounding technique.
`Note that from the properties of the matrix Cl(w)C(w),
`irrespective of the statistics, we can always express the noise
`variance as
`
`02(C(w)) = <—1————
`M—N+l
`>3
`.
`2
`[=1
`lz,((o)l
`
`1t
`7
`
`>..
`
`(14)
`
`where <->u, = 311% I Hdw and 2,-(03) = q>,?‘((o)C1(w) where
`
`71:
`
`~
`_ T
`¢,-((n) are the eigenvectors of the matrix M. We now note that
`for each frequency
`
`M—N+l
`
`(tan) = .2“.
`1:
`
`I zi(w) I 2
`
`(15)
`
`is Gamma distributed with probability density
`
`0cK—r e—a
`P01) - ——_(K—1)!
`
`(16)
`
`where K =M —N +1.
`
`Making use of these facts, an upper bound on the average
`probability of error is given by (see Appendix B)
`
`_
`
`P. =ECP.(C(w» s dim [F]
`
`02 M—N
`
`1743
`
`(17)
`
`where dM_N =
`
`16-5 '
`
`- [2(M—N)—1]
`-
`(M —N)l
`to be a loose upper bound, it does indicate that when the
`number of antenna elements is not much greater than the
`number of users or interferers we only lose the diversity
`benefit from one additional antenna.
`
`. While this may appear
`
`As an illustration, suppose that M —N =1, i.e., one more
`antenna element than users. Our bound indicates that ESI /p
`for a binary system when 02:1. On the other hand, when only
`.
`.
`— 1
`flat fading is present, we can expect PCS—2.
`
`In actual Monte Carlo simulation and evaluation of
`
`averages presented below, we found that the average error
`rates were much lower than predicted from (17).
`Before proceeding, we note that with a two ray model of
`frequency-selective fading with N==1
`(no interference),
`[2]
`provides bounds showing that
`the average bit error rate
`decreases with increasing time delay between the two
`multipath rays when optimum combining and equalization is
`used. For this two ray model, the ijth element of C(03) is
`given by
`
`‘iji
`
`017(0)) = aij+bije
`
`(18)
`
`where aij and by are complex Gaussian random variables with
`zero mean and variance 1/2, and “c, is the time delay between
`the two rays.
`To gain insight into the behavior of average error rate
`versus delay spread, we used Monte Carlo simulation to derive
`1000 channel matrices C and numerically calculated the
`average bit error rate for each channel from (12). The entries
`in C are given in (18). The bit error rate averaged over these
`1000 C matrices is shown in Figures 2 and 3 for p/og = 18
`dB. Figure 2 shows the average bit error rate versus t/T,
`where T is the symbol duration, for M =N with a) frequency—
`selective fading of
`the desired and interfering signals,
`t1=r2= -
`- -=1:N=1:, where 11 is the time delay between the two
`multipath rays of the desired signal and '52,
`~
`-
`- ,IN is the time
`delay of the interfering signals, b) frequency-selective fading
`of the interferers only, 11:0, 12=' - -=1:N=1:, and c) frequency-
`selective
`fading
`of
`the
`desired
`signal
`only,
`11:1,
`12: -
`- -=1:N=O. At t/ T - 0, the simulation results for M - 1, 2,
`and 3 should be equal to the theory (flat-fading) point shown.
`The simulation results differ from the theory because only
`1000 samples were used due to CPU time limitations. For all
`three values of M, the bit error rate (BER) decreases with 'c/ T
`until ‘t/T = 1, and then remains approximately constant,
`because the signals in the two rays are uncorrelated in this case
`since the bandwidth of the signal is equal to the data rate. At
`1:/ T - 1, the simulation results for a) 11:12: -
`-
`' =1IN=T are in
`agreement with theoretical results [2] for a single signal with
`optimum equalization, within the sampling error, with slightly
`degraded performance for cases b) and 0). Thus, with
`
`

`

`1744
`
`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 42, NO. 2/3/4, FEBRUARY/MARCH/APRIL 1994
`
`10"
`
`
` M=N, plo§= 18 dB
`— a) T1=T2=...TN=T
`
`
`—- b) T1=O,TZ=...TN=T
`..... C)T1=’C,12=...TN=0
`
`Theory
`(Flat Fading)
`
`
`
`
`
`
`1o-3
`
`T/T
`
`Fig. 2. Effect of frequency-selective fading for M=N, with optimum
`combining and equalization.
`
`III. EXPERIMENTAL RESULTS
`
`To demonstrate and test the interference nulling ability of
`optimum combining in a fading environment, an experimental
`system was built. Figure 4 shows a block diagram of the
`experiment, which consisted of 3 users, a 24 channel Rayleigh
`fading simulator, 8 receive antennas, and a DSP32C processor
`at
`the receiver. The three remotes’
`signals used QPSK
`modulation, at a common 50 MHZ IF frequency, consisting of
`a biphase data signal and a quadrature biphase signal with a
`pseudorandom code that was unique to each user. This
`pseudorandom code was used to generate the reference signal
`at the receiver (see [3,4]) that was used to distinguish the
`users. Thus half of the transmitted signal energy was allocated
`for reference signal generation only. The fading simulator
`generated the 8 output signals for the antennas by combining
`the three remotes’ signals with independent flat, Rayleigh
`fading between each input and antenna output. The fading rate
`of the simulator was adjustable up to 81 Hz. The outputs of
`the simulator were demodulated by the 8 antenna subsystems,
`A/D converted, multiplexed, and input to a DSP32C. This
`DSP32C used the Least Mean Square (LMS) algorithm ([10],
`see also [3,4]) to acquire and track one of the remote’s signals.
`With our program in the DSP32C,
`the maximum weight
`update rate was 2 kHz, and the data rate was set to 2 kbps for
`convenience (although any data rate greater than 2 kbps could
`have been used). The step size of the LMS algorithm was
`limited to keep the change in weights small enough so that the
`data was not significantly distorted by the weights and so that
`the algorithm remained stable.
`Experimental results were obtained for the case of equal
`(averaged over the Rayleigh fading) received—power signals, as
`in the theoretical results of the previous section. Thus, with
`two interferers, the desired—signal—to-interference-power ratio
`was -3 dB and the BER without optimum combining was
`approximately 0.5. Our experimental results showed that
`optimum combining reduced the BER below 10’2 (suitable for
`mobile radio) even with a fading rate of 81 Hz. Note that this
`corresponds to a data rate (2 kbps) to fading rate ratio of 25,
`which is much faster fading than in most wireless systems (see
`Sections 4 and 5). Thus,
`the experiment
`successfully
`demonstrated that 2 interferers with power equal to the desired
`signal can be suppressed for a 3-fold capacity increase (i.e., 3
`users in one channel) in a fast fading environment. Noise on
`the circuitry backplane limited the accuracy of the A/D to
`6 bits, which did not allow verification of the 6-fold diversity
`improvement predicted by (11) for M=8 and N=3, or precise
`calculation of the level of interference suppression.
`
`IV. APPLICATION TO 15-54
`
`To illustrate the application of adaptive antennas to
`proposed wireless communication systems, in this section we
`consider the proposed North American standard for digital
`mobile radio, 18-54. In this cellular TDMA system, 3 remotes
`communicate with the base station in each 30 kHz channel
`
`within a 824 to 849 MHz (mobile to base) and 869-894 MHz
`(base to mobile) frequency range, at a data rate of 13 kbps per
`user using DQPSK modulation. Each user’s slot contains
`
`Theory
`(Flat Fading)
`u:
`‘33 10-4
`
`.2
`
`1°
`
`10'3
`
`10'5
`
`10-6
`
`
`
`‘
`M = N+1, plo§= 18 dB
`—— a) t, =12=...tN='r
`—— b) r1=o,t2=...
`----- c) r1=t,1:2=...
`
`(Bwnd)
`
`- Theory [2]
`
`O
`
`5
`
`‘E/T
`
`1,0
`
`1 5
`
`Fig. 3. Effect of frequency-selective fading for M=N+1 , with optimum
`combining and equalization.
`i
`
`fading and optimum combining and
`frequency—selective
`equalization with M antennas, each of the N =M users have the
`same performance as that of a single antenna system without
`interference.
`:
`
`Figure 3 shows similar results for M =N +1. Thus, with
`M =N +1, we can achieve dual diversity for all users, with each
`user having the performance gain of a single antenna/user
`system with frequency-Selective fading.
`' Therefore, our
`simulation results show that our results for flat fading also
`hold with
`frequency-selective
`fading
`and
`optimum
`equalization.
`'
`
`

`

`WINTERS et al.: THE IMPACT OF ANTENNA DIVERSITY
`
`l 745
`
`9 Faded Signal
`
`Fading
`Simulator
`
` Rayleigh
`
`0 Fading Rate
`
`Fig. 4. Experimental system.
`
`324 bits, including a 28 bit synchronization sequence, 12 bit
`user identification sequence, plus 260 data bits, resulting in a
`data rate for each channel of 48.6 kbps (24.3 kbaud)[l].
`In small cells in urban areas, the multipath delay spread is
`usually a fraction of a symbol, and equalization is not needed.
`However, in larger cells, e.g., in suburban or rural areas, the
`delay Spread may be as large as a symbol and,
`in this
`frequency-selective fading environment, equalizers may be
`used at both the base station and mobiles. Base stations use
`
`two antennas for reception with selection or postdetection
`combining (see below), while two antennas are only an option
`at the mobile. This is due to the fact that mobile to base
`
`station transmission requires greater improvement than the
`reverse link, because portable phones, which transmit
`less
`power, must be accommodated along with the phones in
`vehicles. Thus,
`today there are two classes of mobile
`transmitters: portables and mobile units, as well as two classes
`of mobile receivers:
`those with and without diversity. A
`frequency reuse factor of 7 is generally used in order to
`provide adequate service for all classes of transmitters and
`receivers, which means that for each user there are up to 6
`cochannel interferers two cells away.
`The 18-54 application of optimum combining differs from
`the systems studied in Sections 2 and 3 in that, typically, the
`number of interferers is greater than the number of antennas,
`but the interferers have lower power than the desired signal.
`Thus, in 18-5 4 optimum combining cannot completely null all
`interferers, but can decrease their power in the array output by
`a few dB. This can suppress interference below the noise level
`and decrease the required receive signal-to-interference-plus-
`noise ratio (SINR), which permits lower frequency reuse
`factors and, thus, higher capacity (as shown below).
`
`A. Mobile To Base
`
`Let us next consider how adaptive antennas can be used to
`improve the performance and increase the capacity of this
`system. We will first consider the weaker link from the
`mobile to the base station. Figure 5 shows a block diagram of
`the system to be considered. At the base station there are
`multiple antennas, but only one antenna at each mobile
`(multiple mobile antennas will be considered later). The
`antennas are positioned such that the fading of each signal at
`each antenna is independent (see Section 2.2). At the base
`station, the received signals are linearly combined to reduce
`
`the effects of multipath fading and eliminate interference from
`other users. Figure 6 shows a block diagram of the M element
`adaptive array. The signal received by the ith antenna element
`is passed through a tapped delay line equalizer (only two trips
`are shown in the figure for simplicity) with controllable
`weights. The weighted signals are then SUmmed to form the
`array output. Note that the tapped delay line equalizer is
`required only in areas with large delay spread.
`In congested
`urban areas, there would be only one tap per antenna.
`The weights can be calculated by a number of techniques.
`Here, we will consider two techniques, the LMS algorithm (as
`in Section 3) [10] and Direct Matrix Inversion (DMI)[10].
`With DMI, the weights are given by
`A—1A
`w = Rxxrxd ,
`
`(19)
`
`where
`
`w =[w11 ---wML]T ,
`
`<20)
`
`wij is the weight for the jth tap 0n the i antenna element, the
`superscript T denotes transpose, L is the number of taps in
`each equalizer, M is the number of antennas, the receive signal
`cross—correlation matrix is
`A
`
`K
`Rn =1/K.21x(i)x7k(i) ,
`J:
`
`(21)
`
`K is the number of samples used,
`
`X = [in)xi(i—1)‘“X1Ci-L+1)"‘xMU-L+1)]T .(22)
`
`xi(l) is the received signal at antenna i in the lth bit interval,
`the reference signal correlation vector is
`K
`
`fix, = 1/K.21x(j)r*(i)
`J:
`
`,
`
`(23)
`
`the superscript * denotes complex conjugate, and r(j) is the
`reference signal. The reference signal is used by the array to
`distinguish between the desired and interfering signals at the
`receiver. It must be correlated with the desired signal and
`uncorrelated with any interference. The generation of the
`reference signal is discussed below.
`The LMS algorithm has lower computational complexity
`than DM1 and its complexity increases linearly with the
`number of taps, while DMI’s complexity increases much faster
`than linearly because the technique uses matrix inversion (19).
`The LMS algorithm converges to the optimum weights at a
`slower rate than DMI, however, and its convergence speed
`depends on the eigenvalues of Rxxs i.e.,
`the power of the
`desired signal and interferers. Thus, weak interferers are
`tracked at a much slower
`rate _ than the desired signal.
`Although this was not a problem in the experiment of
`Section 3, where the desired signal and interference had the
`Same power, it is a serious problem in 18-54. As shown in
`[11], the LMS algorithm cannot track weak interference in
`18-54. DMI, however, has a convergence speed that
`is
`independent of the signal powers and can converge (with less
`
`

`

`1746
`
`IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 42, NO. 2/3/4, FEBRUARY/MARCH/APRIL 1994
`
`
`
`Fig. 5. Cellular radio system with multiple antennas at the base station.
`
` 37/
`
`S2
`
`Mobiles
`
`Base Station
`
`Fig. 6. Block diagram of an M element adaptive array.
`
`than a 3 dB SNR degradation) to the optimum weights With
`only 2ML samples (K in (21))
`[10, p. 297].
`In [11], we
`showed that with 2 antennas and 1 interferer, DMI can acquire
`and track both the desired signal and interferer in 18-54, with
`the performance of optimum combining within 1 dB of the
`predicted ideal
`tracking performance. Thus, we will only
`consider DMI for 18-5 4.
`
`Next, consider the reference signal generation. For weight
`acquisition, we will use the known 28 bit synchronization
`sequence as the reference signal, using DMI to determine the
`initial weights. After weight acquisition,
`the output signal
`consists mainly of the desired signal and (during proper
`operation) the data is detected with a BER that is not more
`than 10‘2 to 10—1. Thus, we can use the detected data as the
`reference signal. Note that since there will be processing
`delay in determining the data (generally, a few msec, which is
`not perceptible to the user), DMI must use delayed samples of
`the received signal and array output.
`For 18-54, the fading rate can be as high as 100 Hz (for
`
`75 mph (120 kin/hr) vehicles at 900 MHz), and thus with
`24.3 kbaud the channel can completely change in as little as
`243 symbols. This is slow enough so that the channel does not
`change significantly over the window of symbols, K, used by
`DMI for acquisition (K=14) and tracking (K=14 was used in
`[11])-
`Another issue is how to distinguish the desired user’s
`signal
`from other users
`in other cells.
`In 18-54,
`the
`synchronization sequence for a given time slot is the same for
`all users, but is different for each of the six time slots in each
`
`frame. Since base stations operate asynchrOnously, signals
`from other cells have a high probability of having different
`timing (since there are 972 symbols per frame) and being
`uncorrelated with the reference signal for the desired signal.
`The 12 bit user identification code can be used to verify that
`the correct user’s signal has been acquired.
`Let us now consider the improvement in the performance
`and capacity of 18-54 with optimum combining.
`In congested
`urban areas with small delay spread,
`the performance
`improvement with optimum combining can be calculated from
`previous
`papers. When equalizatiOn
`is
`not
`required,
`differential detection of the DQPSK signal can be used,
`followed by postdetection combining of the signals from the
`two antennas. Theoretically, such a system requires a 17.2 dB
`average SINR to operate at an average B