MIMO Channel Capacity for Fixed Wireless: Measurements and Models H. Xu, M. Gans, N.Amitay, R.A. Valenzuela, T. Sizer, R. Storz, D. Taylor, M. McDonald and C. Tran Bell Labs/Lucent Technologies R-111, 971 Holmdel-Keyport Rd Holmdel, N J 07733,
[email protected] (732) 888-7029 Abstract-- Recent breakthroughs in the application of information theory have shown great capacity increase by deployihg multiple transmitting and multiple receiving antenh&s as compared to conventional single antenna systems. This work presents an experimental verification of the theoretical capacity prediction and a summary of measurement results for 10 fixed wirelss locations in suburban New Jersey.
there is no multipath due to the scattering, the dimensions of the arrays produce the distinct spatial signature for each of the transmitted signals.
A . Measurement setup
The narrowband measurements were performed at 2.44 GHz. At the transmitter, a linear horizontal array with 5 antennas was used. Each antenna element is a panel I. INTRODUCTION antenna with 15" HPBW and 13 dB gain. The spacing In a multiple-input-multiple-output (MIMO) system, between two adjacent antennas is 0.52 m. At the receiver, such as Bell Lab Layered Space-Time (BLAST) system [l], both vertical and horizontal linear arrays are used. Each independent data streams are transmitted from Nt, anten- array has 4 elements with 26" of HPBW and 15 dB of nas and jointly detected from N,, receiver antennas. T h e gain. The two arrays form a cross, resulting in a total of 7 ory has shown that, for a fixed total transmitted power, the receiving antennas. The geometry of the antennas is shown system capacity grows linearly with the number of anten- in Figure 1. nas ri = min{Ntx, NrZFin a highly scattering environment. Due to the scattering environment, signals from different transmitter antennas produce different field patterns over the receiver antennas, and thus can be distinguished by signal processing. Initial experiments performing statistical verification of MIMO theory have been reported in [2], [3], [4], [5], [6], where statistics of channel capacity were measured for random channel, realizations. This paper presents results and models derived from MIMO channel measurement campaign over fixed wireless Iinks. The first part of the paper shows the channel model for the MIMO system in the near field of the antenna arrays, and experimental verification of capacity in a controlled propagation environment. The second part of the paper presents the capacity measurement results from 16 fixed wireless links in suburban New Jersey with different antenna heights. Some of the calibration and initial meaFig. 1. Link setup. surement results are presented in [3], [7], [8]. The measured channel transfer matrix is H with dimension of N,., by N t x . The measured narrowband channel spectrum efficiency, C (in bits/sec/Hz), is given by
11. VERIFICATION
OF CAPACITY IN A CONTROLLED PROPAGATION ENVIRONMENT
This paper shows the propagation results in a controlled free space environment, where the channel can be modeled exactly. The comparison of the measured results and the theoretical prediction provides a direct verification of the BLAST theory. The experiment was performed in free space in the near field of the antenna arrays. Although
0-7803-70M-8/01/$10.000 2001 IEEE
c = log,{ll+
--HtHI} P Ntz
where p is an intended average system SNR per each receiver antenna branch, (XIdesignates the determinant of a matrix X, H t is the complex conjugate transpose of H ,
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and I is an identity matrix having the same dimension as H t H ; i.e., Ntx by N t x .
D. Results
The measured results are presented in Figure 4. As a comparison, the channel capacities for a supremum chanB. Near field model nel, a Rayleigh iid channel [l],and a keyhole channel are Most of existing channel models considers link distances also presented. The supremum capacity is the theoretical in the far field of the antennas, where plane waves are upper limit of the channel capacity for fixed numbers of anassumed at the receiver. For the link considered in this tenna elements and system SNR. It is achieved when H is work, however, we must consider the near field effects of full rank with all singular values equal. This corresponds to the antenna dimensions on the channel transfer matrix. an artificial case where a perfectly decoupled channel is asThe propagation model is shown in Figure 2. As shown sumed for each transmitter-receiver antenna pair, and each in Figure 2, the element positions in the horizontal array of the transmitted signals is received by all of the receiver at transmitter are described by vector Rt with azimuthal antennas without any interference. A keyhole capacity is angle 8 1 and elevational angle $1. Similarly, the element the theoretical lower limit on the capacity, where H has positions in the horizontal and vertical arrays at the re- only one nonzero singular value [9]. ceiver are described by vectors R,1 and R r 2 , respectively. As shown in Figure 4 , the measured and theoretical caThe transmitter receiver separation is given by d. pacities in free-space match very well. The difference at Based on this model, the unnormalized channel transfer 30 dB of system SNR is only 0.25 bps/Hz. In the near coefficient, G(i,j ) , between the ith transmitter and the j t h field, the spacing of the receive elements allow them t o obreceiver antenna is given by: serve the curvature of the wave front from each transmit element in a non-linear fashion. Furthermore, this nonlinear phase progression is different for each transmit element. This causes the rows of the H matrix to become where L ( i , j ) is the distance between the ith transmitter independent. It can be shown that the capacity in (1) inand the j t h receiver antennas in wavelengths, $(i) and + ( j ) creases from the case when H is a dyad and all rows are are the initial phases at transmitter i and receiver j, re- dependent to where the rows become independent [9]. As spectively. The normalized channel transfer matrix H is a result, although the amplitude of each G ( i , j ) are virtuachieved by dividing G by the square root of the average ally equal, the phases vary from element to element. By power strength of G ( i , j )as follows increasing the transmitter-receiver separation, the effects of wavefront curvature decrease and the received waves ap(3) proach plane waves. When the separation i.i fiufficiently large, the rows of G(i,j ) shall become dependent (different only by a scalar coefficient) so that H becomes a dyad, and the capacity shall be close to that of a key-hole system. At The theoretical capacity is calculated by substituting 830 m (approximately 6750 wavelengths at 2.44 GHz), for example, the capacity approaches the capacity of a keyhole Htheory into (1). system.
C. Phase stability In the near field, the spatial separation of different channels is mainly due to the phase differences between different antennas. As a result, the experimental verification of the near field channel capacity is extremely sensitive to the phase stability of the measurement system. After careful calibration, the measured phases are very stable over the time of interests. Figure 3 shows an example of the phases of the signals transmitted from transmitter antenna one to each of the receiver antenna chain relative to receiver antenna 3, i.e. q51i - $13. This measurement was taken in a windy day, which resulted in slight variation in phase for antennas 5-7. In fact, the phase variations for antennas 5 and 6 are in the same direction, which are opposite from antenna 7. This is because the antenna 4 is fixed, therefore antenna 5 and 6 move in opposite direction from antenna 7 under windy conditions. The free-space calibration is performed in clear days with no wind.
111. MEASUREMENT RESULTS
OVER FIXED WIRELESS
LINKS
The measurements were performed in 16 locations in the suburban environments. The base station was set up on the top of Crawford Hill at antenna height of 35 m, and the remote heights were 10 m and 5 m. This section will present results of capacity CDF of all the measured locations, effects of remote antenna height, and effects of different array orientations (horizontal or vertical) on capacity. Cumulative distribution function (CDF) of the measured spectrum efficiency is presented in Figure 5 for 10 m and Figure 6 for 5 m remote antenna heights. CDFs of both measured results and theoretical results are shown. The keyhole matrix and Rayleigh iid distributed channel matrices are presented as references. These reference curves are calculated for both 4 x 5 and
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