MIMO Channel Capacity on a Measured Indoor Radio Channel at 5.8 GHz

Transcription

1 MIMO Channel Capacity on a Measured Indoor Radio Channel at 5.8 GHz Rickard Stridh and Bjorn Ottersten * Dept. of Signals, Sensors & Systems Royal Institute- of Technology SE Stockholm, Sweden {stridh,otterste}Qs3.kth. se Peter Karlsson t Electrical & Electronical Engineering University of Bristol, United Kingdom Peter. KarlssonQbristol. ac. uk Abstract Multiple transmitters and receivers can be used to provide high link capacity in future wireless systems. Herein, an analysis of indoor environment Multiple- Input-Multiple- Output measurements in the 5.8 GHz band is performed and the possible increase in capacity, utilizing multiple transmitters and receivers is examined. The investigation shows that in the measured indoor environment, the scattering is suficiently rich to provide substantial link capacity increases. Furthermore, the effect of intra-element element spacing on the channel capacity is studied, Finally the possible Hiper- LAN/2 MIMO channel capacity, based on the measurements, is examined. 1 Introduction Utilizing multiple transmitters and receivers to communicate over a Multiple-Input-Multiple-Output (MIMO) channel can provide substantial increases in channel capacity [7]. An important condition for the MIMO channel to support these increases is that the environment provides sufficient multi-path or rich scattering propagation resulting in a high rank channel. The introduction of Wireless Local Area Networks (WLAN) motivates the use of multiple antennas on both access point and terminal sides. The terminal in such a WLAN could be a laptop computer or a handheld computer, both giving opportunity to carry multiple antennas. ~ This work is supported by the Swedish Foundation for Strategic Research through the Personal Computing and Communication program and by Telia Research AB. talso with Telia Research AB, Sweden The purpose of this investigation is to examine the capacities of MIMO channels in a realistic office environment and see if the scattering is sufficiently rich to decorrelate the relationship between the transmitters and receivers. The capacity calculations are based on non-line-ofsight indoor measurements at 5.8 GHz from a typical office environment at Telia Research i Malmo, Sweden [1][5]. Similar results for the 1.9 GHz band, have recently been reported [3]. In [4] MIMO channel capacity for different physical narrowband channels (Line-ofsight and Non-line-of-sight) are investigated. This paper is comprised of three parts. First the information theoretical background is given followed by a description of the system and measurement setup. Then, the analysis of the measurement data is presented and compared to the results based on simulated channels. An example for a HiperLAN/2 channel concludes the results. 2 Data Model and Channel Capacity 2.1 Channel The channel is assumed to be Multiple-Input- Multiple-Output (MIMO), according to Figure 1. Denote the number of inputs (transmitters) by nt and the number of outputs (receivers) by nr. The MIMO narrow-band channel response may be modeled by a channel matrix H = [hl h2... h,,], where hi is the 7 2. ~ x 1 channel vector containing the gain and phase responses from transmit antenna i, i = 1...n~, to the receivers. The nr x 1 received complex baseband signal y(t) is modeled as y(t) = Hs(t) + n(t) (1), /00/$ IEEE 733

2 with respect to Q is discussed in 2.4. conditions the capacity is [2] Under UIPC Cg:L% = logz det(i,, + LHII*) bits/s/hz (3) nt where (*) denotes the complex conjugate transpose and p is the signal-to-noise-ratio defined in 2.1. Transmitter MIMO Channel Receiver figure 1. Multiple-Input-Multiple-Output channel and antenna arrays with nt = 3 and nr transmitters and receivers, respectively. 2.3 Frequency Selective Channels The classical information theoretical channel capacity is defined for a narrowband and thereby flat channel. For a frequency selective channel the total capacity may be obtained by integrating over the frequency band where s(t) is the transmitted signal and n(t) is additive white Gaussian noise with variance u2. The total transmitted power is P, which is divided over the transmitting elements. The signal-to-noise-ratio p, is the rec:eived power at each receiver branch, divided by the noise variance G:. We distinguish between two transmit power distribution cases: o Uniform Input Power Channel (UIPC) o Non-Uniform Input Power Channel (NIPC) where UIPC may be seen as a case where no channel information is present at the transmitter and uniform power distribution is the natural choice. NIPC allows non-uniform power distribution at the channel input. Thus knowledge about the spatial channel, at the transmitter may be used for NIPC. For all channels, there is a constraint on the maximum transmitted power. 2.2; Capacity 'The Shannon capacity is a measure of the maximum possible rate, that can be transported over a channel, wit8h arbitrarily low bit error probability. The channel capacity can be achieved, with perfect channel knowledge at the receiver and coding of infinite delay. 'The general expression for channel capacity on the nr x nt MIMO channel with additive white Gaussian noise is [6] 1 CMIMO = log, det(in, + -HQH*) bits/s/hz (2) 4 whsere Q = E[s(t)s*(t)]. The transmit power constraint is then stated Tr{Q} 5 P. Maximization of CMIMO 9 1 clog, det(1 +?HiQiH:)Af bits/s (4) i=l ffn where W is the overall bandwidth of the channel. H(f), Q(f) and Hi, Q, are the frequency response for the channel and power distribution for the continuous and discrete frequency case, respectively. The approximation is done converting the integral into a Riemann sum, in order to adopt the expression to the sampled system. This adds another channel option: 0 Non-Uniform Input Power Frequency Selective Channel (NIPF) For the NIPF channel, non-uniform power distribution may be used over both space and frequency i.e. the transmitter may exploit knowledge not only about the spatial channel but also the about channel variations in frequency. For the NIPF channel the power constraint rmay be stated E:==, Tr{Q,} = qp. 2.4 Waterfilling If the MIMO channel H is known at the transmitter, it is possible to use transmitter weights to adapt the transmitted signal to the chaninel and to transform the MIMO-channel into parallel Gaussian sub-channels with a common power constraint.. Assuming parallel Gaussian sub-channels, optimal power allocation over these sub-channels by waterfilling [6] will maximize 2. This corresponds to to the non-uniform input power channel (NIPC) case. Using the methods in [6] for diagonalizing a MIMO channel, we obtain the NIPC 734

3 capacity by maximizing n (5) with respect to e,, where 0, are the singular values of H and cy=, ~i 5 nt. Thus the E* will distribute the total transmitted power over the channel optimally over the spatial subchannels and classic coding may be used on the scalar channels. In the case of frequency selective channel, waterfilling may be performed jointly over both frequency and space components if the channel behavior is known to the transmitter. This corresponds to the non-uniform input power frequency selective channel (NIPF). 3 Channel Measurements The measurements were carried out by Telia Research in their offices, located at the Scandinavian Center in Malmo, Sweden. The general planning of the floor consists of office rooms, open spaces and corridors. Most spaces are separated by walls, while glass is used in some places. The transmitter was positioned in an office, while the receiver was in an open area. Several channel measurements were carried out in this scenario. The measured channels that were analyzed hereinm correspond to a typical non-line-of-sight situation and the distance from transmitter to receiver was m. The measurements were conducted at 5.8 GHz carrier frequency and the measurement bandwidth was 200 MHz. By sending a pseudo random noise sequence at the transmitter and correlating with the same synchronous sequence at the receiver, complex impulse responses were measured. The data was collected with a synthetic array antenna, using one receiver and one transmitter that were synchronized. Both antennas were of monopole type. Under stationary conditions, the transmit antenna is moved between seven different positions separated by 300 mm, i.e., about six wavelengths. Of these seven positions three are used herein. For each of the seven transmitter positions, the receive antenna is moved linearly between 21 different positions, using a step motor on a track, moving 13 mm (about i), between each position. This corresponds to spatial measurements over in total about five wavelengths. At each combination of transmit and receive positions 20 samples were taken. All measurements have been performed during stationary conditions. The measurement noise is assumed to be neglectable as the peak-to-noise dynamic range of the measured impulse responses exeeds 30 db. Further Figure 2. Capacity for different SNR, with 3 receivers and one, two, and three transmitters, respectively information about the measurement setup and environment may be found in [l]. In order to obtain narrowband channel measurements to use in the capacity expression (5), the wideband channel measurements are narrow-band filtered by applying the Discrete Fourier Transform (DFT) on the data. From each of the 20 broadband measurements, 60 narrow-band channels were taken in the band 5.8 f 0.1 GHz. This results in a total of 1200 narrowband channels, though possibly correlated. The measurements were made in order to find spatial channel characteristics for the HiperLAN/2 system, that is currently standardized to operate at the 5 GHz band. Thus it is of interest to investigate what capacity may be possible on a HiperLAN/2 RF channel of 20 MHz. The measurement data corresponds to 10 such channels. 4 Results The capacity for the measurement data is computed and compared to the capacity for simulations performed using channel matrix elements, that are zero-mean complex Gaussian, independently and identically distributed (IID). The simulated channel corresponds to a Rayleigh fading channel under the most favorable conditions that can be expected on average in an uncontrolled environment, i.e., totally uncorrelated matrix elements in the channel matrix. 735

4 ./... : IC' 1I 12 I3 I II IO 20 Figure 3. Cumulative distribution function of the capacity for different numbers of receivers. Three transmitters at an SNR of 20 db are used Narrowband channel capacity In order to investigate spatial characteristics of the MIMO channel, each channel matrix is normalized to give the gain IlHllg = ntnr where 11. 1; denotes the Etobenius norm- This normalization removes the influence of the variation in time and frequency but keeps the spatial characteristics, that is the interest herein. As with the measurement data, the simulated data is normalized IIH"D1l$ = ntnr to allow comparison with the capacity for the measured channel. The capacity for different- signal-to-noise-ratios, with three receivers and one, two, and three transmitters is shown in Figure.2. Note the substantial increase in capacity as the number of transmitters increases from one to three. As a reference the simulated curve for the IID channel is plotted as well, indicating low correlation among the elements in H under these clonditions. The following results are given for the an SNR fixed at 20 db. Increasing the number of receive and transmit antennas will also increase the capacity. This increase is indicated in Figure 3, which shows the cumulative distribution function for the capacity for different numbers of receivers. The capacity increase is initially large until the channel rank reaches its maximum, 3 (the number of receivers equals the number of transmitters nt = 3). As expected, the increase for nr -> nt follows a logarithmic curve, i.e., is due to an SNR, increase from noise averaging over the channels. Also note that the variations in capacity are much more limited when using more receive antennas due to diversity gain from more sub-channels. Figure 4. Cumulative distribution function of the channel capacity for different intra-element distances. The SNR is 20 db and three elements are used in the transmitter and receiver array, respectively. By picking out three of the receivers in the receive array it is possible to see how the intra-element distance influences the capacity. In Figure 4 the cumulative distribution function of the capacity is shown for different intra-element distances. Note th(at the capacity is close to the statistical limit alreday a.t an element distance of A = 2X. The capacities for UIPC and NIPC as functions of the-number of receivers are shown in Figure 5. For UIPC, the transmitter has channrel knowledge and thus, optimal power allocation is possible. The NIPC capacity is greater than the UIPC capacity, especially for the cases when nr 5 nt = 3 (channel rank is less than 3). Then the transmit power is directed into the subspace that is visible to the receiver, i.e., related to the nr non-zero singular values, and power waste is avoided. For the case of nr > nt the gain is smaller and thecapacity converges to the capacity of the UIPC as the transmit power is not recovered at the receiver. 4.2 HiperLAN/2 Channel Capacity Assuming that the 200 MHz; measurement bandwidth at 5.8 GHz corresponds to 10 HiperLAN/2 channels, the MIMO capacity has been calculated for one such channel. Herein the channel matrix normalization is performed over a complete 20 MHz channel to also allow variations in frequency i.e. IlL, llhlll$ = qntnr. As a comparison HiperLAN/2 is specified for a user data rate of 36 Mbits/s at signal-to-noise-ratio 20 db and the Shannon scalar channel capacity at signal-tcnoise-ratio 20 db is 20 Mbits/s x log2(l + 20dB) = 736

5 Figure 5. Comparison of the channel capwity for UIPC and NIPC. The measured channel is compared to the simulated IID channel. Three transmit elements are used and the SNR is 20 db. The receiver intra-element distance is 4 Figure 6. Cumulative distribution function of the capacity for at HiperLAN/Ztype 3 x 3 MIMO channel for different power options at SNR 2OdB. The receiver intra-element distance is $ 133 Mbits/s. In Figure 6 the capacity for a 3 x 3, 20 MHz MIMO channel is shown for the three channels assumed. Using the NIPF assumption, more than 80% of the channels reach a-capacity of 300 Mbits/s. It may seen that there is some gain when waterfilliig over the spatial channels, while when that is done, the further gain by waterfilling over the frequency band is small. 5 Conclusions Indoor MIMO channel measurements at 5.8 GHz have been analyzed in terms of channel capacity. Comparisons have been made to a simulated IID MIMO channel (under the same gain normalization) which corresponds to the most favorable situation in an uncontrolled environment. We conclude that for this experimental setup, the environment provides adequate multi-path propagation resulting in a high rank channel and a significant capacity increase compared with a low rank channel. For an intra-element distance at about 2X, the results are indistinguishable from the IID channel case. Applying the results on a HiperLAN/2 3 x 3 example RF channel more than 80% of the channels reach a capacity of more than 300 Mbits/s at 20 db SNR. References ceedings Nodkkt Radiosymposium 1999, pages NRS, Lund, Sweden, [2] G. J. Foschhi. Layererd space-time architecture for wireless communication in a fading environment when using multiple antennas. Bell Labomtories Technical J~~mal, 1(2):41-59, Aut [3] C. C. Martin, J. H. Winters, and N. R. Sollenberger. Multipleinput-multipleoutput (MIMO) radio channel measurements. In Proceedings IEEE Sensor Amy and Multichannel Sa& Processing Workshop, Boston, USA, March [4] D. McNamara, M. Beach, P. Karlsson, and P. Fletcher. Initial characterization of Multiple-Input Multiple Output (MIMO) channels for spacetime communication. In Proceedings IEEE Vehicular Technology Conference, Japan, Sept [5] R. Stridh and B. Ottersten. Spatial characterization of indoor radio channel measurements at 5 GHz. In Proceedings IEEE Sensor Amy and Multichannel Signal Processing Workshop, Boston, USA, March [SI I. E. Telatar. Capacity of multi-antenna gassian channels. Technical Memorandum, Bell Labomtories, October 1995 (Published in European Thansactiow on Telecommunications, Vol. 10, No. 6, pp , Nov/Dec 1999), [7] P. W. Wolniansky, G. Foschini, G. Golden, and R. A. Valenzuela. V-blast: an architecture for r&i very high data rates over the rich-scattering wireless channel. In Proceedings URSI International Symposium on Signals, Systems, and Electronics., pages , IEEE, New York, NY, USA, [l] C. Bergljung, P. Karhn, and.h. Borjesson. Spatial propagation Characteristics in the 5 GHz band. In Pro- 737