Multiple-antenna communication systems: An emerging technology

Transcription

1 Multiple-antenna communication systems: An emerging technology Systèmes de communications multi-antennes: une technologie émergeante Paul Goud Jr., Christian Schlegel, Witold A. Krzymien, and Robert Hang Λ A recent development in wireless communications is the application of multiple-input multiple-output (MIMO) systems to radio communications via use of multiple antennas. In order to investigate the technology s potential, an experimental MIMO system containing two four-element antenna arrays (4 4) has been developedat the University of Alberta. The system is used to obtain MIMO channel measurements in a typical indoor office environment in the ISM band (92 928MHz). Measurement campaigns have been performed using different antenna spacings and two different types of antenna: half-wavelength ( =2) centre-fed dipoles and dual-polarized patches. The measurements are used to calculate channel capacities for an indoor 4 4 MIMO system. The measurements confirm the high capacity potential of a MIMO channel, with ergodic capacity of approximately2 bits per channel use available with either antenna type at a signal-to-noise ratio of 2 db if the antenna element separation is =2 or larger. An introduction to basic MIMO theory, a discussion of the University of Alberta wireless MIMO testbed, and observations regarding the measured indoor MIMO channel are presented in the paper. Un développement récent dans les communications sans fil est l application des systèmes multi-antennes à l émission et à la réception (MIMO ou multiple-input multiple output) dans les communications radio. Afin d évaluer le potentiel de cette technologie, un système expérimental MIMO, doté de deux ensembles de quatre antennes (4 4), a été développéà l Université de l Alberta (University of Alberta). Le système est utilisé pour obtenir des mesures du canal MIMO, dans un environnement intérieur typique, dans la bande de fréquences ISM (92 928MHz). Des séries de mesures ont été prises avec différents espacements entre les antennes et deux types d antennes différentes: dipôles de demi longueur d onde ( =2) alimentés au centre et antennes patch en polarisation double. Ces mesures ont été utilisées pour calculer la capacité d un système MIMO 4 4 dans un environnementintérieur. Les mesures confirment le potentiel de capacité élevée d un canal MIMO. Une capacité ergodique disponible d approximativement 2 bits par utilisation du canal est obtenue avec les deux types d antennes mentionnées et un rapport signal à bruit de 2 db, pourvu que l espacement entre les antennes soit d au moins =2. Une introduction aux bases de la théorie MIMO, une discussion du banc de test MIMO de l Universitédel Alberta et des observations sur le canal intérieur MIMO mesuré sont présentées dans cet article. I. Introduction Multiple-input multiple-output (MIMO) wireless systems, which use arrays of antennas instead of single transmit and receive antennas, hold the promise of providing data rates far exceeding those of conventional wireless systems []. Such MIMO systems operate by transmitting multiple signals in the same frequency band and at the same time over multiple transmit antennas. At the receiver, multiple antennas are also used, and the received correlated signals are processed to separate the different transmitted data streams. MIMO communications is made possible by the extension of receiver processing to include spatial dimensionality as well as time (spatio-temporal processing). Multiple propagation paths, as occur in a scattering propagation environment, become distinguishable at the MIMO receiver due to small differences in arrival times and can be used to carry additional information across the channel [2]. Although the idea of using multiple antennas is not new it finds application in such techniques as diversity combining and beamforming only MIMO systems approach the information-carrying-capacity potential of such channels. It is likely that future applications of MIMO technology will include both fixed and mobile uses for indoor as well as outdoor environments. An example of a potential mobile application for MIMO communica- Λ Paul Goud Jr., Christian Schlegel, Witold A. Krzymien, and Robert Hang are with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta T6G 2V4. Witold A. Krzymien is also with TRLabs, Edmonton, Alberta. pgoud@ee.ualberta.ca tions has recently been studied in [3], which describes an investigation on using the technology for high-speed (around Mb/s) communication with subway trains. A MIMO system for residential fixed wireless access has been developed by Iospan Wireless (now part of L-3 Communications Inc.) [4]. Another company, Antenova Ltd, is examining the use of MIMO for laptops and handheld consumer devices [5]. A MIMO chipset has already been developed by Airgo Networks, a startup company in Silicon Valley [6]. A MIMO system with N t transmit antennas and N r receive antennas utilizes a channel with N tn r separate paths, and the gains for these paths are described using an N t N r matrix H. The information theoretic capacity, i.e., the maximum throughput of a MIMO channel, is dependent upon the characteristics of its transmission matrix H, in particular its singular values. As shown in Section II, these depend on the propagation environment, which ultimately determines the capacity of MIMO channels. In general, a rich scattering environment, as occurs in indoor wireless communications, tends to produce channels with high capacity. Since wireless channels are inherently complex and difficult to characterize, obtaining channel measurements is the only accurate and reliable method of determining the yet not fully understood capacity potential of such MIMO systems. In order to measure the capacity of MIMO systems in typical propagation environments, a flexible and mobile MIMO testbed containing up to 4 4 arrays has been developed in the icore High Capacity Digital Communications (HCDC) laboratory at the University of Alberta in Edmonton, Alberta. In this paper, we present results of several MIMO channel measurement campaigns for non-line-of-sight channels in an indoor office en- Can. J. Elect. Comput. Eng., Vol. 29, No. /2, January/April 24

2 2 CAN. J. ELECT. COMPUT. ENG., VOL. 29, NO. /2, JANUARY/APRIL 24 vironment, using two different types of antennas: standard =2 dipole and specially designed dual-polarized patch antennas [7]. The singular values of the measured channel gain matrices are calculated and analyzed along with the MIMO channel capacities. In Section II of this paper we discuss the capacity formulas for MIMO channels and explain the impact of system and propagation environmental parameters. We then discuss implementation issues along with the need to perform MIMO channel measurements in Section III. Layering processing is described in Section IV. Section V gives a description of our testbed and our system validation tests. The MIMO testbeds that exist at other universities are analyzed in Section VI and compared to our design. In Section VII, we show how our campaigns were conducted and present the results for them. Finally, Section VIII gives conclusions and outlines planned future research. Baseband Signals Parallel RF Stages Parallel RF Stages Figure : Basic communication system for MIMO channels. Received Baseband Signals II. The multi-antenna MIMO channel A. Channel model and capacity A MIMO transmission system uses N t transmit and N r receive antennas. Each antenna i transmits symbols from a complex symbol alphabet, each with energy E si per signalling interval, such that P i Esi = E s is constant for each use of the channel. These transmit symbols are modulated by a suitable pulse waveform, up-converted to the desired transmission band, and sent over the N t transmit antennas. The signals from the receive antennas are mixed down to baseband, sampled, and fed into the receiver. A basic block-level diagram of a MIMO system is shown in Fig.. The wireless transmission channel is a linear channel, and, assuming that timing recovery has been accomplished, the received sampled signal y jl for the j-th receive antenna at time l is given by y jl = XNt i= p Esih ijc il + jl; () where jl is a sample of circularly symmetrical complex Gaussian noise with variance N, c il is the sampled transmitted signal, and h ij is the normalized complex path gain from transmit antenna j to receive antenna i. It contains all linear effects on the signal, such as propagation power loss and phase shifts, fading due to multipath, crosstalk, antenna coupling, and polarization. We have furthermore assumed that the symbol rate is low enough such that frequency selectivity caused by time-of-arrival differences between the various multipath replicas of the received signal is not an issue that manifests itself noticeably. This implies symbol rates of about MBd or less for indoor transmission, and about 5 kbd or less for outdoor situations [8]. The entire MIMO channel can now be succinctly characterized by the linear algebraic relationship y = HAc + n; A = p Es pes2... pesnt ; (2) where H is an N t N r rectangular matrix of channel gains h ij, and c is a vector of N t transmitted symbols c il. The information theoretic capacity of the discrete channel in (2) can be calculated from basic information theoretic concepts [9] as C I = log 2 det I + + ρnt HEH [bits/channel use]; (3) Figure 2: Optimal signal processing if the channel is known at the transmitter. where ρ = E s=n is the signal-to-noise ratio per symbol, 2 3 E s E = E s2 E s EsNt 7 5 ; (4) and H + is the conjugate transpose of H. Since the channel parameters are time-varying, C I is interpreted as the instantaneous channel capacity for a given channel realization H. For a time-varying channel this capacity has to be averaged over all realizations of the MIMO channel matrix H to calculate the ergodic channel capacity C = EH(C I ). Telatar [] has presented closed-form solutions for C in the case where the h ij are independent complex Gaussian fading channel gains. The channel matrix H can be decomposed via the singular value decomposition (SVD) method [] into the product H = UDV + ; (5) where U and V are unitary matrices, i.e., UU + = I, and VV + = I. The matrix D contains the singular values fd ng of H on its diagonal; these values are the positive square roots of the non-zero eigenvalues of HH + or H + H. Note that D may not be a square matrix, which simply means that the number of non-zero singular values can be no larger than the minimum size of the matrix, and is in fact equal to its rank. The SVD allows us to write the channel equation in an equivalent form as y = UDV + Ac + n; U + y = ~y = D~c + ~n; (6) where ~c = V + Ac. This result leads to parallel Gaussian channels ~y n = d n~x n +~n n,asshown in Fig. 2. The capacity of the MIMO channel is now determined by the well-

3 GOUD JR. / SCHLEGEL / KRZYMIEN / HANG: MULTIPLE-ANTENNA COMMUNICATION SYSTEMS 3 known waterfilling theorem [2] as C I = NX n= log 2 + d2 ne n = N NX n= log 2 d 2 n μ N ; (7) where E n is the energy per symbol allocated to channel n, and N = min(n r;n t) is the rank of H. This capacity is achieved with the waterfilling power allocation: E n = μ N N d 2 ; n d 2 <μ; (8) n N E n =; μ; (9) d 2 n where μ is the waterfilling level such that P E n = E s.ifthe channel is known at the transmitter, the signal strategy shown in Fig. 2, which is based on the SVD, achieves capacity by transforming the channel into a set of parallel channels. However, channel knowledge is not typically available at the transmitter, and the only choice we have is to distribute the energy uniformly over all component channels. This leads to the symmetric capacity C sym = NX n= log 2 + d2 ne s Y N =log N 2 + d2 ne s : () tn N n= tn Introducing (M), the Q spectrum (set Q of eigenvalues) of M, and using the facts det(m) = (M) and ( + (M)) = det(i + M), we obtain the equivalent formulations: Y N C sym = log 2 + d2 ne s () N n= tn = log 2 det I + Nr + ρnt HH (2) = log 2 det I N r + ρ H + H : (3) N t Fundamentally, the capacity of a MIMO channel is governed by the singular values of H which determine the channel gains of the independent equivalent parallel channels. B. Capacity potential and limitations of MIMO channels If the channel paths h ij are uncorrelated, most channel realizations are of high rank with the eigenvalues of HH + distributed according to a Wishart distribution []. The case of equal singular values represents a limiting case where the rows h j of H are orthogonal and h j h i = ffi ijn r, implying d 2 n = N r, and the capacity is given by C high = NX n= log 2 + d2 nρ = N log N 2 + Nrρ : (4) t N t This capacity increases linearly with the minimum of the number of elements in either of the two antenna arrays. On the other hand, if the component channels are completely correlated, as occurs in scatterfree long-distance wireless connections (e.g., in a satellite-ground radio link), all rows h j of H, the array response vectors, are approximately equal, and H has only one non-zero singular value, d 2 = N tn r.asaresult C low ß log 2 ( + ρn r) : (5) In this case the channel capacity grows only logarithmically with the number of (receive) antennas. Real-world situations will lie somewhere between these two extremes, with the capacity determined by the complex propagation environment in which the system has to function. This leads to the necessity to carefully analyze and measure such Normalized Power (db) Distance (m) Figure 3: Sample received power profile for an indoor office environment. candidate environments to obtain precise values. In fact, for scatterfree propagation the array response vectors become correlated very rapidly (see also [3]) and the channel matrix H loses rank, turning the MIMO channel into nothing more than a fancy conventional wireless link. Furthermore, the capacity potential of a MIMO channel requires relatively high-power transmitters, as can be shown in the following way: if the signal-to-noise ratio ρ is low, a Taylor series approximation of log( + x) ß x for small x lets us develop both (4) and (5) as C high ß N Nrρ ; C low ß N rρ; (6) N t both of which now grow linearly with the array sizes. This result also indicates that for N t» N r, which implies N = N t, correlation in the channel has no effect on capacity for low SNR values. The sole effect of an increased number of antennas is that of gathering more received power. Communications is fundamentally power-limited, and the additional dimensionality offered by a high-rank MIMO channel cannot be exploited. From the physical model it is evident that the geometry of the propagation environment plays a significant role. The transmission strategy for both low-rank MIMO channels as well as low-snr MIMO channels is identical and straightforward. Concentrate all transmit power on a single antenna and use maximum-ratio combining of the N r receive antennas to feed a single receiver. Of course, the transmit antenna array can be used to shape the transmitted beam to direct power to the desired receiver. These are the well-known traditional beamforming techniques. III. MIMO channels in the real world In order to better understand MIMO channels in real-world environments, accurate MIMO channel measurements are needed. One issue with wireless channels is the large power variations that occur in the received signals due to multipath fading if one or both of the terminals are mobile. Fig. 3 is a plot of the received signal power obtained from measurements with the HCDC MIMO testbed for a single transmitreceive antenna pair in an indoor office environment without automatic gain control. It illustrates the rich multipath environment, which results in power fluctuations. Clearly visible are the signal fades approximately every wavelength, i.e., every 3 cm. If a receiver moves through this signal field, the spatial fading pattern turns into timevarying signal fading. As can be appreciated, channel tracking under

4 4 CAN. J. ELECT. COMPUT. ENG., VOL. 29, NO. /2, JANUARY/APRIL Channel Capacity (bits/channel use) Mean capacity: 2.3 bits/use Capacity standard deviation: 2.6 bits/use Distance (m) Figure 4: Sample 4 4 MIMO channelcapacity profile for an indoor office environment; ρ =2dB. such conditions is a major challenge for MIMO systems, where there are N r N t such channels which vary largely independently. Channel tracking, however, is essential for MIMO communications since the complex channel gain information is needed to separate the coexisting signals. In the absence of channel tracking, orthogonal spacetime codes [4] or differential space-time modulation [5] have to be used, both of which severely limit the achievable maximal data rates. Fortunately, and at first glance perhaps paradoxically, despite the power fluctuations that occur in the received signals, the MIMO channel capacity itself is very stable. This is due to the fact that the large number of component channel gains tend to average out, presenting an average MIMO channel to the receiver at all times. In other words, it is very unlikely that all of the channel paths will be in a deep fade at the same time, provided that antenna spacing is sufficient. The capacity of the 4 4 MIMO channel, one of whose components is the fluctuating signal in Fig. 3, is shown in Fig. 4. Astonishingly, the channel capacity fluctuates with a standard deviation of only about % of the average. Capacity bits/dimension Capacity bits/dimension Orthogonal Optimal MMSE Eb/N [db] (a). Orthogonal Optimal MMSE Eb/N [db] (b) IV. Layered processing Figure 5: Achievable capacities with linear MMSE layering of an ideal MIMO channel: (a) N t=n r =2; (b) N t=n r ==2. Apart from the fundamental problem of acquiring precise timing for the symbols, which we shall not discuss in this paper, MIMO receivers face the task of demodulating potentially very large signal sets. As an example, consider a 6 6 MIMO system with 8PSK modulation employed on each transmit antenna. Each space-time symbol will therefore consist of 3 6 = 48 bits, which corresponds to 2 48 ß 3 4 signal points. When such large symbol sets are handled, maximum-likelihood demodulation becomes infeasible, and advanced receiver processing techniques, such as signal layering, pioneered by Foschini [6] [7], are required. Layering involves separating the received space-time symbols into independent data streams corresponding to the different transmitted signals. This is done by a combination of nulling (zero-forcing) of interfering signals and successive cancellation of previously decoded signals. Foschini [6] shows that this method can achieve the capacity of the MIMO channel in the limit of large signal-to-noise ratios. This is not particularly surprising, since it is well established that successive interference cancellation can achieve the capacity of a multiple access channel [9], [8]; in this case, a MIMO channel. One of the difficulties is that successive interference cancellation is very complex and entails long delays. Alower-complexity alternative to (space-time) successive interference cancellation is simply to filter the received space-time symbol by an appropriate linear layering filter, such as a decorrelator or minimum mean-square error (MMSE) filter [9]. Both of these filters can achieve suppression of the interference caused by the channel gain correlation at the cost of enhancing the system noise. The performance of the MMSE filter is superior to that of the decorrelator for all values of the signal-to-noise ratio, and the two are equal as the SNR!. Tse and Hanly [2] have calculated the residual noise of the MMSE filter for random channels, such as an ideal MIMO channel; the capacities of the different layers can be calculated from their results. Fig. 5 shows the capacities of MMSE-layered MIMO systems for two different values of N r=n t. The figure shows the achievable capacity normalized per dimension as a function of the available bit energy to noise power spectral density ratio, E b=n. The figure shows two cases: (a) N t=n r =2, i.e., there are twice as many transmit antennas used as receive antennas, and (b) N t=n r ==2, i.e., there are more receive antennas than transmit antennas. Several observations can readily be made. If the system is underloaded, i.e., there are more receive antennas than transmit antennas

5 GOUD JR. / SCHLEGEL / KRZYMIEN / HANG: MULTIPLE-ANTENNA COMMUNICATION SYSTEMS 5 AWGN Capacity Capacity bits/dimension MMSE Capacity n= n=5 n=2 n= n= Matched Filters Figure 7: One station of the mobile MIMO testbed E b/n Figure 6: Achievable spectral efficiencies using iterative linear layering filters. (this situation can arise when a channel rank is significantly smaller than the size of the antenna arrays), then linear layering is very efficient in that the obtained capacities per transmit dimension are virtually identical to that obtainable with an ideal optimal receiver (shown as the solid optimal curve in the figure). On the other hand, if more transmit antennas are used, then linear layering may not be efficient, especially for large values of the SNR. Note that the results in Fig. 5 are general in the sense that they apply to all MIMO systems as long as N t;n r are large. Note that in the range of about E b=n = 2 to 6 db, simple iterative filters with two stages outperform matched filtering and virtually achieve the capacity of the more complex and nearly ideal MMSE filter. Furthermore, these values of E b=n are quite reasonable, since the total symbol energy to noise power spectral density ratio E s=n = RE b=n, where R is the rate of the MIMO system, which typically is very large. For example, with 2 antennas, 8PSK, and rate 2=3 error control codes on each data stream, R = 4bits. Therefore E s=n = 8 to 22 db, values which require high-power transmitters. Even for larger values of E b=n, two, five or at most stages in an iterative filter approximation achieve most of the available information theoretic capacity. These values are independent of the size of the system, which could be hundreds of antennas, and therefore a multiple-stage filter is significantly less complex than an MMSE matrix inverter. The resulting layered channel can now be operated just like a conventional single-input, single-output channel, for which powerful turbo coding techniques approach capacity almost arbitrarily closely [24]. The MMSE linear layering filter requires the inverse of an N r N r filter, which itself may be rather complex for large systems and high target data rates. Specifically, the receiver needs to compute [8] M l;mmse = HH + + N I : (7) Low-complexity alternatives can be found by appealing to stationary iterative methods for solving linear algebraic equations; these are computationally efficient methods to compute or approximate matrix inverses [2] [22]. Given a linear algebraic equation the stationary iterative solution x = M u; (8) x n+ = x n fi (Mx n u) (9) converges to the correct solution with an exponentially vanishing error as long as M is invertible. Applying it to our system in [22], we can show that x (n+) = + Nt N r H+ y + Nt N r HH+ +(N )I C A x (n) (2) has the fastest convergence. The iterations are started with the arbitrary initial vector x () = H + y. Using random matrix theory, per-dimension capacities can be calculated [23] and are shown in Fig. 6 for various iterations of the optimal stationary iterative filter. The solid lines for n =and n = indicate the capacities of the matched filter receiver (no iterations) and of the full-blown MMSE filter, respectively. The load N t=n r =:5. V. Testbed description The mobile MIMO measurement system developed at the University of Alberta consists of independent transmitter and receiver stations. Each station is comprised of a field-programmable gate array (FPGA) development board for baseband processing, a custom RF module (for up- or down-conversion and power amplification) and a custom antenna array structure. A PC is used to process captured data from the receiver FPGA board. A photograph of one mobile station of our testbed (excluding the laptop computer and USB cable) is shown in Fig. 7. A. Signal processing aspects All signal processing functions are implemented on GVA-29 FPGA development boards manufactured by GV and Associates Inc. Each GVA-29 board contains four Analog Devices AD9762 digital-toanalogue converters (DACs), four Analog Devices AD9432 analogueto-digital converters (ADCs), two Xilinx Virtex-E FPGAs and a Xilinx Spartan-II FPGA. Four-channel RF modules were custom-built for this project by SignalCraft Technologies Inc. Each transmit module receives the spread signals at an IF of 2:5 MHz and up-converts them to the ISM band ( MHz). The signals can be amplified to a maximum output power of 2 dbm per channel. The receive module mirrors the functions of the transmit module. The four signals received from the antennas are amplified and down-converted from the ISM band to 2:5 MHz. On both sets of RF modules, only one local oscillator is used at each frequency stage to generate the carriers that mix with the four input signals. This ensures that no phase shifts are introduced between the four channels by the modules, and that the different received signals are not rotated with respect to each other.

6 6 CAN. J. ELECT. COMPUT. ENG., VOL. 29, NO. /2, JANUARY/APRIL 24 The patch antenna array has the potential advantage of employing two orthogonal polarizations, while the dipole antenna array uses only a single polarization. This means that in a 4 4 MIMO system with patch antennas, ideally each transmitted signal is affected by only one significant interfering signal. It is then natural to conclude that reduced interference would lead to a higher MIMO channel capacity. However, the scattering that will occur in a multipath radio environment results in rapid loss of polarization separation. Figure 8: Block diagram of the transmitter signal processing chain (single channel). Figure 9: Block diagram of the receiver signal processing chain. Filter An FPGA image has been developed for the transmitter which generates and simultaneously transmits four filtered 5 kchips/s spread spectrum signals (see Fig. 8). The spreading sequences used are orthogonal Walsh codes of length 32 multiplied by a pseudorandom m-sequence [25] to ensure good correlation properties. The chip pulse has a truncated square-root raised-cosine shape with a cut-off frequency of 5 khz and a roll-off factor of :3. The four filtered signals are up-converted digitally to an IF of 2:5 MHz before being sent to the DACs. At the receiver (see Fig. 9) all of the signal processing is performed on the FPGA development board. The four parallel down-converted signals are received at an IF of 2:5 MHz from the RF receive module. The signals are sampled simultaneously by the ADCs at 5 million samples per second (Msps) and passed into an FPGA. In the FPGA, the signals are digitally down-converted to baseband and then decimated to Msps (2 samples/chip). Subsequently, they are convolved through a square-root raised-cosine matched filter with the same characteristics as the modulation pulse-shaping filter. A proprietary parallel synchronization algorithm [26] is used to synchronize the receiver. Each received signal is correlated with stored copies of the four pseudonoise (PN) spread signals that were used in the transmitter. The correlation operation generates four gain values at each receive antenna. The four sets of gain values are arranged into a complex 4 4 correlation matrix for each sample instant. The individual matrix elements are squared, and subsequently all 6 values are added together. B. Electromagnetic aspects Two types of antenna arrays are used with our testbed. One array type is comprised of four half-wavelength ( =2) centre-fed dipoles, and the other consists of two dual-polarized patch antennas [7]. The centre-fed dipoles are created by mounting =4-length monopole antennas onto conductive sheets. For both array cases, the antennas were placed in a row so as to make a broadside array. Each patch antenna contains two co-located elements with orthogonal polarizations. Both antenna types have potential advantages and disadvantages with respect to increasing the capacity of the MIMO channel. Performing identical measurement campaigns with both array types allows us to determine which antenna type yields higher channel capacity. The dipole antenna has the potential advantage of having a uniform 36 ffi radiation pattern in the plane perpendicular to itself, whereas the patch antenna has a radiation pattern that is nearly uniform over less than 8 ffi in the two perpendicular radiation planes. The dipole antenna s wider radiation pattern leads one to expect it to provide a higher capacity, since it creates a richer multipath environment. The transmitted signals from the dipole antenna array radiate in all directions, resulting in reflections and scattering off more objects. Also, the receiver antennas detect incoming waves from all directions instead of only from a hemisphere. A consideration concerning the link budget is the efficiency of the antenna: what fraction of the electrical energy entering the antenna connector actually radiates from the antenna as electromagnetic energy. Energy is lost due to antenna dielectrics and protective covers. A rough measurement of the efficiency of an antenna can be obtained using an unobstructed line-of-sight (LOS) channel. For such a channel, the theoretical received power can be calculated using the transmission formula [27]. A comparison of the measured received power with the theoretical received power (assuming perfectly efficient antennas) will determine the antenna efficiencies. Efficiency measurements were performed for both the dipole and patch antennas. Our testbed was set up with one transmitter antenna and one receiver antenna. The transmitter and receiver stations were placed a few metres apart. An efficiency of 74% for the dipole antenna and 8% for the patch antenna was measured and calculated. Thus, the dipole antenna has a clear advantage over the patch antenna if the link power budget is an issue. In order to verify that the polarization separation of our patch antenna arrays is good, experiments were conducted to measure the cross-polarization discrimination. The experiment measures the amount of power emitted in one polarity that is received by the antennas in the cross-polarity. The experiment is performed by placing the two antennas of the receiver station very close (6 to 65 cm separation) to the antennas of the transmitter array. This separation is large enough to avoid near-field electromagnetic effects but small enough to create a strong line-of-sight path with few multipath effects. Using this testbed setup, each of the four transmitter signals is radiated separately from its corresponding antenna while the power at all four received antennas is measured. Table shows the measured relative power of the received signals with cross-polarization. As can be observed in the table, the powers of the received cross-polarized signals are :9 db to 7: db below the power of their corresponding received co-polarized signal. Although our measured cross-polarization discrimination values are not as large as when the antennas are used in an ideal transmission environment [7], they are still large enough to ensure that cross-coupling will have a minimal effect on our channel gain measurements. In order to assess the error in the channel gain measurements obtained with our system, measurements were made for an uncoupled line-of-sight MIMO channel [28]. This LOS channel was created by removing the antenna arrays and connecting the four RF outputs from the transmitter to the four RF inputs of the receiver with cables. For this uncoupled LOS channel, the diagonal elements (h ii, i =;::: ;4) of the channel gain matrix correspond to the connected paths and should have the same magnitude. All the off-diagonal values (h ij;i 6= j) represent the non-existent cross paths and should be zero. The deviation in the measured values from this expected result represents the system error.

7 GOUD JR. / SCHLEGEL / KRZYMIEN / HANG: MULTIPLE-ANTENNA COMMUNICATION SYSTEMS 7 The averaged normalized results from 8 measurements are shown in Table 2 and demonstrate that the error introduced by the system is low. Measured gains of all connected paths are less than :5 db of each other. The power measured in each of the non-existent cross channels is at least 27 db below the power measured for connected paths. VI. MIMO testbeds at other laboratories Many universities and corporations around the world have developed testbeds in their labs and are conducting research in this area. An examination of the testbed designs and experimental activities of other teams adds perspective and truly shows why MIMO is an emerging technology. Of the many testbeds in existence, three are discussed below and compared to the University of Alberta MIMO testbed. These testbeds exist at Brigham Young University (Provo, Utah), at Virginia Polytechnic Institute and State University (Blacksburg, Virginia), and at the Canadian Communications Research Centre (Ottawa, Ontario). All three of the research teams have thus far used their testbeds for obtaining channel measurements. The MIMO testbed at Brigham Young University [29] is a flexible system that can be expanded up to a 6 6 architecture. It operates in the range :8 GHz to 6 GHz, and the transmitter can amplify each BPSK signal up to :5 W. At the receiver, blocks of sampled data are captured and stored in a PC for off-line processing. Channel estimates are obtained using a correlation and averaging technique. The Virginia Tech Space-Time Advanced Radio (VT-STAR) testbed [28] is a 2 2 MIMO testbed that operates at 25 MHz on a bandwidth of 75 khz. The VT-STAR transmitter can radiate up to 28 dbm from each antenna. In contrast to the FPGA boards used in the University of Alberta testbed, VT-STAR uses digital signal processing boards for implementation of its baseband algorithms. In addition, a different receiver algorithm employing a linear processing rule is used for estimating the MIMO channel parameters. The Radio Communications Technologies team at the Communications Research Centre has developed a flexible PC-based MIMO testbed [3] similar to that at Brigham Young University. The testbed can be scaled up to an 8 8 architecture. It requires a 25 MHz radio bandwidth and can be set to operate at any frequency in the range 2 MHz to 2:4 GHz. The transmitter can radiate up to 25 dbm from each antenna. MIMO channel estimates are derived at the receiver in a fashion similar to what is done on the University of Alberta testbed. A pseudonoise sequence spread signal is radiated from each transmit antenna, and correlations of the received signals with PN sequencecopies stored at the receiver are performed. VII. Measured capacity results A. Details of measurement campaigns The fifth floor of the Electrical and Computer Engineering Research Facility (ECERF) building on the University of Alberta campus was selected as the location for the indoor channel measurement campaigns. The ECERF building employs steel, concrete and drywall construction, which is typical of many modern office buildings. Four campaigns were performed in total. Three of the campaigns used antenna arrays of dipole antennas, and one used dual-polarized patch antennas. In all cases, the antennas at each station were placed so as to create a broadside array. For the three dipole antenna campaigns, the four antennas were spaced at distances of =8, =4 and =2 at both stations. For the patch antenna campaign, the two microstrip patch elements were spaced =2 apart. Once we had obtained channel gain data in our measurement cam- Table Measured cross-polarized power in the patch antenna arrays (relative to the main co-polarized path) Radiating transmitter antenna Relative power Cross path (db) Relative power Cross path 2 (db) 2:9 2:3 2 7: :9 3 7: 4:7 4 6:9 2: Table 2 Average squared path gain values foranuncoupled LOS channel Channel path Power (db) Channel path Power (db) h :33 h 3 3:3 h 2 34:23 h 32 32:32 h 3 37:73 h 33 : h 4 32:62 h 34 34:33 h 2 29:4 h 4 3:7 h 22 :6 h 42 3:84 h 23 3:22 h 43 27:63 h 24 37:47 h 44 :26 paigns, the matrices of measured gains were normalized according to H = G s N rn t jjgjj 2 ; (2) where jjgjj 2 is the squared Frobenius norm of G, i.e., the sum of the squared magnitudes of the elements of G. Consequently, the Frobenius norm of H, normalized according to (2), becomes equal to p N rn t. The purpose of normalizing the gain matrices is to eliminate the effect of propagation power loss on the calculated capacity. The MIMO channel capacities were calculated from H using (3) with ρ set to 2 db. For comparison, idealized 4 4 MIMO channel matrices of uncorrelated gains were also generated by a computer. Each element of each computer-generated matrix is created using an independent complex Gaussian random number generator with zero mean and unit variance per dimension. The capacities of the computer-generated channels were calculated using (3) after being normalized. Channel gain matrices generated in this fashion have been used in several MIMO capacity studies [3]. B. Channel measurements and comparisons Fig. shows the complementary cumulative distribution function (CCDF) curves for the three dipole antenna campaigns along with the simulated Gaussian case [32]. Two observations can be made by comparing the curves. First, the mean capacity of the simulated Gaussian channel is about 2 bits/channel use higher than the highest mean capacity of the dipole configuration. This difference may be due to a small specular component present in the MIMO channel. Nevertheless, the measurements clearly demonstrate high available capacity. The second observation is that the capacity drops as the antennas are placed closer together, which is not surprising since greater correlation will occur between the received signals. Fig. shows the CCDF curves for the =2-spaced dipole and =2- spaced patch antenna cases [33]. A slightly higher capacity can be observed for the patch antenna array case. The CCDF curve for the =2-spaced dipole array in Fig. is slightly different from the curve

8 8 CAN. J. ELECT. COMPUT. ENG., VOL. 29, NO. /2, JANUARY/APRIL 24 /8 Spaced Dipole Array /4 Spaced Dipole Array /2 Spaced Dipole Array Simulated Gaussian /2 Spaced Dipole Array /2 Spaced Patch Array Simulated Gaussian Probability Capacity > Abscissa Probability Capacity > Abscissa Channel Capacity (bits/use) Channel Capacity (bits/use) Figure : CCDF of the measured channel capacity; ρ =2dB. Figure : CCDF of the measured channel capacity; ρ =2dB. for the =2-spaced dipole array in Fig.. This is due to the fact that different locations were used for the transmitter antenna array. Another meaningful comparison is that of the singular values (SVs) of the channel gain matrices for the four different measurement campaigns. MIMO channels which exhibit higher channel capacity have singular values which are approximately equal, while channels with lower capacity have fewer dominant singular values. Fig. 2 shows the histogram of the measured SVs for the dipole antenna array campaign when =2 element spacing is used. The solid curve shows the theoretical Wishart distribution [] for an independent Gaussian channel with twice as many receive as transmit antennas (i.e., with a number of significant SVs which is half the size of the array). Hence, the curve represents the distribution of SVs for a purely diffuse 2 4 MIMO channel. Its good match with the first cluster of the histogram suggests that there is approximately a rank-two contribution from diffuse propagation components. The second cluster of SVs with large values around 3 to 3:5 likely results from specular propagation paths. VIII. Conclusion and future outlook There are several intriguing extensions to the work that we have presented here. One is to obtain channel measurements for a much larger system (e.g., N t = N r =6)todetermine whether the same throughput potential relative to the upper-limit case exists, i.e., whether there is enough scattering in the channel for large capacity gains. This question is undoubtedly dependent on the particular transmission environment (indoor, outdoor, indoor-outdoor, etc.), and measurements are currently underway. Finally, it will be valuable to expand our system to transmit data and establish how much of the MIMO channel capacity is achievable by different communication system structures. We are currently pursuing these research avenues. Acknowledgements The authors gratefully acknowledge the funding for this work provided by the Alberta Informatics Circle of Research Excellence (icore), TRLabs, the Natural Sciences and Engineering Research Council (NSERC), the Canadian Foundation for Innovation (CFI) and the National Sciences Foundation (NSF) of the United States. As calculated from the data presented in Fig., the mean MIMO channel capacities for the two =2-separation cases are 2:3 bits/channel use (patch antenna case) and 2: bits/channel use (dipole antenna case). It is worthwhile to compare these values to those derived from the limiting-case equations (4) and (5). For ρ =2dB and N t = N r = 4,wecan calculate C high = 26:6 bits/channel use and C low = 8:6 bits/channel use. Thus, the mean capacities for our typical indoor office environment reach approximately 8%ofthe ideal upper-limit case. A better appreciation of the potential data-rate increase can be obtained with a different explanation of the upper-limiting-case equation (4). The capacity potential that is defined by this equation equals the capacity of N t separate orthogonal channels, e.g., different frequency bands. Thus, with a 4 4 system using a MHz frequency band, we obtain 8% of the capacity of single-antenna links using four MHz bands. 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