Capacity Optimization and Modelling of frequency selective WLAN indoor MIMO Channels based on measured data

Transcription

1 Capacity Optimization and Modelling of frequency selective WLAN indoor MIMO Channels based on measured data A. Knopp, M. Chouayakh, B. Lankl The University of the Bundeswehr Munich (Germany) Institute for Communications Engineering, Werner-Heisenberg-Weg 39, Neubiberg Abstract: Motivated by channel measurements in different indoor locations we will show that the WLAN indoor MIMO channel is characterized by few dominant transmission paths mainly corresponding to the LOS path and some strong reflections. In the contrary to the common statistical flat Rayleigh fading channel model we will explain that the WLAN channel is widely deterministic and frequency selective. Furthermore we calculate the channel capacity from the measured data and we show its dependence on the geometrical arrangement of the transmit and receive antennas and the characteristics of the location. Here strong variations are observed and therefore we present some promising approaches that could be valid to reduce these capacity variations and enhance the overall capacity. Keywords: beamforming 1 Introduction MIMO channel, capacity, LOS, WLAN, Multiple Input - Multiple Output (MIMO) wireless communication systems provide a highly applicative possibility to increase the channel capacity. Especially in the context of wireless local area networks (WLAN) such MIMO applications promise great benefits as their importance has been increasing for the last years and here high data rates along with improved availability are desired. In this context it is inevitable to find valid channel models for the possible communication channels. Many current approaches use statistical channel models, which find their origin in mobile communications. However, indoor WLAN applications are distinctly different in many crucial characteristics, which leads to the need of the current models adaption and it turns out that in the sequel further endorsements are necessary to enhance the overall capacity. This is discussed in the course of this paper. Hence, the rest of the full paper will be structured as follows: In section 2 we will describe our assumptions for a typical indoor WLAN channel and present a simplified theoretical and widely deterministic channel model. In section 3 we will discuss this channel model with respect to the achievable MIMO channel capacity and we will show approaches for geometrically optimized antenna setups along with methods of signal processing aiming at an enhanced capacity. In section 4 we will present and explain our results obtained from measured data and we will calculate the channel capacity for different antenna arrangements. Finally, our work will be concluded in section 5. 2 WLAN channel modelling In the context of MIMO applications and their achievable channel capacity indoor WLAN channel models are commonly statistical ones that concentrate on the modelling of numerous and variously reflected waves, which arrive at the receiver via the non line of sight (NLOS) transmission paths. A similar strategy of channel modelling is regularly performed in mobile communication scenarios. These systems are characterized by narrow bandwidths, wherefore the channel can be treated flat and information is provided only on the magnitude level distribution, which can be modelled by a Rayleigh process [1]. Additionally the direct line of sight (LOS) link can be incorporated, which leads to the well known Rice propagation model. This statistical approach is widely used when discussing early WLAN transmission systems and it is incorporated in the popular, cluster based indoor channel model introduced by Saleh [2] and in the sequel in its spatial extensions, e.g. in Spencer s model [3]. Taking a look at the achievable MIMO capacity for such statistical channels it turns out, that the achievable MIMO capacity is comparatively high [4], as long as the receive signal correlation, which depends on the antenna spacing, is kept low. According to [5] this is achieved by antenna spacings of about half-wavelength (λ/2). Contrarily, in the case of a dominant LOS component the signals at the receiver are correlated and therefore the simple approach of antenna spacing half-wavelength is no longer valid as it can not exploit the maximum MIMO capacity. Here further measures have to be developed to access the maximum capacity gain, which are hardly investigated as commonly the statistical modelling approach is used in terms of MIMO systems [6], [7]. We will further discuss this topic in section 3. First motivated by the wideband measurements performed by Kunisch and Pamp [8] and in the contrary to the statistical Rayleigh modelling of the magnitude derivation we propose a deterministic channel model to a greater extent. Considering the huge bandwidth of current WLAN standard IEEE , which is typically 100 times the one of GSM systems, the narrowband assumption of a flat fading channel does not hold and therefore the channel clearly is frequency selective. Furthermore, for a typical WLAN scenario we assume a setup with more or less fixed antenna positions that could be exemplarily described as follows: the access point is mounted at the ceiling and the mobile unit is positioned on a desk in front of a working person. The mobile moves only slowly and within a narrow radius. The transmit signal reaches the user via a direct link and via few dominant reflected paths, mainly caused by

2 the walls, which surround our setup. This reflection layers are denominated R1,..., R5 in the sequel. Of course there are additional diffuse transmission paths, where the signal is reflected twice or more often, but these paths are considered to contribute only a negligible amount of signal energy and hence, they are skipped. Besides, slowly moving objects (e.g. walking persons) among transmitter and receiver are considered whose reflection factors are small. We will validate our assumptions in the sequel by measurements. Preliminary to the discussion of our measurements results in section 4 we will derive a simple deterministic channel model, that regards the assumptions explained in the last paragraph. For a time variant frequency selective single input - single output (SISO) system the deterministic impulse response y(t) depending on the time t is given by the equation L 1 y(t) = a l (t)x(t τ l ), (1) where x(t τ l ) denotes the delayed transmit signal and τ l delineates the delay along transmission path l out of L possible transmission paths. Furthermore, a l (t) weights the receive signal on path l by a time variant complex deterministic Gaussian process, that models the attenuation factor for path l and the disturbance of the channel caused by the Doppler effect [1]. Besides we assume the channel being time invariant for one measurement as it is short enough to fulfill this condition within the expected amount of motion in the channel. Hence, the output signal is a superposition of L delayed versions of the input signal and therefore the time variant channel impulse response results in L 1 h(τ,t) = a l (t)δ(τ τ l ). (2) The Fourier transform with respect to τ delivers the time variant transfer function depending on the frequency f L 1 H(f,t) = a l (t)e j2πfτ l. (3) For a time variant frequency selective M N-MIMO system consisting of N transmit and M receive antennas the vector of receive signals y(f) C M 1 is calculated from the transmit signal vector x(f) C N 1 and the channel transfer matrix H(f,t) C M N by y(f) = H(f,t)x(f) + η(f), (4) where η(f) C M 1 denotes the additive Gaussian noise. We assume the noise to be zero-mean complex Gaussian with covariance matrix R η = E[ηη H ] = σ 2 η1 M, where 1 M C M M denotes the identity matrix and σ 2 η is the noise power at each receive antenna. According to equation (4) the time variant channel transfer matrix H(f, t) can be delineated consisting of the two parts H(f,t) = H LOS (f,t) + H NLOS (f,t) = R a l11 (t)e jα l 11 (f). a lm1 (t)e jα l (f) M1... a l1n (t)e jα l (f) 1N a lmn (t)e jα l MN (f), (5) where the case l = 0 describes the direct (LOS) transmission paths, while l = 1,...,R includes all the dominant reflections caused by the R different reflection layers. The phase angle α lij for the transmission path between the i- th receive and the j-th transmit antenna is connected to the signal s delay τ lij by the equation α lij = 2πfτ lij. Similarly, the factor a lij (t) incorporates path loss as well as Doppler effect and, where appropriate, the attenuation due to reflections. It is assumed to be constant over frequency for the considered bandwidth. As mentioned before, there are lots of reflections besides the few dominant ones, but we assume their signal energy to be negligible compared to these strong ones and for the sake of clarity we skipped them in our simplified model. So the channel is modelled deterministic. An approach to decompose the channel transfer matrix into a deterministic part and a stochastic one was introduced by [9]. Obviously, the geometric assembly as well as the characteristics and positions of the surrounding walls and scatterers decisively influence the appearance of the channel transfer matrix, especially as the delay τ lij is linked to the length of the transmission path L lij by the speed of light c 0, i.e. τ lij = L l ij c 0. Due to this geometric dependence the accessible channel capacity is determined by the characteristics of the environment and by the chosen antenna setup. This is described more detailed in the next section. 3 Channel capacity and optimization According to [4] and [9] when uncorrelated transmit signals are presumed the time variant channel capacity for a frequency selective MIMO-channel in the absence of channel knowledge at the transmitter is calculated from C(t) = B ( )] log 2 [det 1 M + σ2 x H(f, t)h H (f, t) df, (6) 2 where B denotes the transmission bandwidth, 1 M C M M is the identity matrix, σx 2 denotes the mean transmit power, that is allocated to each transmit antenna and 2 constitutes the noise power at each receive antenna under terms of zero-mean, additive white Gaussian noise. Furthermore (.) H abbreviates the complex conjugate transpose. As mentioned in the previous section we assume for the sake of simplicity for the indoor scenario only slowly moving objects compared to the transmission time for one block of data and therefore, if our assumption holds, the time variant capacity from equation (6) reduces to the time invariant equivalent ( )] C = log 2 [det 1 M + σ2 x B 2 H(f)H H (f) df. (7) We will show by the results from measurements in section 4, that the time variant capacity varies very slowly as a function of the time for the chosen WLAN scenario.

3 From equation 7 it can be observed that the capacity is optimized by finding the optimal matrix entries in the channel transfer matrix H(f) depending on the frequency f. In a deterministic channel this can be resolved by geometrically optimizing the antennas position within the given environment. To illustrate this approach, a simple example is presented for the case of nonexisting reflections, i.e. the transmit signal is broadcasted to the receive antennas only via the LOS transmission path. This scenario covers the assumption, that the signal energy transmitted over the direct link is much higher than that of any reflected path what means that the capacity is dominated by the strong LOS component. Especially in the case of only few reflections this assumption is valid as it can be observed from figure 2 where besides the LOS paths one reflection layer was assumed. However, in small rooms with only short delays for the reflected signals and many reflection layers the assumption looses validity. For simplicity we consider 2 transmit and 2 receive antennas. The two antenna arrays are positioned broadside to each other and the arrangement is symmetric regarding the distances between the antenna elements at the transmitter and the receiver, i.e. L 11 = L 22 = L d and L 21 = L 12 = L c, where L ij denotes the distance between the i th receive and the j th transmit antenna. Furthermore a time invariant communication system is assumed. In this case the channel transfer matrix H C 2 2 is given by [ ] 1 e jα H = e jα, (8) 1 where w.l.o.g. the common phase angle and path loss of all matrix entries was already eliminated. The parameter α = 2π L/λ denotes the phase angle difference between the transmission paths, L = L c L d at the frequency segment f. Of course there is a difference in the path loss between the four transmission paths but as their length difference is small, this difference in the path loss also gets negligible in our simplified example. Using this transfer matrix the expression for the channel capacity is calculated from equation (7) as C = B log 2 [(1 + 2 σ2 x 2 ) 2 (2 σ2 x 2 cos α) 2 ], (9) and in the case of α = π 2 + kπ, where k can be an arbitrary integer, it gets its maximum value of C max = 2B log 2 (1 + 2 σ2 x σ ). This optimum angle α η 2 opt corresponds to the short path length difference of L = λ 4 and therefore a condition is found, how the antennas have to be arranged to reach the maximum capacity in the correlated channel. If the distance between transmitter and receiver is for example 2 m the antenna spacings at both sides have to be chosen about 35 cm for a frequency of 2.4 GHz according to the desired path length difference. This simple example shows a possibility to optimize the channel capacity even in deterministic MIMO channels in the case of a flat fading and it explains, that here an antenna spacing much larger than half-wavelength has to be chosen. Similar approaches were discussed in [10] and [11], but these papers also cover only special antenna arrangements without giving a general and systematic prescript, how such arrangements can be found for an arbitrary MIMO system. For the deterministic WLAN channel it must be bargained for huge variations of the achievable channel capacity as reflections may degenerate the LOS signal component, which the system was optimized for. Therefore several strategies are conceivable to cope with these echoes by methods of signal processing. There are various possibilities that could be thought to enhance the capacity by changing the system s parameters. A larger bandwidth, for example, would reduce the degrading influence of single reflections as the resolution in time would increase. This ultra-wideband (UWB) approaches are already known from SISO systems. A further combination with Direct Sequence Spread Spectrum systems that use Rake receivers to resolve the transmission paths could also enhance the accessible capacity. A further promising approach we want to discuss a little more detailed is to replace every receive antenna by several antenna elements which could be used in different ways. To validate the following ideas by simulation we assumed a simple scenario as it is illustrated in figure 1. Here every black dot reph r11 h r12 h 11 h 12 λ 2 w 1 w 2 w 3 w 4 Figure 1. illustration of the simulation model resents one omnidirectional antenna element and the setup was geometrically optimized for the LOS signal components according to the above description by finding the optimum antenna spacing d depending on L and λ. Furthermore we replaced every receive antenna by at maximum four antenna elements that are spaced λ 2. The entries of the corresponding transfer matrix are described by the h ij and h rij and the parameter d r describes the variable distance between the first transmit antenna and the only reflection layer that is presumed exemplarily. The two dashed boxes at the first receive antenna group mark two different approaches for the receive signal processing that we will describe in detail in the following paragraph. In the course of the simulation we took into account the path loss of every transmission path by a factor a that was normalized in a way, that the shortest one L 0 got zero path loss, i.e. a = L 0 /L ij. The reflection factor of the reflection layer was presumed to equal one. The results for the simulations described in the sequel are depicted in figure 2 for different positions of the reflection layer when the capacity is normalized by the maximum value possible for the case of nonexisting reflections in the given scenario. Of course the different scenarios provide different maximum MIMO ca-

4 pacities depending on the number of antennas and for the reason of comparability we used this normalization. We presumed a signal to noise ratio of 10log 10 ( σ2 x σ 2 η ) = 20 db, where the definition of σ 2 x being the transmit power per transmit antenna and σ 2 η being the noise power per receive antenna was consequently used in all scenarios. It is clear that in the common case of only one antenna element per receive antenna the exemplary reflection causes incursions in the channel transfer functions and therefore degenerates the channel capacity if it superposes adversely with the LOS signals. As well, in the case of constructive superposition the capacity can be enhanced by the reflection. This can be seen from the upper part of figure 2. Obviously, in the case of only one reflection layer the capacity incursions are comparatively small. With growing distance between the reflection layer and the antennas the additional path loss further reduces this degradation and it might not be necessary in this case to perform any measures to avoid the incursions. On the other hand one must be aware, that the reflections influence comes to the fore if the number of reflection layers increases and so measures of capacity enhancement are maintainable by all means. The first approach to smooth the channel capacity could be to increase receive diversity by building an asymmetric 8 2 MIMO system, where the former two receive antennas are replaced by 4 antenna elements each. It is important that the optimum antenna spacing is kept constant. In the lower part of figure 2 the result for such a case of 8 receive antennas is drawn. It clearly can be observed that the channel capacity curve can be smoothed significantly due to the increased receive diversity and that the overall capacity reaches the maximum possible, as the geometrical arrangement is nearly optimal for every transmit-receive antenna combination. The importance of this optimal arrangement turns out more clearly, if the capacity curve for the case of antenna spacing d = λ/2 at both the two transmit and all of the receive antennas is observed. Here the capacity distinctly falls below the maximum value possible for an 8 2-MIMO system, what again stresses the necessity of larger antenna spacings than half-wavelength. A further approach to reduce the incursions in the capacity is to eliminate the reflections by methods of beam forming at the receiver. We will again demonstrate this on the basis of the arrangement in figure 1. Here one receive antenna is replaced by a group of antenna elements but the system still stays a 2 2-MIMO system. Every group of receive antenna elements is a beamformer consisting of 4 elements, whose beampattern B θ (θ) is given by B θ (θ) = w H v θ (θ), (10) where w is a vector containing the 4 complex weighting factors for every antenna element and v θ (θ) is the array steering vector that incorporates the spatial characteristics of the beamformer given by the arrangement of its elements [12]. When the weights are firstly assumed to equal one, our beamformer has its main beam at θ = 90 and therefore fingers the signals via h 11 without attenuation while the reflections as well as the transmission path h 12 are attenuated. In the sequel we will call this beamsteering as the weights have no influence. If the distance L is large compared to the antenna spacing the angle θ 1 (figure 1) does not vary much from the beamsteerers main direction and so this transmission path is only slightly attenuated. Due to this fact the beamsteerer performs worse in the case of small distances d r between the reflection layers and the antennas. For large d r the result is vice versa as the reflections are received outside the main beam what causes a high attenuation. A reason for the relative capacity laying above the value 1 the amplitude gain of a beamsteerer, which in the case of 4 elements at maximum equals 4, must be taken into account. This gain is in the sequel reduced by the beamsteerer s noise enhancement caused by the additional low noise amplifiers (LNAs) of the beamformer. Hence, compared to the 2 2-MIMO system the noise power must be multiplied by factor 4 per antenna group, when uncorrelated noise sources for the antenna elements are presumed. In our simulation both effects were taken into account without any normalization. An extended approach could be, to implement a real beamformer by optimizing the weighting vector w with respect to the capacity. There are different strategies to achieve this aim. We could try for example to form a single beam for every arriving transmission path per antenna and combine the received signals afterwards with additional time shifts that were chosen to achieve maximum capacity. Of course it would be necessary to form a lot of sharp beams and here a significantly higher number of antenna elements must be used. A less complicated idea is to form a beampattern that provides a weight of Null in the direction of the reflections and high weights in the direction of the LOS transmission paths. To give an example we followed the latter strategy for our scenario in figure 1. As we know four samples of the desired beampattern for the four angles of the incoming transmission paths per antenna, i.e. B θ (θ 1 ) = B θ (θ 2 ) = 4 and B θ (θ 3 ) = B θ (θ 4 ) = 0 we can calculate w for complex weights according to the equation [ ] 1 w = V H θ B θ, (11) where B θ = [B θ (θ 1 ),B θ (θ 2 ),B θ (θ 3 ),B θ (θ 4 )] T is the vector with the four samples of the beampattern and V θ = [v θ (θ 1 ),v θ (θ 2 ),v θ (θ 3 ),v θ (θ 4 )] is the array steering matrix that includes the pattern s spatial characteristics at the sampled angles. Here a gain of 4 was chosen for the beampattern as this gain can be achieved by the antenna array itself without additional weights and the weights would have values smaller than 1 if a lower gain was desired. However, it seems not to be sensible to attenuate the receive signal and so the minimum gain must be 4. The capacity in the case of this beamformer instead of each of the two receive antennas is depicted by the last curve in the lower part of figure 2. It can be seen that the strategy is valid to smooth the capacity curve as long as the angles of arrival AOAs of the reflections are distinctly different from the LOS main direction. The reason for capacity degradation in the case of small angle differences can be found in the noise enhancement that on the one hand occurs due to the additional LNAs as described above and on the other hand is further enhanced as the noise is weighted by w just like the receive signal. As the weights get very high val-

5 To proof our assumptions concerning the channel model and its achievable capacity we carried out measurements in a WLAN environment. These measurements were executed using a channelsounder with 2 transmit and 2 receive antennas. A WLAN carrier frequency of 2.4 GHz was chosen with a bandwidth of 80 MHz around this carrier. In WLAN applications usually a bandwidth of 20 MHz is used, so that we can achieve a higher resolution in time than those systems, albeit our bandwidth ranges within the same order of magnitude. For the channel estimation we used Perfect Squares Minimum Phase Constant Amplitude Zero Auto Correlation (PS-MP CAZAC) [13] sequences as pilot signals. We assume that the channel remains time invariant during one measurement cycle of the 4 transmission paths like in section 2. The whole measurement cycle took about 25 µs. The measurements were taken in two different office environments, a large office scenario and a comparatively small one to achieve different delays and path losses of the reflections. The exact dimensions of the two locations were as follows. large office: length: 15 m, width: 7 m, height: 3 m; small office: length: 5.30 m, width: 3.50 m, height: 3 m. In both offices the surrounding walls were characterized by sheetrock, steel and large windows and we always had carpeted floor. Furthermore the locations were typically office furnished. We used two vertically polarized, nearly omni-directional dipole antennas at both transmitter and receiver and the transmitter and receiver antenna arrays were basically placed broadside to each other, whereupon the antenna spacing could be varied from half-wavelength to 6 times the wavelength. During all measurements the center points of the two antenna arrays were separated 3 m. All the time persons were arbitrarily moving around and between the antennas. Figure 3 shows exemplarily the magnitude and phase of a typical measured channel transfer function for one of the four transmit-receive antenna links in the small office scenario. The lower part of the figure displays the mean mag- Figure 2. Capacity for different setups, B=20 MHz (typ. WLAN), SNR=20 db, λ=12.5 cm ues in the case of small angle differences for the paths the noise enhancement increasingly degrades the capacity. So it must be summarized that the beamformer is valid only for large AOAs of the reflections but it is obvious too, that with an increasing number of reflections it gets harder to finger only the LOS paths, especially if the number of antenna elements is not increased further. However, this simple examples clearly illustrate promising approaches to enhance the overall capacity in the described WLAN scenarios. 4 Results from measurements Figure 3. exemplary channel transfer function nitude and phase derived from 1000 measurements with fixed antenna positions. The upper part shows, how the momentary value of the magnitude varied over the 1000 measurements in the form of a histogram plot. From the figure it can be observed, that the channel transfer function is clearly frequency selective. Clearly, the magnitude does not follow a Rayleigh distribution, quite the contrary the momentary magnitude barely varies from its mean and at best a Rice propagation model could be supposed only for a narrow frequency bin. This result is also confirmed by the impulse responses shown in figure 4. The 50 snapshots from one antenna link were sequentially derived in steps of 1 sec and arbitrarily extracted from the 1000 measurement cycles. Here two scenarios are addressed, the left hand fig- Figure 4. exemplary impulse responses ures show the case of λ/2 spaced antennas at both transmitter and receiver for the two locations, while the right hand figures display the case of significantly larger antenna spacings. In both cases a small number of dominant transmission paths is distinctive and resolvable, whereupon only few of them carry the predominant part of signal energy. This becomes obvious especially from the upper left hand figure where the plotted impulse responses

6 show stronger variations. Here the snapshot of impulse responses certainly covered motion between transmitter and receiver arbitrarily and therefore it varies a little more than in the other cases. Focussing on the channel capacity of this 2x2-antenna MIMO system, the results are given in figure 5. Here, based on 1000 measurement cycles, the cumulative distribution function (CDF) for the channel capacity for the two locations and different antenna spacings is shown. The capacity CDFs were calculated according to equation (9) from the measured data regarding the real signal to noise ratio of the channelsounder 20log 10 ( σ2 x σ 2 η ) = 85 db. That means we did not normalize the measured channel transfer matrix in any way and assume a fictive SNR, but used the real SNR and the measured channel transfer matrix including the path loss (for a distance of 3 m about 50 db) and further attenuations, e.g. the reflection factors of the reflection layers. In the advance of the measurement Figure 5. empirical CDFs for the channel capacity we always tried to arrange the antenna arrays manually in a way that we could get the highest capacity possible within the room with the restriction of an exact separation of 3 m. It can be observed, that in the case of large antenna spacings and broadside arrangement of the arrays we always achieved larger capacities than for small antenna spacings. This result we ascribe to the LOS signal component that according to section 3 can be assessed only via optimized antenna spacings. In the case of λ/2 antenna spacing in the small room we could obviously find a suited setup to exploit the reflected waves in terms of the capacity. In the large room the capacity for this case is much smaller as the reflected signals are attenuated more distinctly. It can also be recognized that for perpendicular antenna setup the capacity always stayed small as this arrangement marked a keyhole scenario with respect to the LOS component. Last, the high steepness of the CDF curves points again to a deterministic channel which as a corollary leads to a determinism in the channel capacity. 5 Conclusion Supported by results from measured data we showed the frequency selective indoor WLAN MIMO channel being strongly deterministic and characterized by only few dominant transmission paths, that can be resolved according to the accessible bandwidth. Instantiated by different setups, we showed the channel capacity highly depending on the current geometric conditions of the scenario and the location and furthermore being also widely deterministic for a chosen setup. As a corollary there are two steps of optimizing the channel capacity: the first step deals with the geometrical optimization of the antennas, especially if there is a strong LOS component that can be exploited. Due to unavoidable reflections the capacity will suffer incursions and so the second step of optimization deals with additional measures of signal processing and diversity to further enhance the capacity. First hints on possible measures were also given in the course of this paper. References [1] M. Pätzold, Mobile fading channels, John Wiley & Sons, 2002 [2] A.A.M. Saleh, R.A. Valenzuela, A statistical model for indoor multipath propagation, IEEE J. Select. Areas Commun., vol.5, 1987, pp [3] Q.H. Spencer, B.D. Jeffs, M.A. Jensen and A.L. Swindlehurst, Modelling the statistical time and angle of arrival characteristics of an indoor multipath channel, IEEE J. Select. Areas Commun., vol. 18, no. 3, Mar. 2000, pp [4] E. 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