Measurement Campaign - 傳播對室外多輸入多輸出系統容量影響之研究

(a) (b)

Fig. 3-2 RUSK vector channel sounder. (a) Transmitting unit. (b) Receiving unit.

3.2 Measurement Campaign

There are four measurement sites illustrated in Fig. 3-3. Detailed experimental setup or arrangement at each site is given as follows:

Measurement sites National Chiao Tung University Guang Fu campus Site 1 along route no.1 with total route length: 50m (12700 snapshots)

Site 2 along route no.2 with total route length: 170m (36700 snapshots)

Site 3 along route no.3 with total route length: 200m (4200 snapshots,)

Site4 along route no.4 with total route length: 250m (4800 snapshots)

Moving speed

route no.1 and route no.2 : Speed=2~3 km/hr route no.3 and route no.4 : Speed=10 km/hr

Tx-Rx distance route no.1 15~50m Propagation delay time 1.6 s for route no.1.

6.4 s for route no.2, route no.3 and route no.4

We name site-ij as the particular propagation condition i along the measurement distance in route -j i.e., site12 means the LOS condition along route no.2, site23 means the OLOS condition along route no.3, site34 means the NLOS condition along route no.4

The propagation environment at each site is described as the following table.

Table 1- descriptions of the propagation environment at each route.

route no. Propagation situation Local environment

route no.1

Fig. 3-3 Measurement sites in the NCTU campus

MIMO channels can be modelled either as double directional channels or as vector (matrix) channels. The former method is more related to the physical propagation effects, while the latter is more emphasized on the effect of the channel on the system. Another distinction is whether to treat the channel deterministically or stochastically. In the following, we outline the relations between those description methods.

The deterministic double directional channel is characterized by its double directional impulse response. It consists of L propagation paths between the transmitter and receiver sites. Each path is delayed in accordance to its excess-delay

i, weighted with the proper complex amplitude a e_i ^j ⁱ and each direction of departure (AOD) _{T i}_, associated with the corresponding direction of arrival (AOA)

R i. The channel impulse response matrix h is

, ,

absolute time t; also the set of multipath components (MPCs) contributing to the propagation will vary, N N(t). The variations with time can occur both because of movements of scatters, and movement of the transmitter. The number of paths L can become very large if all possible paths are taken into account. In our experiments, the total number of resolvable multipath components was between 193 and 769. We simulate the deterministic channel applying the site-specific method to describe the direct wave, specular reflection waves, and single and multiple-over-rooftop diffracted waves. Once the site-specific method, i.e. deterministic method, is finished, the field strength distribution, power delay profile and power azimuth profile are shown in Fig. 3-4, we survey the multipaths in propagation, only one path is single rooftop diffracted wave accompanied with other 31 corner diffracted multipaths and acquire different realizations of the channel and proceed this procedure 15 times to obtain the complete channel matrix H_{4 4}. Based on the theory of reciprocity of antenna, we obtain AOD by interchanging the position the transmitter and receiver.

AOA _T , AOD _R in route no.1 case is approximately 0 . Repeating the ⁰ procedure above for 100 times gives an ensemble of channel realization and computes the capacity and plots a cumulative distribution function (CDF) for the MIMO channel capacity. Fig.3-4 gives the power delay profile and power azimuth profile of measurement for LOS of route no.1 and Fig 3-5 gives the time averaged Delay-Azimuth Spectrum of measurement of route no.1.

Fig 3-4. The field strength distribution of propagation, power delay profile and power azimuth profile for LOS of route no.1 in the left straight side, the ones which

transmitter and receiver are interchanged shown in the right straight.

Fig 3-5 Time Averaged Delay-Azimuth Spectrum of measurement of route no.1

Fig 3-6 (a)

Fig 3-6 (b)

Fig 3-6 (a) Field strength distribution of route no.2 and the Power Delay Profile and Power Azimuth Profile of route no.2 (b) Time Averaged Delay-Azimuth Spectrum of

measurement of route no.2

Fig 3-7 (a)

Fig 3-7 (b)

Fig 3-7 (a) Field strength distribution of route no.3 and the Power Delay Profile and Power Azimuth Profile of route no.3 (b) Time Averaged Delay-Azimuth Spectrum of

measurement of route no.3

Fig 3-8 (a)

Fig 3-8 (b)

Fig 3-8 (a) Field strength distribution of route no.4 and the Power Delay Profile and Power Azimuth Profile of route no.4 (b) Time Averaged Delay-Azimuth Spectrum of

measurement of route no.4

3.3 Measurement data extraction

By examining the measurement raw data, we extracted the angle-of-arrival (AOAs), angle-of-departure (AODs), delays and azimuths of the multipath components [10].

Using the commercial software Matsys to obtain

(1) Time-variant Impulse Response h t( , , )s , where t represents observation time, represents delay time, s represent channel, we take this to evaluate whether the environment is clean i.e. observing the Power Delay Profile had a trend of decaying along the propagation distance as time is going. In Fig. 3-9, we observe that (a)~(c) power level increases as time goes by and (c) appear apparent decaying situation at some measurement, the same bandwidth. In Fig. 3-9 (c), there is a time difference between the strongest receive signal power and next strong one around 0.25~0.3us, i.e.

the multipath propagate to arrival receive array more over 75~90m. From these Power Delay Profiles, we recognize (a)~(c) as OLOS, NLOS and LOS, respectively and take these snapshots for data processing.

Fig. 3-9 The impulse response of (a) top (b) bottom left (c) bottom right figure presents the measurement during different observation time

(2) Delay-Azimuth spectrum extract multipath amplitudes from various azimuths and delays. We used Unitary ESPRIT (a parametric subspace estimation method incorporating forward-backward averaging) algorithm for detecting the information of direction to obtain time-variant delay-azimuth spread h_t_{, ,} ( , , )t . There are two kind of sampling result

Spatial sampling-for fixed (delay), extract multipath from various azimuths

Temporal sampling-for fixed (azimuth), extract multipath from various delay bins.

From these two processing, we are ready to compute the effective multipath number under some environment and root mean square delay spread and azimuth spread, which can be used to evaluate the dispersionness of propagation.

Delay spread ( )=

(3)Frequency response H(t, f, s) to obtain the corresponding MIMO capacity.

According to the propagation delay time and measurement bandwidth, we obtain 193 (or 769) delay bins in the Power Delay Profile and 193 (or 769) multipaths in the time domain contribute to the capacity through the Fourier transform in the frequency domain illustrated in Fig. 3-10. From consecutive snapshots received by array, we take a bundle of snapshots, depends on the element spacing, total measurement distance and moving speed, for representing the signal bursted out from one transmit antenna. Take the data of route no.1 10 element spacing at the transmit end for example, we need 312 snapshots to simulate the one transmit antenna, other three transmitter done in the same way. While the frequency responses from four transmitters are produced and averaged, we obtain a transfer channel matrix H^{4 4 193}^{x x}

(or H^{4 4 769}^{x x} ) and normalize to ²

, ij 1

i j

h , the normalization of channel matrix is in

order to remove the path loss, the superscript of 193 (or 769) represents the frequency bins resolved from bandwidth and then compute the capacity of each frequency bin based on (5). This concept is merely like the expression below

( 6 0 ) ( 6 0 ) ( 6 0 ) ( 6 0 )

We view the capacity of different frequency bins sas the contribution of multipath and average it to obtain the corresponding array capacity for a sampled measurement.

Fig 3-10 (a) Fig 3-10 (b)

Fig. 3-10 The frequency response (a) and impulse response (b) of the channel

The procedures of Unitary ESPRIT to obtain AOA and AOD listed as below [11]

1. Initialization Form the matrix X C^{M N D} from the available measurement M represents an M-element sensor array composed of m pairs of pair-wise identical, but displaced sensors (doublets), i.e. M=4, N represent the number of selected snapshots, i.e. N=10, D represents the number of delay bins, i.e. D=193.

2. Signal Subspace Estimation Determine the real matrix T{ }X ^{M 2N D}

and compute the SVD of T{ }X (square root approach) or the eigendecomposition of T{ }X T{ }X ^H (covariance approach). The d dominant left singular vectors or eigenvectors will be called E_s ^{M d D}. Estimate the number of sources d, if d is not a priori.

We consider an efficient computation of a particular transformation T ( ). It transforms an arbitrary complex matrix C^{p q} into a real p x 2q matrix, denoted by T (X). The block matrices G ₁ and G₂ should have the same size, we set them as

2 5 1 and G2 ^x

G C , ₂ represent the 2 x 2 exchange matrix with ones on its

antidiagonal and zeros elsewhere, i.e. ₂ 0 1

[ ]

1 0 , g^T 0 since M is even. Then an efficient computation of T{ }X ^{M 2N D} from the matrix X only requires p x 2q real additions. Notice that d N.

3. (Total) Least Squares Solve the overdetermined system of equations

1E s 2Es

4. Eigenvalue decomposition Compute the eigenvalue decomposition of resulting solution

Chapter 4 Impact of propagation on capacity

Chapter 4 Propagation and Antenna Arrangement Effects on MIMO Capacity

4.1 Propagation effect

Propagation at different conditions such as LOS, OLOS and NLOS may influence MIMO capacity. Here, we analyze the measured result along each route to see how the capacity changes as the conditions, propagation distance or local scatterer distribution varies, which is shown in section 4.1.1. Comparison between the measured result and the computed results from the ray-tracing based hybrid model will help to investigate the coupling effect between the element spacing and local scattering on the MIMO capacity. This is illustrated in section 4.1.2.

4.1.1 Measured result analysis

Figure 4-1 illustrates three CDFs of the measured MIMO capacity for LOS, OLOS and NLOS conditions along route no.1. There are three CDF curves to show the results of LOS, OLOS and NLOS conditions. The averaged capacity is 13.1102 bps/Hz for LOS condition, 14.9382 bps/Hz for OLOS condition and 15.65 bps/Hz for NLOS condition. It is found that the capacity in the LOS condition is smaller than that of the OLOS or NLOS condition. It is because that the rms AOA angular spread of the LOS condition is smaller than that of latter two conditions. The larger multipath angular dispersion will lead to less spatial correlation between receiving signals, i.e., larger capacity. This result is shown in Figure 4-2 where larger rms angle spread leads

capacity of LOS, OLOS and NLOS conditions, respectively. Similar results are found in the figure 4-4 for route no.2, figure 4-5 for route no.3 and figure 4-6 for route no.4.

Fig 4-1 The CDF of the measured MIMO capacity for LOS (*), OLOS (o) and NLOS ( ) conditions along route no.1. The averaged capacity is 13.1102 bps/Hz for LOS

condition, 14.9382 bps/Hz for OLOS condition and 15.65 bps/Hz for NLOS condition.

Fig 4-2 capacity versus rms angular spread of AOA for LOS (*), OLOS (o) and NLOS ( ) conditions

11 12 13 14 15 16 17

4x4 for MIMO outdoor along LOS of route no.1

LOS

4x4 for MIMO outdoor along OLOS of route no.1

OLOS

Fig 4-3 (b)

12 13 14 15 16 17 18 19 20 21 22

Figure 4-3 The histogram of MIMO capacity for (a) LOS, (b) OLOS and (c) NLOS conditions.

Fig 4-4 The CDF of the measured MIMO capacity for LOS (*), OLOS (o) and NLOS ( ) conditions along route no.2. The averaged capacity is 23.258 bps/Hz for LOS

condition, 24.623 bps/Hz for OLOS condition and 24.8787 bps/Hz for NLOS condition.

Fig 4-5 The CDF of the measured MIMO capacity for LOS (*), OLOS (o) and NLOS ( ) conditions along route no.3. The averaged capacity is 21.7373 bps/Hz for LOS

condition, 23.8253 bps/Hz for OLOS condition and 25.732 bps/Hz for NLOS condition.

Fig 4-6 The CDF of the measured MIMO capacity for LOS (*), OLOS (o) and NLOS ( ) conditions along route no.4. The averaged capacity is 24.1806 bps/Hz for LOS

condition, 25.8532 bps/Hz for OLOS condition and 27.6917 bps/Hz for NLOS condition.

4.1.2 Comparison among different routes

Fig 4-7 (a)~(c) illustrates the CDF of capacity of different routes for LOS, OLOS and NLOS respectively. From these three figures, we can obtain that the capacity performance of route no.1 is always smaller than that of others despite the LOS, OLOS and NLOS conditions. The performance of MIMO capacity along route no.2, route no.3 and route no.4 has some degree of resemblance. Since the distinctions of the measurement in the route no.1 with that of other three are the propagation distance and local scatterers, so we sample the capacity from measurement along the propagation distance for each route shown as Fig 4-8 and apply hybrid model shown as Fig 4-9 to investigate the effect of propagation distance on the capacity performance. In the same way, we compare Fig 4-10 with the figure applying hybrid model shown as Fig 4-11 for each route to investigate the effect of local scatterers on the capacity performance.

Fig 4-7 (a)

Fig 4-7 (b)

Fig 4-7 (c)

Fig. 4-7 (a) The CDF of capacity of LOS in each route, (b) the CDF of capacity of OLOS in each site and (c) the CDF of capacity of NLOS in each site. There are four CDF curves to show the results of LOS condition of route no.1, route no.2, route no.3 and route no.4 in Fig 4-7 (a), four CDF curves to show the results of OLOS condition of route no.1, route no.2, route no.3 and route no.4 in Fig 4-7 (b) and four CDF curves

to show the results of NLOS condition of route no.1, route no.2, route no.3 and route no.4 in Fig 4-7 (c).

Fig 4-8 obviously presents that the capacity performance of shorter propagation distance 50m is indeed inferior to the one of other longer propagation distance. It despitse that propagation distance effect at each route does not exhibit regular trend and larger capacity deviation. Another information given by Fig 4-8 is that the standard deviation of capacity of propagation distance 50m is the smallest among the measurement results. This phenomenon tells us that transmitted signals through longer propagation distance may experience more complex channel so that causing more multipaths in the channel. In this way, the transmitted signals received by the opposite array will be less correlated each other, resulting in larger capacity fluctuation. Fig 4-9 shows that the computed results of CDF of the measurement along propagation distance. All are resembled except one in asterisk line sampled from route no.1 along propagation distance 50m.

Fig 4-10 shows the capacity variation of the LOS condition of measurements in all routes. It also provides us with the information of standard deviation of capacity sampled from all measurements, although the standard deviation of capacity in route no.1 is almost equal to the one in route no.3, the averaged capacity of measurements along route no.1 is much smaller than that of measurements along route no.3. This vehicles and pedestrians surrounded the transmitter in the LOS of route no.2 and route no.4 so that the transmitted signals within an extremely large rms angular spread of

AOA propagated to the receive array, resulting in transmitted signals less correlated each other. That is why the standard deviations of capacity of route no.2 and route no.4 vary dramatically. Fig 4-11 shows the computed results of CDF of LOS with local scatters in all measurements plus the case of LOS in route no.1 without local scatterer. From figure 4-8 to 4-11, we conclude that the propagation distance and local scatterers around transmit end array will affect the capacity performance.

Fig 4-8 The capacity variation of different propagation distance D from measurement with standard deviation of the capacity _{C D}_, ₅₀_m 0.9568 bps/Hz, _{C D}_, ₁₅₀_m 1.3368 bps/Hz, _{C D}_, ₂₀₀_m 1.2761 bps/Hz, _{C D}_, ₂₅₀_m 1.8584bps/Hz and _{C D}_, ₃₀₀_m 2.5649

bps/Hz.

Fig 4-9 The CDF of capacity for different propagation distance applying hybrid model

Fig 4-10 The capacity variation of LOS along different routes with standard deviation of capacity _{C route no}_, _.1 0.718 bps/Hz, _{C route no}_, _.2 1.3745 bps/Hz, _{C route}_, _no.3 0.7187

bps/Hz and _{C route}_, _no.4 1.8458 bps/Hz.

Fig 4-11 The computed CDF of the MIMO capacity for routes no.1-4 by using the hybrid model.

Fig 4-12 shows the averaged capacity of each route. It is found that in every route the capacity of LOS condition is always smaller than that of the OLOS or NLOS condition. It is because that the existence of direct path will reduce the rank of the channel matrix, which becomes a dominant factor in reducing the MIMO capacity.

Fig 4-12 The averaged MIMO capacity for each route.

4.2 Element spacing effect

In this section, we investigate the impact of MIMO element spacing on capacity through the measured data. Comparison between the measurement result and the computed results using the ray-tracing based hybrid model will help to investigate the coupling effects between the element spacing and local scatterers on the MIMO capacity. Section 4.2.1 will introduce the measurement of MIMO element spacing for LOS, OLOS and NLOS conditions. Section 4.2.2 provides the computation results using the hybrid model. Section 4.2.3 compares the measurement and computed MIMO capacity.

4.2.1 Measurement Result Analysis

Fig 4-14 gives the capacity variation under LOS with MIMO element spacing for route no.1 and Fig 4-15 corresponding CDF of different element spacing. Figure 4-14 indicates that the capacity increases as the element spacing increases. Since the element spacing increases, the array aperture is approximately M x d , beamwidth is _t inversely proportional to aperture and resolution is inversely proportional to beamwidth, hence the larger array ( d_t larger) resolves multipaths more, the propagation of MIMO channel filled with multipaths lead to the capacity to increases.

Figures 4-16 (a), (b) and (c) demonstrates the histograms of MIMO capacity with element spacing 10 ~ 30 along route no.1, respectively. Similar results are found in the figure 4-17 (a) for route no.2, figure 4-17 (b) for route no.3 and figure 4-17 (c) for route no.4.

Fig 4-14 The capacity variation under LOS with MIMO element spacing for route no.1 with standard deviation of capacity _C_, ₁₀ 0.7009 bps/Hz, _C_, ₂₀ 1.1148

bps/Hz and _C_, ₃₀ 0.7592 bps/Hz

Fig 4-15 The CDF of different element spacing for LOS along route no.1. The averaged capacity is 13.1102 bps/Hz for ¹⁰ condition, 14.0516 bps/Hz for

20 condition and 14.7373 bps/Hz for ³⁰ condition.

Fig 4-16 (a)

Fig 4-16 (b)

Fig 4-16 (c)

Fig 4-16 histogram corresponding to MIMO capacity for LOS along route no.1 with

(a) 10 (b) 20

Fig 4-17 (a) The CDF of different element spacing for LOS along route no.2. The averaged capacity is 23.258 bps/Hz for ¹⁰ condition, 23.6484 bps/Hz for

20 condition and 24.0421 bps/Hz for ³⁰ condition.

Fig 4-17 (b) The CDF of different element spacing for LOS along route no.3. The averaged capacity is 21.7373 bps/Hz for ¹⁰ condition, 22.4905 bps/Hz for

20 condition and 24.0012 bps/Hz for ³⁰ condition.

Fig 4-17 (c) The CDF of different element spacing for LOS along route no.4. The averaged capacity is 24.2358 bps/Hz for 10 condition, 25.83 bps/Hz for

20 condition and 26.3559 bps/Hz for ³⁰ condition.

Fig 4-18 illustrates the ensemble average capacity with MIMO element spacing of measurements. As the figure indicated, there will be a trend that capacity becomes

large as the MIMO element spacing increases for each route. Note that the values shown in the Fig 4-18 are obtained from averaging statistically 100 times.

Fig 4-18 The averaged capacity with MIMO element spacing for all measurements

4.2.2 Computation with the Hybrid model

From [12], a hybrid spatio-temporal radio channel model combines a site-specific model with a statistical model; we simulate the MIMO propagation with different element spacing and local scatters around the transmitter, in the process of adding the local scatters to investigate effect on MIMO capacity, there are three categories of local scatters effect, they are the category of 3 local scatters and scatter radius 2m with 4 different transmit element spacing 10 , 20 , 30 , shown in Fig 4-19 (a); the category of scatter radius 2m and transmit element spacing 10 with 2 to 6 local scatters, shown in Fig 4-19 (b); the category of 3 local scatters and transmit element spacing 10 with 3 different scatter radius 2m, 3m, 4m, shown in Fig 4-19 (c). In Fig. 4-19 (a), we note that the ensemble capacity will increase as the element spacing increases since the array aperture is approximately M x d , beamwidth is

inversely proportional to aperture and resolution is inversely proportional to beamwidth, hence the larger array ( d larger) resolves multipaths more, the _t propagation of MIMO channel filled with multipaths results in capacity increases. Fig 4-19 (b) and (c) present the degree of freedom of local scatter and scatter radius essentially perturb the MIMO channel and decorrelate it such that capacity distributes wider. This says the scatters within scatter radius around the transmitter will have

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