4.1 Propagation effect
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, 50m 0.9568 bps/Hz, C D, 150m 1.3368 bps/Hz, C D, 200m 1.2761 bps/Hz, C D, 250m 1.8584bps/Hz and C D, 300m 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 ( dt 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
(c) 30
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 impact on the MIMO capacity with 13.35% variation.
Fig 4-19 (a)
Fig 4-19 (b)
Fig 4-19 (c)
Fig.4-19 (a) CDF of capacity applying hybrid model for different element spacing.
The averaged capacity is 15.1589 bps/Hz for 10 condition, 16.6232 bps/Hz for
20 condition and 17.4488 bps/Hz for 30 condition. (b) CDF of capacity between 6 propagation under the condition of scatter radius 2m and different number
of local scatterers and propagation without considering local scatter. (c) CDF of capacity for different scatterer radius
The scatter effect illustrated in the figure 4-19 (b) and (c), the simulation applying hybrid model, is obvious, we realize the sources of scatterers in the real environment not only confined with the wall effect but also the pedestrians, trees, vehicles etc, hence the environment issues of propagation will have great impact on capacity. Next we will illustrate the CDF of capacity of measurement and hybrid model more clearly to investigate the variation of capacity due to propagation for 4 sites.
4.2.3 Comparison
From [6], given an ensemble of matrices generated by considering the density of scatters, the distribution of channel matrices is primarily a function of the number transmit and receive antennas and the density of scatters in units of 12
dt , where d is
the element spacing of arrays. At some large distance R~dt m, , the contribution of a scatters to an entry in the channel matrix is attenuated by the inverse of the distance squared 12
R . The number scatters in a differential annulus increase linearly with distance, but the effects of the scatters combine incoherently so that the contribution grows slowly than R and the integrated contribution from radius R to is finite.
Fig.4-20 (a)~(d) provide the comparison of CDF of capacity of different element spacing between the measurement and hybrid model for route no.1, route no.2, route no.3 and route no.4, respectively. For route no.1 to route no.4, we consider the measured capacity of three kinds of element spacing in LOS propagation and applying hybrid model taken three kinds of element spacing into account. The ensemble average of the CDF of capacity for each element spacing does not differ from the one applying hybrid model significantly; but there is still a trend existed that the ensemble average of capacity of 30 is the largest among three kinds of element spacing for each propagation of routes; Since aperture of array becomes larger, the beamwidth tapered increasingly therefore the resolution improves so the larger array i.e., larger element spacing, the resolved multipaths more to obtain higher capacity. From these four figures, the curves of the hybrid model can probably fit that of the measurement due to the local scatters added. Hence, we can conclude that the existence of local scatters around the transmit end array will affect the capacity performance again although its capability is limited stated from [6].
To this end, we tabulate the mean capacity of different element spacing of each propagation for all routes as table-2.
Fig 4-20 (a)
Fig 4-20 (b)
Fig 4-20 (c)
Fig 4-20 (d)
Fig 4-20 The comparison of CDF of capacity of different element spacing between the measurement and hybrid model for (a) route no.1, (b) route no.2, (c) route no.3 and (d)
route no.4, respectively.
Table 2-Mean capacity [bps/Hz] for three propagation, which has three kinds of element spacing of 4 routes
Routes
Route no.1 Route no.2 Route no.3 Route no.4
10 13.1102 23.258 21.7373 24.2358 standard deviation of capacity, standard deviation of rms azimuth spread of AOA and standard deviation of rms azimuth spread of AOD shown as Table-3. From this table we consider the bandwidth effect on the capacity. Fig 4-21 illustrates the capacity versus signal bandwidths. It is found that the capacity increases as the signal bandwidth increases for the LOS, OLOS or NLOS propagation situation along route no.1. It is because that as bandwidth becomes large, time resolution decreases [14];
hence array resolved more multipaths perturbed the signal correlation between transmitter and receiver. Figs 4-22 presents the maximum, minimum and mean values for each propagation of different bandwidth of routes. Similar results of MIMO capacity versus signal bandwidths can be found in the figures 4-23, 4-24 and 4-25 to stand for route no.2, route no.3 and route no.4, respectively.
Fig 4-21 The capacity versus signal bandwidths for three propagation conditions LOS, OLOS and NLOS along route no.1
Figs 4-22 The maximum, minimum and mean values for three propagation conditions LOS, OLOS and NLOS of different bandwidth along route no.1
Fig 4-23 The capacity versus signal bandwidths for three propagation conditions LOS, OLOS and NLOS along route no.1
Fig 4-24 The capacity versus signal bandwidths for three propagation conditions LOS, OLOS and NLOS along route no.3.
Fig 4-25 The capacity versus signal bandwidths for three propagation conditions LOS, OLOS and NLOS along route no.4.
4.3.2 Angle Spread Effect
From Table-3 we realize the fact that capacity and azimuth spread of AOA present a positive correlation shown as Fig 4-23, but indifferent with azimuth spread of AOD. Azimuth spread of AOA means the angle dispersion caused by multipaths propagating in the channel owing to ground reflection wave, corner diffracted wave, scattered wave etc. These mulitpaths can disturb the propagation channel of signals resulting in the transmitted signal received by array less correlated, even uncorrelated.
But angular spread of AOD means the angular dispersionness from transmitter; it does not yet propagate through MIMO channel to interference the capacity, hence the azimuth spread of AOD does not present obvious correlation with capacity. The condition hold for site2, site3 and site4, we note that the capacity of LOS in site1 is smaller than that of site2, site3 and site4, since scatters existed in the environment and site1 is LOS with open-area, short distance but for the site2, site3 and site4 cases, we can resolve the scattered wave in terms of time resolution and azimuth resolution to
observe how the channel interfered by the scatters shown Fig 4-24. Figure 4-24 provides the Delay-Azimuth Spectrum of measurement data and the resolved scattered wave (*) on the time and azimuth resolution and CDF of capacity for subchannels and eigenvalue distribution of measurement for site2 (a), site3 (b) and site4 (c) since we have realized the impact of propagation on capacity. While we compute the number of scatter waves, an assumption of single bounce is made. From the number resolved, Site2-28, Site3-59, Site4-89, we realize the scattered waves impinged on transmitter more, the propagation channel decorrelated more, hence the capacity will have a significant improvement.
Table-3 the mean capacity, standard deviation of capacity, standard deviation of rms of azimuth spread of AOA and standard deviation of rms of azimuth spread of AOD
for all measurement sites.
Site3
Fig 4-26 (a) capacity versus rms azimuth spread of AOA for route no.1
Fig 4-26 (b) capacity versus rms azimuth spread of AOA for route no.2
Fig 4-26 (c) capacity versus rms azimuth spread of AOA for route no.3
Fig 4-26 (d) capacity versus rms azimuth spread of AOA for route no.4
Fig 4-27 (a)
Fig 4-27 (b)
Fig 4-27 (c)
Figure 4-27 the Delay-Azimuth Spectrum of measurement data and the resolved scattered wave (*) on the time and azimuth resolution and CDF of capacity for subchannels and eigenvalue distribution of measurement for (a) route no.2 (b) route
no.3 and (c) route no.4.
Chapter 5 Conclusion distance, bandwidth and angular spread are also considered. The measurement using the RUSK channel sounder was carried in the National Chiao-Tung University campus.
As far as propagation conditions are concerned, the capacity in the NLOS condition ensures a high probability to be larger than the LOS and OLOS conditions due to larger angular dispersion. As for MIMO system with the same element spacing located at different routes, capacity increases due to transmitted signals disturbed by the local scatter so that the spatial correlation of receiving signals decreases.
Environment must be complex enough to disturb the spatial correlation of receiving signals so that capacity becomes larger.
For the different element spacing effect, capacity of MIMO system under particular site increases due to the resolution of multipaths seen from the receive end array increases. From hybrid model, we know that local scatters surrounded by the transmit end array will cause large capacity fluctuation.
For the bandwidth effect, MIMO capacity will increase as the signal bandwidth increases. This phenomenon is hold for each route under this measurement.
angular spread of AOA increases since the multipaths propagated within larger rms angular spread of AOA probably experienced complex channel so that disturb the spatial correlation of signals. Finally, we evaluate the complexity of the channel influenced by local scatters using the number of resolved scatter waves based on temporal and angular resolution.
References
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