Effective Degrees of Freedom (EDOF)

The notion of multipath richness is less formal than capacity and there are several potential measures that could be used. Here, the concept of Effective Degrees of Freedom (EDOF) [2] will be used. This measure is based on the fact that for an N × N channel with rich multipath (fully decorrelated channel), a capacity increase of N bits is obtained when doubling the transmitted power. A correlated channel, i.e. a channel with fewer multipaths, will exhibit a smaller capacity increase. Hence, a convenient measure of the multipath richness is the slope of the capacity curve defined as

( )

2 ₌0

∂

= ∂ ^δ

ρ

_δ

δ ^C

EDOF

(2-7) By rewriting the capacity expression in (2-1) [9] as

( ) ∑

^{{ }}

Where

λ

_k denotes the singular values of the normalized channel matrix it is straightforward to calculate the derivative in (2-7)

( ) _∑

^{{ }}

The EDOF is then obtained as

{ }

Note that the EDOF is a real number in

[

^0,min

{

^{n ,}_T ⁿ_R

} ]

. A LOS channel with one dominant propagation path will yield an EDOF close to one while a rich NLOS channel will be close tomin

{

n ,_T n_R

}

. For channels in between these, the EDOF will essentially be the minimum of the number of transmit and receive antennas or the number of propagation paths with non-negligible strength [33]. Unfortunately, the EDOF measure depends on the SNR since the number of independent transmission channels that rise above the noise floor depends on the SNR. In this paper the EDOF will be calculated assuming a medium SNR of 10dB.

Chapter 3

Measurement System and Environment

In a typical indoor environment, due to reflection, refraction and scattering of radio waves by structures inside a building, the transmitted signal most often reaches the receiver by more than one path, resulting in a phenomenon known as multipath fading. In UWB pulse transmission, the effect is to produce a series of delayed and attenuated pulses (echoes) for each transmitted pulse.

In order to fulfill the requirement of higher data rates and capacities for future indoor wireless communications, numerous research programs are now underway and focused on evaluating and characterizing the wireless radio channel so that proper radio architectures with omni-directional UWB antennas on MIMO can be designed and implemented efficiently. This requires obtaining the channel characteristics in different environments, the UWB-MIMO channel measurement methods are proposed for analyzing each composition of multipath response. Later we will classify the propagation scenarios into following six categories:

1. LOS (Line-of-Sight) with light and heavy clutter (scenarios I and II).

2. NLOS (Non-Line-of Sight) with light and heavy clutter (scenarios III and IV).

3. LOS and NLOS in a guided environment such as corridors (scenarios V and VI).

3.1 Measurement System and Setup

In order to obtain the channel characteristics, the UWB channel measurement is performed to analyze the MPCs. An Agilent 8719ET Vector Network Analyzer (VNA) is

exploited to measure the channel response between two ends. The transmitted signal is sent from the VNA to the transmitting antenna through a low-loss 10-m coaxial cable.

For our measurement operation, we use a pair of omni-directional UWB antennas by Electro-Metrics (EM-6865), which frequency range is 2-18 GHz and antenna gain is 0dBi.

The signal from the receiving antenna is through a preamplifier (with a gain of 30 dB) via a low-loss 30-m coaxial cable and then returned to port 2 of the VNA. For UWB-MIMO application, the swept frequency band is from 3.5GHz to 4.5GHz (1GHz of frequency span).

With 1.25MHz steps corresponding to 801 points, we would be able to detect multipath with a time delay up to 800ns. Besides the network analyzer, the time-domain channel response can be obtained by taking the inverse Fourier transform (IFFT) of the frequency-domain channel response. Table 4 lists the main parameters in the measurement.

Because Agilent 8719ET is a SISO system with 2 omni directional antennas at both ends, we have simulated the 4x4 MIMO channels by moving the Tx and Rx to the ULA (Uniform Linear Array) fixed points. During the measurement, both the Rx and Tx antennas are at a height of 1.5m above the ground. And the measurement system that we used is shown in Figure 3-1, 3-2, 3-3.

Table 4 The main parameters in the measurement

Parameter Value

Frequency band 3.5GHz to 4.5GHz

Bandwidth (frequency span) 1GHz Number of points over the band 801

Transmitted power 10dBm

Preamplifier gain 30dB

Antenna gain 0dBi

Low loss cable Low loss cable

Low loss cable Low loss cable

Agilent 8719ET

Fig. 3-1 Block digram of the measured system

Fig. 3-2 A photo of the frequency domain channel sounding system

Fig. 3-3 A photo of the UWB antenna.

3.2 The Description of Measurement Environment

The measurement was performed in

1 floor (site A),^st 2 floor (site B and C), ^nd 7 ^th floor (site E), and 8 floor (site F) of the Microelectronics and Information System ^th Research Center (MISRC) and 2 floor (site D) of the 4^{nd th} Engineering Building at the National Chiao-Tung University, Hsinchu, Taiwan. The layout is shown in Fig. 3-4.

In order to compare the difference of capacity, EDOF and correlation for varied Tx-Rx distance in the scenarios I, II, III and IV, we do some measurement at site A, B and C. At site A, path 2 is measured at 1 floor of the MISRC and NLOS is always existed in path 2. ^nd At site B, path 1 is measured at 2 floor of the MISRC and LOS is always existed in path ^nd 1. At site C, both path 3 and path 4 are measured at Room 213 of the MISRC. And LOS is always existed in path 3. For instead of LOS, the NLOS exists in path 4. In the path 1, 2, 3, and 4, we take the samples when the Tx antenna array moves every 1m.

In order to analyze how the local scatterer affects the UWB-MIMO capacity and correlation in the scenarios I, II, III and IV, we carry out the measurement in site D. The Room 202 and 203 are all enclosed with concrete walls and wooden doors. All of them are clustered with wooden chairs. During the measurement, we don’t move these chairs to stand for the environment with local scatterers (scenarios II/IV). And then we move these chairs far away Tx, Rx to stand for the environment without local scatterers (scenarios I/III).

We adjust the element spacing of the virtual antenna arrays to investigate how the

capacity varies is with different antenna spacing in the scenarios I, II, III and IV. At P1, P2,

P3, P4, P5 and P6, both Tx and Rx antenna spacing is changed from 0.1λ to 2.0 λ . In order to know the difference between LOS and NLOS condition, we measure at P1, P3 &

P5 under the LOS condition, and P2, P4 & P6 under NLOS condition.

In order to compare with the difference of varied antenna array orientation in the scenarios II, IV, V and VI, we do some measurement at site E and site F. For each transmit antenna position, the complex transfer functions were recorded for 10 receive antenna positions, 5 positions with the broadside of the virtual antenna perpendicular to the LOS (orientation I) and 5 positions with the broadside parallel to the LOS (orientation II). The array broadside orientation is shown in Fig. 3-5.

The frequency response data have been exploited to analyze the UWB-MIMO channel characteristics. We observe the frequency response between 3.5GHz to 4.5GHz with 801 sweep points. Detailed measurement sites are shown in Table 5.

Fig. 3-4 (a) Site A: 1 floor layout of the Microelectronics and Information System ^st Research Center (MISRC)

Fig. 3-4 (b) Site B: 2 floor layout of the MISRC ^nd

v

Fig. 3-4 (c) Site C: Lab 213 layout of the MISRC

Fig. 3-4 (d) Site D: 2 floor layout of the 4th Engineering Building ^nd Rx

Fig. 3-4 (e) Site E: 7 floor layout of the MISRC ^th

Fig. 3-4 (f) Site F: Lab 810 layout of the MISRC

Tx Tx

Rx Rx

Tx Tx

Rx Rx

Fig. 3-5 Receiver antenna broadside (a) perpendicular (orientation I)

(b) parallel to the direct path (orientation II) (b)

(a)

Table 5 Measurement sites

Location Distance (Tx-Rx) Measurement

Scenarios

(Room 202, 203 of the 4th Engineering Building) Tx14-Rx6=3m Tx15-Rx6=7m

Chapter 4

Propagation, Array Arrangement and

Bandwidth on UWB-MIMO Capacity and Channel Correlations

To investigate the capacity and correlation properties of the UWB-MIMO channel under various propagation, array arrangement and bandwidth will be an interesting and important subject. In this chapter, the effects of propagation range, local scatterers, antenna spacing, array orientation and bandwidth on the UWB-MIMO capacity, EDOF and correlation are investigated through the measurement.

4.1 UWB-MIMO capacity, EDOF and correlations evaluation

From Eq. (2-2), the 4×4 MIMO capacity is given by

The capacity is calculated with

ρ

=10

dB

and the measured 4×4 UWB-MIMO channel matrix, T (i is the time or snapshot index), which is realized through the _i measurement by Agilent 8719 ET vector network analyzer. The normalized UWB

channel H was calculated from (2-3) and (2-4), where _i

η

^{^}_k is the normalization factor estimate.

From Eq. (2-10), the EDOF is then obtained as

{ }

And from Eq. (2-5) (2-6), the spatial correlation coefficient at Tx, Rx between elements are calculated.

4.2 Propagation Range Effect (Scenarios I/II/III/IV)

To investigate the propagation range effect on capacity, EDOF and correlations, we perform the measurement for a (4×4) UWB-MIMO system in two kinds of indoor environments: one in the lobby with light clutter (site A and site B) and another in the laboratory with heavy clutter (site C). We also consider the LOS and NLOS situation in two environments (scenarios I/II/III/IV). During the measurement, the antenna array broadside orientation direction is always perpendicular to the direct-path direction.

4.2.1 LOS with light/heavy clutter (scenarios I/II)

From Fig. 4-1 to fig. 4-2 illustrate the capacity, EDOF and correlations versus Tx-Rx distances in the LOS condition (scenarios I/II). By the chart of Fig. 4-1, we can find that in the scenario I, when Tx-Rx distance is in near distance, the capacity will be lower. But when distance is added to 10m, the capacity will not be changed obviously for distance increase. The reason is that because the Tx and Rx is very close, the correlations are relative higher at 1m, 2m and 3m (noted from Fig.4-1 (c) (d)). The LOS clutter strongly raises the correlation and then will cause the capacity reduced. In Fig. 4-1 (b) (EDOF vs.

distance) can find the same tread as Fig. 4-1 (a).

From fig. 4-2, we can find that capacity, EDOF and correlations are all similar for

various distances in the scenario II. The reason is that there are heavy clutters in the laboratory so that when the Tx-Rx is in near distance, multipath will increase (compare with the scenario I), then correlations are not as high as the scenario II.

(a) (b)

(c) (d) Fig 4-1 Measured results at site B (in LOS condition in scenario I)

(a) Capacity versus distance; (b)EDOF versus distance;

(c)

ρ

_Tx versus distance; (d)

ρ

_Rx versus distance

(a) (b)

(c) (d)

Fig 4-2 Measured results at site C (in LOS condition in scenario II)

(a) Capacity versus distance; (b) EDOF versus distance;

(c)

ρ

_Tx versus distance; (d)

ρ

_Rx versus distance;

4.2.2 NLOS with light/heavy clutter (scenarios III/IV)

Fig. 4-3, 4-4 illustrates the capacity, EDOF and correlations versus Tx-Rx distances in NLOS condition (scenarios III/IV). The main difference of Figs.4-1 (site B), 4-2 (site C) and Figs. 4-3 (site A), 4-4 (site C) is that there are many scatterers in the site C (compare with site A/B).

By the chart of Fig. 4-3, we note that in the near distance, there is not a great effect on distance change to capacity, but when distance is during 16~18m, the capacity is low. We can find the reason out in the LAYOUT chart (Fig. 3-5(a)). As Tx-Rx distance is in 16~18m, Tx enter to a wide space and the multipath which RX received is reduced, so that the correlation coefficient is increase and then capacity decreased. The chart of Figs.4-3(c) (d) is the correlation coefficient for Tx, Rx and from the chart we can find that when Tx-Rx distance is in 16-18m, the correlation coefficient is higher.

From fig. 4-4, we can find that capacity, EDOF and correlations are all similar for various distances in the scenario IV. The reason is same with situation II.

Due to above results, we can conjecture that capacity is dependent of Tx-Rx distance in LOS with light clutter, i.e. capacity is lower when Tx-Rx distance in small AS (Angular Spread) of AOA/AOD. But capacity is independent of Tx-Rx distance in the environment with heavy clutter, i.e. capacity is similar for any Tx-Rx distance when AS of AOA/AOD is large.

In addition, to compare Figs.4-1, 4-2, 4-3 and 4-4, we also can find that the capacity is higher under the environment that has scatterers around. With this phenomenon, we have a further discussion in the next section.

(a) (b)

(c) (d)

Fig 4-3 Measured results at site A (in NLOS condition in scenario III) (a) Capacity versus distance; (b) EDOF versus distance;

(c)

ρ

_Tx versus distance; (d)

ρ

_Rx versus distance

(a) (b)

(c) (d)

Fig 4-4 Measured results at site C (in NLOS condition in scenario IV) (a) Capacity versus distance; (b) EDOF versus distance;

(c)

ρ

_Tx versus distance; (d)

ρ

_Rx versus distance

4.3 Local Scatterer Effect (Scenarios I/II/III/IV)

In this section, we analyze that how the local scatterer affects the UWB-MIMO capacity and correlation. In the first, we carry out the measurement in the classroom (site D) and consider the LOS and NLOS conditions (scenarios I/II/III/IV). During the measurement, the antenna broadside direction is perpendicular to the direct path direction. The antenna spacing has 0.25, 0.5, and 1 wavelength.

Fig. 4-5 and fig. 4-6 show the capacity and correlations at two kinds of Tx-Rx distance under LOS condition (scenarios I/II). By the chart of fig.4-5(a), we can find that in the environment with local scatterers, the capacity is higher than the environment without local scatterers under any antenna spacing. And the same tread can be found as

well in fig. 4-6(a). The reason is that the local scatterer reflect more multipath, and more

multipath result in low correlation coefficient (noted from fig.4-5(b)(c), fig. 4-6(b)(c)) and then obtain higher capacity.

The measured result under NLOS condition (scenarios III/IV) is showed in fig. 4-7 and fig. 4-8. We also find the similar outcome as the aforesaid conclusion. So we can conjecture that the environment with heavy clutter will have higher capacity than with light clutter in LOS and NLOS condition.

Furthermore, capacity will be lower when antenna spacing is smaller than 0.5 wavelengths after compare above measured results. Because of this phenomenon, we take the further research in next section.

(a)

(b)

(c)

Fig. 4-5 Local Scatterers discussion under LOS condition in site D (scenarios I/II) (a) Capacity (b)

ρ

_Tx (c)

ρ

_Rx versus antenna spacing at Tx-Rx Distance=3m

(a)

(b)

(c)

Fig. 4-6 Local Scatterers discussion under LOS condition in site D (scenarios I/II) (a) Capacity (b)

ρ

_Tx (c)

ρ

_Rx versus antenna spacing at Tx-Rx Distance=7m

(a)

(b)

(c)

Fig. 4-7 Local Scatterers discussion under NLOS condition in site D (scenarios III/IV)

(a) Capacity (b)

ρ

_Tx (c)

ρ

_Rx versus antenna spacing at Tx-Rx Distance=3m

(a)

(b)

(c)

Fig. 4-8 Local Scatterers discussion under NLOS condition in site D (scenarios III/IV)

(a) Capacity (b)

ρ

^Tx _(c)

ρ

_Rx versus antenna spacing at Tx-Rx Distance=7m

4.4 Antenna Spacing Effect (Scenarios I/II/III/IV)

In the UWB-MIMO system, channel capacity may be improved by adaptively changing the element spacing. Changing the element spacing is a way to provide spatial diversity to a MIMO link without increasing the number of antenna array elements [17].

In this section, we adjust the element spacing of virtual antenna arrays to investigate how

the capacity varies is with small changes in element locations. During the measurement,

the measurement points from P1 to P6 have been selected to consider scenarios I/II/III/IV.

And the antenna broadside direction is perpendicular to the direct path direction.

Fig. 4-9(a) (b) (c) illustrates the capacity, Tx and Rx correlation coefficients versus antenna spacing for LOS condition respectively (scenarios I/II). For comparison, the capacity for a perfect Rayleigh channel is plotted. To this end, 10 random matrices with ⁶ independent, identically distributed complex numbers (normal distribution with zero mean and varianceσ =1) were generated and the averaged capacity was calculated. In the LOS condition, the capacity is low to 6.5 bps/Hz at 0.1λ spacing and dramatically rises to about 10 bps/Hz at 0.5λ spacing. Afterward, capacity grows slowly with the antenna spacing increasing. Both

ρ

_Tx and

ρ

_Rx decrease with antenna spacing increasing.

Fig. 4-10(a) (b) (c) illustrates the capacity, Tx and Rx correlation coefficients versus antenna spacing for NLOS condition respectively (scenarios III/IV). In the NLOS condition, the capacity is low to about 7 bps/Hz at 0.1λ spacing and rise to about 10.5 bps/Hz at 0.5λ spacing. The capacity is not changed while antenna spacing is larger than 1λ.

From the result of this section, we can see that antenna spacing may affect UWB-MIMO capacity significantly under any environment (scenarios I/II/III/IV). And we can find that the capacity increases as the element spacing increases and it saturates when the spacing is larger than 0.5λ . This reveals that the correlation distance between the elements in indoor environments is about 0.5λ .

(a)

(b)

(c)

Fig. 4-9 (a) Capacity (b)

ρ

_Tx (c)

ρ

_Rx versus antenna spacing in LOS condition (P3 belong to the scenario I and P1、P5 belong to the scenario II)

(a)

(b)

(c)

Fig. 4-10 (a) Capacity (b)

ρ

_Tx (c)

ρ

_Rx versus antenna spacing in NLOS condition (P4 belong to the scenario III and P2, P6 belong to the scenario IV)

4.5 Array Orientation Effect

To investigate the array orientation effect on capacity and correlation, we perform the measurement for a (5×5) UWB-MIMO system in two kinds of indoor environments: one is in a corridor(site E, scenarios V/VI), another one is in a laboratory(site F, scenarios II/IV). During the measurement, two kinds of array orientation are considered: the antenna array broadside orientation direction is perpendicular (orientation I) and parallel (orientation II) to the direct-path direction [4] [18].

4.5.1 Measured results in the scenarios V and VI (corridor, site E)

In Fig. 4-11 and 4-12 (site E), the mean capacities for different array size (n_T =n_R) is shown. From Fig. 4-11, we observe a significant different between the capacities achieved by parallel and perpendicular arrays in all distance. The perpendicular array results in a higher capacity gain than the parallel array in LOS condition (scenario V).

This is because the perpendicular receiver array allows additional spatial dimensions of the UWB-MIMO channel by distinguishing between those scatterers on the opposite walls of the corridor with the same distance to the receiver array. The parallel array would be unable to distinguish between these ‘mirrored’ scatterers and hence capacity gain for orientation II is significantly lower. Fig. 4-13 shows the correlation coefficients for scenario V. As expected, the receiver correlation is higher when the broadside of the receive array is parallel to LOS in all distance because perpendicular array will distinguish more multipath, so can reduce the correlation coefficient. The transmit correlations are almost equal for two orientations.

The above effect is that we measured for LOS condition in the corridor (scenario V).

And now let us observe that in case of NLOS condition (scenario VI), whether the characteristic we measure is the same as LOS condition? Fig. 4-12 is the result of measured in the scenario VI. From fig.4-12, we find that orientation I results in a higher capacity gain

than orientation II. The reason is the same as above result. Fig. 4-14 shows the correlation coefficient for the scenario VI.

In addition, we also observe the capacity increases linearly with the number of antenna elements, indicating that there are a sufficient number of strong MPCs providing independent transmission paths for different data streams.

(a)

(b)

(c)

Figure 4-11 Capacity versus array orientations in the scenario V (site E, LOS) (a) Tx-Rx Distance=3m (b) Tx-Rx Distance=7m (c) Tx-Rx Distance=13m

(a)

(b)

Figure 4-12 Capacity versus array orientations in the scenario VI (site E, NLOS) (a) Tx-Rx Distance=13m (b) Tx-Rx Distance=17m

(a) (d)

(b) (e)

(c) (f)

Fig 4-13

ρ

_Tx and

ρ

_Rx versus array orientations in the scenario V (site E, LOS) (a)

ρ

_Tx Tx-Rx Distance=3m (d)

ρ

_Rx Tx-Rx Distance=3m

(b)

ρ

_Tx Tx-Rx Distance=7m (e)

ρ

_Rx Tx-Rx Distance=7m (c)

ρ

_Tx Tx-Rx Distance=13m (f)

ρ

_Rx Tx-Rx Distance=13m

(a) (c)

(b) (d)

Fig 4-14

ρ

_Tx and

ρ

_Rx versus array orientations in the scenario VI (site E, NLOS) (a)

ρ

_Tx Tx-Rx Distance=13m (c)

ρ

_Rx Tx-Rx Distance=13m

(b)

ρ

_Tx Tx-Rx Distance=17m (d)

ρ

_Rx Tx-Rx Distance=17m

4.5.2 Measured results in the scenarios II and IV (laboratory, site F)

Above-mentioned is the measured result in the corridor (scenarios V/VI), and then we observe the result in the laboratory (scenarios II/IV) below. Fig. 4-15 and 4-16 illustrate the capacity for both LOS and NLOS conditions in the laboratory (scenarios II and IV). From Fig. 4-15, in the far distance between Tx, Rx the capacity for orientation I is more than orientation II, but when the near distance between Tx, Rx, it is similar for both orientation. The reason for this phenomenon is that when the distance between Tx, Rx is far, the correlation coefficient will be drop. Therefore, when receiver array broadside parallel to the direct path will cause correlation coefficient increased, then capacity will be drop. But when the distance between Tx, Rx is near, the path of LOS is stronger than others. So both two orientations have high correlation coefficient, and then capacity is low equally. Fig. 4-17 shows the correlation coefficient in the scenario II.

From Fig.4-16 we can see that in the NLOS condition, the capacity is similar for both orientations in all distance between Tx and Rx. This is because no dominant path exists under NLOS scenarios where no additional spatial diversity can be obtained by changing the orientations. Fig. 4-18 shows the correlation coefficient in the scenario IV.

(a)

(b)

(c)

Figure 4-15 Capacity versus array orientations in the scenario II (site F, LOS) (a) Tx-Rx Distance=3m (b) Tx-Rx Distance=7m (c) Tx-Rx Distance=10m

(a)

(b)

(c)

Figure 4-16 Capacity versus array orientations in the scenario IV (site F, NLOS) (a) Tx-Rx Distance=3m (b) Tx-Rx Distance=7m (c) Tx-Rx Distance=10m

(a) (d)

(b) (e)

(c) (f) Fig 4-17

ρ

_Tx and

ρ

_Rx versus array orientations in the scenario II (site F, LOS)

(a)

ρ

_Tx Tx-Rx Distance=3m (d)

ρ

_Rx Tx-Rx Distance=3m (b)

ρ

_Tx Tx-Rx Distance=7m (e)

ρ

_Rx Tx-Rx Distance=7m (c)

ρ

_Tx Tx-Rx Distance=10m (f)

ρ

_Rx Tx-Rx Distance=10m

(a) (d)

(b) (e)

(c) (f) Fig 4-18

ρ

_Tx and

ρ

_Rx versus array orientations in the scenario IV (site F, NLOS)

(a)

ρ

_Tx Tx-Rx Distance=3m (d)

ρ

_Rx Tx-Rx Distance=3m (b)

ρ

_Tx Tx-Rx Distance=7m (e)

ρ

_Rx Tx-Rx Distance=7m (c)

ρ

Tx-Rx Distance=10m (f)

ρ

Tx-Rx Distance=10m

4.6 Capacity Loss

In this section, for a more in-depth analysis of the performance of UWB-MIMO systems at locations with high SNR and high antenna correlation, measurements were done to investigate the effects of SNR and antenna correlation on UWB-MIMO channel capacity. First of all, we define capacity loss (

C

_loss) as The capacity loss for different measurement is calculated for comparing the measured capacity and the optimum case at the same SNR.

In this section, for a more in-depth analysis of the performance of UWB-MIMO systems at locations with high SNR and high antenna correlation, measurements were done to investigate the effects of SNR and antenna correlation on UWB-MIMO channel capacity. First of all, we define capacity loss (

C

_loss) as The capacity loss for different measurement is calculated for comparing the measured capacity and the optimum case at the same SNR.

在文檔中 超寬頻多輸入多輸出系統模型之建構與量測 (頁 22-0)