2013 IEEE Military Communications Conference

A Site-Specific MIMO Channel Simulator for Hilly and Mountainous Environments

Jonathan S. Lu and Henry L. Bertoni NYU WIRELESS Center Polytechnic Institute of New York University Brooklyn, New York, U.S.A. [email protected] and [email protected]

arrival and departure of each multipath arrival (direct, ground reflected, terrain scattered and terrain diffracted) between all TX and RX antenna pairs. The total phase of a terrain scattered arrival for an antenna pair, is determined by the propagation path length and additional phase incurred by scattering. Because available terrain databases have resolution (> 30m) larger than the UHF wavelengths (< 1m) considered in this work, the total phase cannot be deterministically known. Thus, the additional phase is modeled with a uniformly distributed random variable [5] and the path length is found from the geometry of the antennas with the center of the terrain element. Note that even though the total phase of this arrival cannot be deterministically known, the relative phases of this arrival between all antenna pairs are known from the different path lengths. After determining the multipath information of all arrivals, our simulator forms the MxN channel matrix in time or frequency domain. To demonstrate the use of the proposed simulator, we investigate the feasibility of MIMO communications in rural environments using Monte Carlo simulations of 2x2 MIMO radio links in many different types of terrain. An overview of the SISO channel simulator is presented in Section II. The methodology of our MIMO channel simulator is given in Section III, along with closed form expressions for the tapped delay line coefficients and channel frequency response in terms of the channel impulse response. The setup and procedure of the Monte Carlo simulations using our MIMO channel simulator is given in Section IV. The results of the Monte Carlo simulations are analyzed in Section V.

Abstract— This paper presents a real-time site-specific MIMO channel simulator for communication links in rural environments. This simulator first predicts the delay, angle of arrival and departure, and amplitude of the individual multipath arrivals (direct, ground reflected, terrain diffracted, and terrain scattered) for a specified multiple antenna receiver and transmitter link. The predicted multipath characteristics are then used to compute the tapped delay line coefficients and/or frequency responses of the channel between each transmitter antenna and receiver antenna pair, which are the outputs of the simulator. To demonstrate the use of this simulator, Monte Carlo simulations of SISO and MIMO channel capacity for many databases are performed. Conclusions are drawn on the relationship between capacity, terrain roughness and other channel characteristics. Keywords— MIMO Channel Modeling, Mobile, Mountainous Terrain, Rural Propagation, Terrain Scattering

I.

INTRODUCTION

Scattering from terrain can result in a rich multipath radio environment for radio links located in hilly or mountainous terrain [1]. To efficiently predict the multiple-input-multipleoutput (MIMO) channel in rural terrain for UHF band (300 MHz – 3 GHz) military communications, a real-time sitespecific MIMO channel simulator, which accounts for the scattering from terrain, was created from our previously developed site-specific propagation single-input-single-output (SISO) simulator. Previously proposed empirical MIMO channel models [2],[3] simulate the time domain channel in the form of tapped delay lines. The SUI channel model A [2] is the only one to consider hilly terrain. It was developed from 1.9 GHz measurements [4] taken in flat to hilly terrain with light to heavy tree density for fixed wireless applications. The transmit antenna heights in these measurements ranged from 12 to 79 m while the receive antenna height was 2 m. Because of the high antenna heights, relatively gentle terrain and fixed links, this model may only apply to specific radio scenarios in which the line-of-sight (LOS) is dominant. Thus, we have developed a real-time channel simulator which can apply to a greater range of radio scenarios and terrain, while accounting for the sitespecific environment. For a MxN MIMO link, where the mobile transmitter (TX) has N antennas and the mobile receiver (RX) has M antennas, our proposed simulator utilizes the previously developed SISO simulator [1] to predict the local area amplitude, and angles of 978-0-7695-5124-1/13 $31.00 © 2013 IEEE DOI 10.1109/MILCOM.2013.135

II.

RURAL ENVIORNMENT SISO CHANNEL SIMULATOR

In this section we provide an overview of the previously developed SISO channel simulator for rural environments [1]. This simulator is used to predict the local area RMS voltage amplitudes ap, angles of arrival and departure, and initial propagation delays Rp/c of the p = 0,1, .. P arrivals. Here c is the speed of light. A. Vertical Plane Model The Terrain-Integrated Rough Earth Model (TIREM) [6] is used to predict the received power from rays lying in the vertical plane (VP) containing the TX and RX. For line-ofsight (LOS) links, the dominant waves in the vertical plane travel along the direct and ground reflected paths.

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σ (θ1 , θ 2 ) = γ cos m (θ1 ) cos m (θ 2 ) ,

On non-LOS (NLOS) links where one or more ridges separate the TX and RX, radio waves diffract over the ridges. For one diffracting edge, TIREM uses Bullington’s approximation to the 4-Ray diffraction expression [7]. For multiple edges, the Epstein-Peterson method is used [8]. In both LOS and NLOS cases, waves scattered from the troposphere and surface waves are also accounted for [6]. At the higher frequencies and shorter ranges of interest here, these latter effects are not of importance. The RMS voltage amplitude a0 of the VP contribution is found by taking the square root of the TIREM predicted power. The delay of this VP arrival R0/c is also returned by TIREM. Note that in the case of LOS, there may be two rays, but the arrival time will be nearly equal since the separation between the antennas is usually large compared to the antenna heights relative to the ground. Parameters used for TIREM in our simulations are: Earth’s surface conductivity = 0.01S/m; Surface humidity near the antennas = 7.5 g/m3; Surface refractivity = 289; Relative permittivity of earth’s surface = 15; Polarization is VV.

and is seen to satisfy the symmetry condition. In this study we have chosen m = 1 and  = 0.1 (-10 dB) as in [1]. The value of  is independent of frequency when the wavelength is on the order of the surface roughness, or smaller [5]. Thus, aside from the weak frequency dependence associated with diffraction, the ratio of the scattered power to VP power will be nearly independent of frequency in the UHF band where wavelength is less than the expected surface roughness. C. Terrain Visibility Algorithm To apply the bi-static equation (1) to a radio link, we have developed an efficient visibility (viewshed) algorithm to search for the terrain elements visible to both the TX and RX viewshed algorithm. A detailed description of our algorithm can be found in [1]. To increase processing speed of the algorithm by taking advantage of fast integer operations, we approximate the TX and RX locations by their nearest terrain points (correcting for the effect of this assumption on delay and path length is discussed below). Along with “pre-treating” the terrain database, computation time of the terrain scattered contributions and vertical plane contributions is on the order of a mili-second.

B. Terrain Scattering Model For NLOS cases in mountainous or hilly environments, radio waves are expected to be very weak after diffracting over the mountains or hills between the TX and RX. In these cases, scattering from terrain elements visible to both the transmitter and receiver may give significant contributions. Terrain surfaces in hilly and mountainous areas are rough for frequencies in the UHF band. Thus incident radio waves on a terrain surface element are scattered into many directions in addition to the specular direction. For the case when P terrain surface elements have LOS with both TX and RX, the RMS voltage amplitude ap as a result of scattering from the pth terrain element is [5],[9]-[11]

ap =

Pt

λ 2 σ Ap . (4π ) 3 R p21 R p2 2

(2)

III.

RURAL ENVIORNMENT MIMO CHANNEL SIMULATOR

In this section, we present the methodology of our MIMO channel simulator for rural environments using the outputs of the SISO channel simulator discussed in Section II. This MIMO channel simulator predicts the MxN channel matrix in time domain and frequency domain when given the positions of a transmitter array (TX) with N antennas and a receiver array (RX) of M antennas in a terrain database. Also presented in this section are expressions for SISO and MIMO wideband channel capacity. These expressions are used later in our Monte Carlo simulations.

(1)

A. Channel Inpulse Response The (i, j) element of the time domain channel matrix is the baseband channel impulse response hij(t |c) between the ith RX antenna and the jth TX antenna. hij(t |c) can be approximated as a sum of impulses [12], [13] by treating each of the VP and the terrain scattered arrivals to arrive at distinct time intervals.

Here the TX and RX antennas are assumed to be isotropic (Antenna Gain = 1). Also, Rp1 and Rp2 are the distances in meters from the pth terrain element to the TX and RX antennas, respectively. They correspond to a propagation delay Rp/c = (Rp1 + Rp2)/c. The area of the pth terrain element is Ap and its normalized scattering coefficient is . Propagation paths that undergo two or more scatterings, or scattering plus diffraction are expected to be significantly weaker and are not considered. The bi-static scattering coefficient  of a surface element is dependent on the directions (1, 1) to the TX and the directions (2, 2) to the RX, the surface roughness compared to the wavelength, as well as the dielectric constant of the material. In order to satisfy reciprocity, the dependence of  on the two sets of directions must be symmetric. Measurements conducted on surfaces whose statistics are isotropic have found that  is nearly the same for both horizontal and vertical polarizations of the electric field, and the total scattered power depends on the angles 1,2 from the normal, but is independent of the azimuthal angles 1,2 [5]. The generalized Lambert’s Law is commonly used for the scattering coefficient. It is given by

P

hij (t ,τ | ωc ) = ¦ a p e p e jθ

− jωcτ ijp

e

jω p t

δ (τ − τ ijp ) .

(3)

p =0

Here p = 0 refers to the VP contribution from TIREM and p = 1,2, …, P refer to the terrain scattering contributions. Also, ap is the RMS voltage amplitude of the pth multipath ray, p is the additional phase caused by diffraction/scattering in radians, p is its Doppler frequency shift in Hz, and ijp is the propagation delay from the ith RX antenna to the jth TX antenna in seconds. c is the carrier frequency in Hz. As discussed previously, the phase p is modeled as a uniform random variable having values on the interval (0, 2]. This random distribution of the phase has been reported in [5].

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To determine the values of ap, p and ijp, the SISO channel simulator discussed in Section II, is fed the TX and RX positions inside a database. The simulator then returns ap, gridpoint to gridpoint delay Rp/c, and arrival and departure angles for each of the P + 1 multipath as if RX is located at its nearest grid-point and TX is located at its nearest grid-point. The amplitude ap is the square root of the power Pr(p) of the th p multipath and is the same for each TX-RX antenna pair (i, j). This approximation is valid because the separation of TX antennas and separation of RX antennas are all small relative to the multipath distances from the TX to RX. Furthermore, ap is assumed to be frequency independent over the UHF band as discussed in Section II.B. The delay of the pth multipath ray from the grid point nearest the TX array to the grid point nearest the RX array is Rp/c. To determine the delay ijp traveled by the pth multipath ray, we need to simply account for the additional delays caused by the distance offset ‫ݎ‬Ԧ௝ ȉ ݇ሬԦ௣்௑ Ȁห݇ሬԦ௣்௑ ห traveled by the ray from the jth TX antenna to the TX grid-point and the distance offset th ‫ݎ‬Ԧ௜ ȉ ݇ሬԦ௣ோ௑ Ȁห݇ሬԦ௣ோ௑ ห from the RX grid-point to the i RX as seen in th Fig. 1. Here ‫ݎ‬Ԧ௝ is a vector from the j TX antenna to the TX grid-point and ‫ݎ‬Ԧ௜ is a vector from the RX grid-point to the ith RX antenna. ݇ሬԦ௣்௑ Ȁห݇ሬԦ௣்௑ ห and ݇ሬԦ௣ோ௑ Ȁห݇ሬԦ௣ோ௑ ห are unit vectors in the direction of propagation that contain the angle of departure and angle of arrival information of the pth multipath ray output by the SISO simulator, respectively. Thus

τ ijp =

G G G G G G R p + r j
.

c

Rp 2 R p1

G rj TX

ω pij = 2π

c

e

e

jω p t

.

­ sin(π (τ − nTs ) / Ts ) ½ ¾dτ , (8) (π (τ − nTs ) / Ts ) ¿

³ h (t,τ | ω ) ®¯ ij

c

−∞

Substituting (3) into (8), we receive [13] gij( n ) (t | ωc ) = ¦ a p e p e jθ

− jωcτ ijp

e

jω p t

sinc(π (τ ijp − nTs ) / Ts ) . (9)

p

D. Channel Capacity From the channel frequency responses (6), the MIMO channel capacity, and the individual SISO capacities for each TX antenna and RX antenna pair can be computed. The wideband SISO channel capacity at a time t is found by sectioning the wideband channel into U narrowband channels of bandwidth W and then summing the capacities from each channel. Thus,

(5)

U −1

C (t ) = ¦W log 2 (1 + SNR(ωu , t )) .

(10)

u =0

Here, for the uth narrowband channel centered at carrier frequency u, the signal to noise power ratio SNR(u, t) seen at the receiving antenna can be written as the product of the transmit signal to noise ratio SNR0 and the channel frequency response H(=0, t | c=u) using the expression SNR(c, t) = SNR0|H(=0, t |c=u)|2. For the MIMO channel capacity between a TX of N antennas and a RX of M antennas [13], an expression can be similarly written in the form

B. Channel Frequency Response To arrive at a frequency domain expression for the baseband channel Hij(, t |c) between the ith RX antenna and the jth TX antenna, we simply take the Fourier transform of (3), so that jθ p − j ( ω +ωc )τ ijp

∞

gij( n ) (t | ωc ) =

Here ‫ݒ‬Ԧ்௑ and ‫ݒ‬Ԧோ௑ are the velocities of the TX and RX, respectively.

H ij (ω , t | ωc ) = ¦ a p e

RX

where Ts is the sampling period of yij(t,  | c), xj() is the transmitted signal and ݃௜௝ሺ௡ሻ ሺ‫ݐ‬ȁ߱௖ ሻ is the nth tap coefficient. ሺ௡ሻ ݃௜௝ ሺ‫ݐ‬ȁ߱௖ ሻ is defined as

(4)

.

G k pTX

G ri

Figure 1. Terrain scattering from kth visible terrain surface

The Doppler frequency shift ijp accounts for the mobility of the TX and RX term. From [13], it can be expressed in the form G G G G G G f ( vTX
G k pRX

(6)

p

U −1

C (t ) = ¦W log 2 (det( I + SNR0Q (ωu , t ))) .

C. Tapped Delay Lines The temporal channel impulse response hij(t,  | c) (3) between the ith RX antenna and the jth TX antenna can alternatively be represented as a tapped delay line. The received signal in time domain yij(t,  | c) is then expressed as

yij (t,τ | ωc ) =

+∞

¦ x (τ − nT ) g j

s

(n) ij

(t | ωc ) ,

(11)

u =0

If N ı M, Q = H(=0, t |c=u) H*(=0, t |c=u) and I is an identity matrix of order M. If N < M, Q = H*(=0, t | c=u)H(=0, t |c=u) and I is an identity matrix of order N. Note that H(=0, t |c=u) is a M x N matrix of the channel frequency responses and H*( =0, t | c=u) is its conjugate transpose.

(7)

n =−∞

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IV.

MONTE CARLO SIMULATIONS SETUP

1

To demonstrate the use of our simulator, Monte Carlo simulations of MIMO links are performed similar to [1] for terrain databases ranging from flat to mountainous. In the simulations TX and RX each have M = N = 2 isotropic antennas of height 1.8 m high with 1 m separation. They communicate at a 1 GHz carrier frequency (i.e., c = 2*109) with a 20 MHz bandwidth. The transmit power and thermal noise power over the bandwidth are 27 dBm and -101 dBm, respectively. The noise figure is 10 dB. To compute the capacity for a SISO link (10), transmit antenna ܴܵܰ଴ௌூௌை = 118 dB. Assuming an equal transmit power in computing the capacity for a MIMO link (11), ܴܵܰ଴ெூெை = 115 dB for each TX antenna. Results from these simulations are analyzed to determine the relationships between the SISO and MIMO capacities, and terrain roughness H and other channel parameters.

Height Mean [m]

Height STD H [m]

207.1 137.4 29.6 1081.7 188.5

127.6 113.7 5.9 225.7 143.7

Fraction of Valid Links

0.7

0.6

0.4

0

50

100

150 200 250 Terrain Roughness σH [m]

300

350

400

Figure 2. Fraction of links with path loss less than 150 dB versus terrain roughness H. B. Simulation Procedure For the simulation of a radio link located in an artificial database, a 6km x 6km square is placed at the center of the 10 km x 10 km database. A randomly selected point within the rectangle is generated as the TX location of the radio link. The RX location is chosen by randomly choosing a point on a circle of radius R centered at the TX location. The MIMO channel simulator described in Section III, then calls the SISO channel simulator described in Section II, to predict the multipath characteristics for this radio link. From these multipath characteristics, the elements of the channel matrix are then computed using (6). Expressions (10) and (11) are then used to compute the SISO and MIMO channel capacities, respectively. This procedure is carried out 200 times for link lengths R = 0.5, 1 ..., 7 km. This procedure is repeated for artificial databases of H = 5, 50, 100, 200 and 400 m created from those in Table I. Note that the 2 km wide zone about the 6x6km box allows for scattering from distant terrain elements having delays of more than 20 s. V.

MONTE CARLO SIMULATIONS RESULTS

Communication systems have a maximum tolerance for path loss in uplink and downlink. For example, in LTE, the uplink and downlink thresholds are about 163.5 dB [14]. While in HSPDA 3G, the thresholds are about 132.5 dB [15]. In the ensuing discussions, we will use a small area average path loss threshold of 150 dB. The small area average path loss for a link is found by incoherently summing the individual power contributions Pr(p) = ap2 of each arrival [16]. The fraction of links with path loss less than this threshold for each artificial database are plotted versus the H of that database in Fig. 2. Results are grouped by the natural database used to create them. These results are similar to those given in [1] where the probability and severity of terrain shadowing increases with H.

TABLE I NATURAL TERRAIN DATABASES

Arizona Caspian Fort Dix Nepal Washington

0.8

0.5

A. Artificial Terrain Databases The databases used in this work are matrices of terrain elevation samples over a uniformly spaced square grid. Table I lists six naturally occurring terrain databases of grid spacing GS = 90 m. The lateral extent of each database is approximately 10 km by 10 km. Also listed in Table I are the mean and standard deviation H of terrain height in meters. Here H is also called terrain roughness and is a terrain variability metric used to characterize the type of terrain (e.g. hilly, mountainous). Note that because the distribution of terrain heights is not symmetric about the average, 2H is typically greater than the mean height, even though none of the terrain is below sea level. An artificial database with any desired value of terrain roughness can be created from any of the databases in Table I by multiplying the height of all terrain points in a given database by a constant . The resulting artificial database has a terrain roughness H. By this process, artificial databases are created having values of H = 5, 50, 100, 200 and 400 m for all natural databases listed in Table I, which covers the range from rolling to mountainous terrain. We have chosen to use artificial databases so that the influence on the radio channel of the single statistical parameter terrain roughness ɐH could be studied. This choice is made in place of using various natural databases with different values of terrain roughness, so that the interpretation of the influence of ɐH is not clouded by the radio channel dependence on other statistical measures of the terrain.

Map Name

Arizona Caspian FortDix Nepal Washington

0.9

767

To determine the dependence of capacity on different channel parameters and terrain variability, we have chosen to focus on the results of the Fort Dix artificial databases. Note that analyses of results from other databases derived from those listed in Table I, give similar results. Quantitative differences in the analyses may arise from the higher order statistical measures of terrain variation described in [1]. The mean capacity of links having the same TX-RX separation in the H = 5 m (red triangles) and 100 m (blue squares) databases are plotted in Fig. 3. From Fig. 3, MIMO communications is seen to have an advantage over SISO, and the SISO and MIMO capacities are negatively correlated with TX-RX separation. This correlation stems from the decreasing channel gain due to distance dependent propagation loss and the increasing probability of shadowing. At larger distances, the mean capacity is greater for hilly terrain (H = 100 m) than for flat terrain (H = 5 m). This is due to the significant impact of terrain scattering present for hilly links which will be discussed later. To better show the advantage of MIMO communications, we introduce a capacity ratio. It is defined as the ratio of the MIMO capacity to the average of the four SISO capacities of a link. The capacity ratios predicted for links in the H = 5 m (red triangles) and 100 m (blue squares) databases are scatter plotted versus their small area average path losses in Fig. 4. It is seen that the capacity ratio of a link approaches 2 as the path loss increases. To analytically show this relationship, we investigate a narrowband link with one multipath arrival. For this case, the magnitudes of the all elements in the 2x2 MIMO channel matrix (6) are equal, while the phases differ due to the different propagation distances. If we let the path loss approach infinity or equivalently, the magnitude of the arrival approach 0, the logarithms in (10) and (11) can be replaced by first order linear approximations and the ratio approaches 2. This increase in capacity ratio is due to the power gain from having multiple antennas [13]. Thus, for cases in which there is a very dominant arrival relative to other arrivals, as is the case in flat terrain, but high path loss, the capacity ratio is 2. The results for hilly terrain in Fig. 4, show considerably more spread than results for flat terrain. Furthermore, the capacity ratios for H = 100 m at a given path loss are greater or equal to those for H = 5 m. This is also true for other databases of H > 5 m as shown by the median capacity (black diamonds) in Fig. 5. Note that in Fig. 5, each symbol is the median of the capacity ratio results for a database of H. From Figs. 4 and 5, the capacity ratio is found to be positive correlated with H. From Fig. 3, MIMO communications give higher channel capacity compared to SISO. Furthermore, as terrain becomes more mountainous, the use of MIMO is more advantageous as shown by the positive correlation between median capacity ratio and H in Fig. 5. As previously stated, this is due to the richer multipath environment (i.e., larger angle spread and smaller Rician K-Factor) caused by terrain scattering. Note that the K-Factor for a channel is the power ratio of the dominant arrival to all other arrivals. As the K-Factor approaches 0 (- dB), the small scale fading is Rayleigh distributed. To

1400 SISO σH = 5m MIMO σH = 5m

1200

Mean Capacity [Mbps]

SISO σH = 100m MIMO σH = 100m

1000

800

600

400

200

0

0

100

200

300 400 TX-RX Separation[m]

500

600

700

Figure 3. Capacity ratio versus path loss for Fort Dix H = 5 and 100 m databases.

FortDix σH = 5m

2

FortDix σH = 100m

Capacity Ratio

1.8

1.6

1.4

1.2

1 50

100 Path Loss [dB]

150

Figure 4. Capacity ratio versus path loss for Fort Dix H = 5 and 100 m databases. 2

Median Capacity Ratio

1.98

1.96

1.94

1.92 Arizona Caspian FortDix Nepal Washington

1.9

1.88

1.86

0

50

100

150 200 250 Height STD σH [m]

300

350

400

Figure 5. Median capacity ratio versus terrain roughness H.

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ACKNOWLEDGMENTS

emphasize the influence of a richer multipath environment, the coordinate invariant method for computing angle spread [16] is used to compute the angle spread for all simulated links in the Fort Dix H = 5 and 100 m databases. The angle spreads are plotted versus capacity ratio in Fig. 6. It can be seen that the range of angle spreads are larger for H = 100 m, than for H = 5 m and that the capacity ratio is positively correlated with angle spread. The Rician K- Factor are also computed for all simulated links in the Fort Dix H = 5 and 100 m databases and scatter plotted versus capacity ratio in Fig. 6. For links with Rician-K-Factor greater than 20 dB, we have truncated their values to 20 dB. For H = 5 m, the Rician K-Factors are all very high, which corresponds to negligible scattering from terrain and VP dominance. While for H = 100 m, the computed Rician K-Factors span a larger range of values and are negatively correlated with the capacity ratio.

The authors wish to express their appreciation and thanks to Dr. Hung-Quoc Lai formerly of CERDEC, U.S. Army for many stimulating discussions and helpful comments. This work was funded by the Wireless Internet Center for Advanced Technology (WICAT), NSF I/UCRC, Polytechnic Institute of New York University. REFERENCES [1]

[2] [3] [4]

VI.

CONCLUSION

In this work, we present a site-specific MIMO channel simulator for real-time channel prediction. This simulator considers propagation paths that lie in the vertical plane containing the TX and RX and those that are terrain scattered. We have demonstrated the use of this simulator by performing Monte Carlo simulations on 15 databases and computing the SISO and MIMO capacities. Results show that utilizing a MIMO system is usually advantageous compared to a SISO system. For flat terrain, MIMO systems benefit from power gain due to multiple antennas. In mountainous terrain, MIMO systems can better exploit the rich multipath environment caused by terrain scattering. This is shown by the positive correlation of median capacity ratio with terrain roughness and angular spread, and the negative correlation with Rician K-Factor.

Angle Spread [degrees]

60

[5]

[6]

[7]

[8]

[9]

[10]

60

50 40

[11]

50

σH = 5m

σ H = 100m

40

30

30

20

20

10

10

0

[12] [13] [14]

0 1

1.5

2

1

1.5

2

[15] [16]

K-Factor [dB]

20

20

10

10

σH = 5m

0

0

-10

-10

-20

1

1.5 Capacity Ratio

2

-20

σH = 100m 1

1.5 Capacity Ratio

2

Figure 6. Capacity ratio versus Rician K-Factor and angle spread for Fort Dix H = 5 and 100 m databases.

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