As discussed previously the SUI (Stanford University Interim) model can be used to calculate the path loss of a WiMAX link. The SUI model is given as:
- SUI Path Loss Equation
It has five components:
1. The free space path loss (A) up to the reference distance of ‘do’.
2. Additional path loss for distance ‘d’ with path loss exponent ‘n’.
3. Additional path loss (Xf) for frequencies above 2000 MHz.
4. Path gain (Xh) for receive antenna heights greater than 2 m.
5. Shadowing factor (s).
The most important factor in this equation is the distance dependent path loss. The impact of this factor is controlled by the path loss exponent ‘n’. It is well known that in free space the path loss exponent has a value of 2. In more realistic channels its value ranges anywhere from 2 to 6. For SUI model the path loss exponent is calculated as:
where a, b and c are SUI model specific parameters. It is obvious that the path loss exponent decreases with increase in base station antenna height ‘hb’. The path loss exponent for various antenna heights is shown below.
- Path Loss Exponent
It is observed that as the base station antenna height is varied from 10 m to 80 m the path loss exponent for the three scenarios varies from around 5.5-6.0 to 3.5-4.5. Basically what this means is that for higher base station antenna heights the cell radius would be larger. However we need to be careful when making this statement. Higher antenna heights also sometimes results in a weak signal area close to the base station. This is where the antenna downward tilt becomes an important factor. Antenna downward tilt usually has a value around 5-10 degrees. It is somewhat surprising that although it is such an important factor none of the well known empirical models take it into account.
Note: SUI Model was initially formulated based upon the data collected by AT&T Wireless across the United States in 95 existing macrocells at 1.9 GHz.
In the previous post we had compared the path loss of LTE at 728 MHz and 1805 MHz in a free space line of sight channel. This is a very simplistic channel model which tells us that ratio of the received signal strengths at these frequencies can be simply found as:
That is the received signal strength at 728 MHz is 6.15 times higher than the received signal strength at 1805 MHz.
Now let us consider a more realistic channel model known as the COST-231 model. According to this model the path loss (difference between the transmit power and receive power) is given as:
f=frequency in MHz (0.1500 MHz – 2000 MHz)
ht=base station antenna height in m (30 m – 200 m)
hr=mobile station antenna height in m (1 m – 10 m)
d=transmit receive separation in km (1 km – 20 km)
C=3 dB for metropolitan centres
and mobile station antenna correction factor is given as:
Using the above equations with ht=30 m, hr=1 m and d=1 km the path loss at 728 MHz and 1805 MHz is found out to be 100.63 dB and 114.00 dB respectively i.e. there is a gain of 13.37 dB when using the lower frequency. In simpler terms the received signal at 728 MHz would be 21.72 times stronger than the signal at 1805 MHz.
Such a remarkable improvement in signal strength or in signal to noise ratio (SNR) has the potential of increasing the throughput four folds. For example at an SNR of 1.5 dB QPSK 1/2 would give a throughput of 6.00Mbps whereas at an SNR of 14.7 dB a modulation coding scheme (MCS) of 64QAM 2/3 would result in a throughput of 24.01 Mbps.
Modulation Coding Schemes
It is quite well known that wireless signals travel further at lower frequencies. This phenomenon has become particularly important in the context of LTE where a frequency band has been allocated at 700MHz. We would like to quantify the benefits that can be achieved by using this frequency band.
Firstly we find the received signal power at 728 MHz (lowest downlink frequency) and at 3600 MHz (highest downlink frequency) in a free space line of sight channel. The transmit power is set to 1 W and omnidirectional antennas are considered at the transmitter and receiver. The received power for these two frequencies at a distance of 1000 m is found out to be -59.68dBm and -73.57dBm respectively i.e. there is a gain of 13.88 dB by using the lower frequency band. In simpler terms the signal power would be more than 20 times stronger at the lower frequency. This result can also be simply obtained by taking the square of the ratio the two frequencies.
(3600/728)^2 = 24.45
Similarly compared to a frequency of 1805 MHz, the signal at 728 MHz would be more than 6 times stronger.
(1805/728)^2 = 6.1474
Now we turn our attention to the penetration loss i.e. how much would the signal attenuate when passing through a concrete wall. For this we would have to calculate the attenuation constant (alpha) which is given as:
- Propagation Constant
Alpha, the attenuation constant is the real part of the propagation constant gamma whereas Beta, the phase constant, is the imaginary part. These quantities depend upon the frequency, relative permittivity, relative permeability and conductivity of the material. The penetration loss can then be found as -20*log10(exp(-alpha*thickness)). Using the properties of concrete the penetration loss at 728 MHz and at 1805 MHz is found out to be 4.16 dB and 10.38 dB i.e. there is a gain of 6.22 dB when using the lower frequency. In simpler terms the signal at the lower frequency would be more than 4 times stronger. We have considered a concrete wall of 10 cm thickness.
It is quite evident that the frequency of operation plays a big role in determining the propagation loss and the penetration loss. The frequency band of 728-746 MHz would thus be a prized commodity and operators would be willing to pay handsome amount to secure it.
1. We have ignored the reflection that occurs at the interface as its effect is comparably quite small.
2. Following were the material properties of concrete used in the calculation for penetration loss.
Relative permittivity = 4.5775
Relative permeability = 1.0000
Conductivity = 0.055
Relative permittivity = 4.1000
Relative permeability = 1.0000
Conductivity = 0.1300
Since our last post on Verizon LTE coverage within California, Verizon has removed the LTE Coverage Map from its site. Now it only gives a list of cities that have 4G LTE service (just like T-Mobile). So we now move from the West Coast to the East Coast i.e. Virginia. The state that is home to Virginia Tech, one of the finest schools in the country and a breeding ground for Wireless Engineers. It is thus somewhat of a shock to see that Verizon Wireless has no 4G LTE footprint in the state of Virginia. The only place that it intends to deploy 4G in near future is Bristol Virginia. It claims that by the end of 2013 it would have 4G coverage throughout the US where 3G service is currently available.
As in California T-Mobile has a much wider coverage with many smaller cities getting 4G service. The list includes: Alexandria, Mclean, Newport News, Norfolk, Petersburg, Portsmouth, Reston, Richmond, Roanoke and Lychburg. So although Verizon might be winning the speed race it is definitely not winning the coverage race (at least in CA and VA). And with AT&T T-Mobile merger also a possibility early next year Verizon is set to face some stiff challenge.
Given below are the results of a 4G speed test conducted by PC Magazine in the Northeast.
- 4G LTE Speed Test
The above results show that in areas where 4G coverage is available Verizon allows for average download speeds that are twice that of T-Mobile. The upload speeds are somewhat similar. Overall Verizon is by far the best in terms of the Mobile Speed Index, with T-Mobile in second spot and AT&T at third.
It’s very easy to get lost in the jargon when selecting a simulation tool for planning your wireless network. You will be faced with complex terminology which would not make much sense. You will be told that ray-tracing is the solution to all problems and outperforms all other techniques. However ray-tracing is only accurate when the following factors have been considered.
- Granularity of the terrain database
- Granularity in field calculations
- Accuracy in representation of building materials
- Accuracy in modeling the various propagation phenomenon
- Upper limit on the number of interactions