## Analysis of LightSquared’s New Proposal

In their latest proposal, LightSquared has offered some concessions to mitigate their impacts with GPS. They have offered the following adjustments to their technical design:

- Limit the received power within the region 50m to 500m to under -30 dBm
- Limit the degradation due to LS signals to under a 1 dB degradation in C/N0
- Move the satellite GPS augmentation signals to the upper portion of the MSS Spectrum (above 1,536 MHz), and offer filters with 40 dB rejection at 1,536 MHz

On the first item of their proposal, the analysis below shows that in free-space, the received power from a LightSquared tower will exceed -30 dB by as much as 21.5 dB (power received at 50m from a 62 dBW EIRP base station at a 10m antenna height). However, if the average loss is more urban-like (loss exponent of 2.7), the the received power drops to more than 3 dB below the -30 dBm limit they have set.

The FCC dictates that free-space loss be used in all calculations. However, urban environments are not free-space, actual attenuation is often larger than free-space. Such facts indicate that LightSquared is betting that propagation loss in excess of free-space is more likely, and they will not have to reduce their transmit power and reduce their transmit power. Although calculated, this is a risky bet. Measurements on GPS receivers made by LightSquared indicate that many general purpose GPS receivers perform well when subjected to LightSquared interference below -30 dBm with the exception of the precision GPS receivers that use augmented GPS information. This brings up the second and third aspects to their proposal.

It seems LightSquared has dropped their opposition to using a 1 dB drop in received GPS signal-to-noise ratio (or Carrier-to-noise density ratio, C/N0) as the bench mark for performance. This is a positive step forward. Many standards use a 1 dB criteria as the limit of harmful interference. In fact, some satellite regulations require interference be limited to a C/N0 degradation of less than 0.25 dB, so 1 dB is quite gracious. Furthermore, it is measurable.

The last point in their proposal is the effect of their carrier on the precision receivers. This is a more difficult issue as the receivers are designed to receive augmented GPS signals transmitted over satellites using the LightSquared frequency band. To solve this, LightSquared has proposed consolidating the GPS augmentation signals at the upper portion of their band, and supplying the precision GPS receivers with external filters that provide the needed rejection/attenuation of the LightSquared carrier in lower portion of the band. The analysis they present in their FCC proposal indicates that the degradation to precision receivers is limited, but the question remains if manufacturers and system operators (such as John Deere, Inc.) would accept such additions.

In short, *LightSquared has indeed made concessions by taking on more risk relative to interference with GPS receivers, such concession will make their system roll-out and set-up much more difficult/expensive. Furthermore, while LightSquared may now have a technically workable proposal for their initial roll-out, it still does not provide access to the upper portions of their spectrum in the long-term. If an agreement is not reached for that spectrum, LightSquared will have one-half the capacity their current business model assumes. Not a pretty picture for investors. *

**Analysis of Received Power Limitation to Below -30 dBm**

LightSquared has offered a maximum received power level of less than -30 dBm within a circle of 50m to 500m around its towers. This level seems currently based upon their latest test results of GPS receivers to their current frequency plan of using only the lower 10MHz portion of their spectrum.

In addition, a sectored antenna is assumed with a downtilt of 7 degrees.Below is an analysis that examines the received power levels at GPS receivers from three different height Light Squared

The plot below shows the region around the tower where LightSquared intends to limit the received power to less than -30 dBm. The minor ticks are every 10m showing the resolution to which LightSquared will measure the power levels.

Starting with the power limitation on the ground, we can write an equation for the received power, Pt=PrGv/FSL. This is the transmit power times the antenna pattern divided by the spreading loss (aka, free-space loss). The average propagation loss is a function of the distance from the transmit source, the frequency, and the average loss exponent. Free-space loss has a loss exponent of 2. The formula is shown below.

The distance from the transmit source may be determined from the Pythagorean theorem assuming the tower antenna height and the distance from the tower base.

Combining these two equations shows and plotting as a function of transmit antenna height (10, 20, and 30 meters), we have the following free-space propagation loss for the three tower antenna heights. As shown, there is little difference between the tower heights.

The plot shows that the loss across the area surrounding a tower varies from a minimum of 71 dB to over 90 dB. However, if the loss exponent is increased to 2.7, representing a suburban envioronment (urban environments have even higher exponents), the loss increases to 98 dB to over 120 dB (top, green line).

The maximum effective isotropic radiated transmit power (EIRP) for LightSquared is 62 dBm, and the following plot shows the maximum received power at a GPS receiver from a 20m tower along the 50m to 500m distance LightSquared has defined. The top curve (blue) shows the power received assuming free-space loss. Note that since the FSL nearly the same for the three tower heights, this is what typical interference calculations for GPS receivers would use. This shows a received power level of -8.8 dBm, or 21.2 dB higher than the -30 dBm specified by LightSquared’s proposal. However, if the environment is more like an suburban environment, the received power is -33.5 dBm, or 3.5 dB better than the -30 dBM in the proposal.

However, the situation is better when including the effects of a sectored cellular antenna. The antenna pattern will further attenuate the LS signal as the GPS receivers move closer to the tower.

A cellular antenna such as the Kathrein 724222 or 742223 has a 20 degree half-power beam width (HPBW), and the cellular operators typically point the antennas down to the ground (called a down tilt angle). Typical downtilt angles vary from 3 degrees to 8 degrees. For this analysis, 7 degrees is used. If we assume a parabolic elevation antenna pattern, then along the maximum azimuth pattern, the antenna directivity is shown below (*Downtilted Base Station Antennas –A Simulation Model Proposal and Impact on HSPA and LTE Performance*, Fredrik Gunnarsson, Martin N Johansson, Anders Furuskär, Magnus Lundevall, Arne Simonsson, Claes Tidestav, Mats Blomgren).

This antenna model assume a side-lobe level of -20 dB.

The geometric angle to the mobile terminal from the base station transmit antenna may be determined from simple trigonometry resulting in the following plot.

As shown, the angle to the GPS user is is below 32 degrees.

Combining the angle calculations into a antenna equation, and calculating the the received power to a GPS receiver results in the following equation( as a function of the distance from the tower). Plotting the equation for the various tower heights, frequency and loss exponent.

Plotting the above equation for three antenna/tower heights (10m, 20m, and 30m) shows that the received power when the antenna pattern is included. The worst case is for a 10m tower antenna height, 50m away with a received power of -8.5 dBm. Next is the 20m tower height with a received power of -10.6 dBm, and finally the 30m tower with -14.1 dBm. Notice, however, that the power levels increase above this within the 50m circle for the lower tower heights. This is also where one might expect free-space loss (exponent=2) to be more prevalent.

Increasing the loss exponent to 2.7, the received power is -33.1 dBm, -35.4 dBm, and -40.1 dBm for tower heights of 10m, 20m, and 30m, respectively.

Subtracting the -30 dBm from the above plot indicates the level of additional attenuation required for LightSquared to meet their proposed power limit. The plot below shows the maximum attenuation they would need to achieve (for free-space) is approximately 21.5 dB (10m antenna tower). This is a substantial reduction in power levels. However, if the loss exponent is increased from 2 (free-space) to 2.7, LightSquared actually has margin!

Note that this risk is mitigated by the probability that a GPS receiver will be within it 50 meter radius of the tower. If we assume that GPS receivers are uniformly distributed around the tower, we can calcuate the probability that GPS receivers are within the a particular distance from the tower. As shown, 99% of the users are further away than 50m, and 95% are more than 110m away from the tower.

**THE BOTTOM LINE.** This is the key point of LightSquared’s proposal. By shifting to received power, typcial interference analysis would indicate that LightSquared would have to reduce their power level by 21.5 dB to 40.5 dBm. However, by taking the risk that most areas will be experiencing something greater than free-space loss, LightSquared has a greater opportunity to operate at their current power levels. This is not incorrect reasoning, but it does involve a calculated risk. Flat, open regions that experience nearly free-space loss will indeed have to operate at reduced power, and in those regions, LightSquared will require more towers to cover the same area, or have to accept less capacity.

**Companion Receiver Analysis**

It’s insightful to examine how the received power from a LightSquared tower compares to typical GPS receiver characteristics. From this analysis, we can determine the internal attenuation that GPS receivers likely have to the lower LightSquared carrier. A usefull resource for GPS calculations is from National Instruments (http://zone.ni.com/devzone/cda/tut/p/id/7189). This states that a good value to use for the received power from GPS satellites is -136 dBm, and that typical receivers have a noise figure between 2 dB and 5 dB.

The GPS receiver sensitivity may be determined from the following equation.

Calculating the receiver noise density for a 10 dB noise figure:

This is equal to a receiver C/N0 of:

For a 1 dB degradation in C/N0, the required interference noise density (-5.8 dB from the receiver noise density)

If the interfereing LightSquared signal is received at the specified -30 dBm, or a noise density of -100 dBm (-30 dBm-10Log(10MHz), then nearly 76 dB of added attenuation is needed to achieve a 28 dB CNR. Such attenuation is possible when there are no intermodulation products created in the receiver front-end, and the receiver tests performed by LightSquared appears to support this. However, the situation requires even more receiver attenuation when we consider the expected maximum average received power calculated from above.

When the received power is incorporated with the required interference noise density produced by LightSquared’s carrier, the required receiver attenuation exceeds 90 dB when 50m from the tower.