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**Chapter 2.****Theory**

* Link Margin*

**Introduction**

One of the most important aspects of designing a LMDS system or any other wireless communication system is the link margin. It would not be wise to design a system that is on the verge of failure. Therefore, all communication systems are over designed. In a LMDS system the amount of margin or over design required is determined by the desired link reliability.

**Percent Reliability**

LMDS links are generally designed to deliver a certain probability of outage due to rain. This however does not take into account outages from other sources such as equipment failure and power outages. Nevertheless, when taking into account link reliability, a dominant cause of an outage in an LMDS link is rain attenuation.

The microwave link designer determines from customer requirements what level of reliability is required for the link. The reliability is usually specified in a percent availability. Some typical availability values are 99.9, 99.99%, and 99.995%. When spoken these percent reliabilities might be called ‘three-nines’, ‘four -nines’, and ‘four – nines and a five’ respectively. Reliability can also be specified in percent outage, which is 100% minus the percent availability.

**Clear Weather Margin**

The clear weather margin is the amount by which the received signal strength exceeds the receive threshold during clear weather conditions. The clear weather margin and link distance allow the link reliability to be determined. When given the link reliability the maximum link distance can be determined by iteration.

**Receiver Sensitivity**

This specification is needed to calculate the link margin. The receiver sensitivity is the minimum signal required to obtain a particular bit error rate. This is usually measured for a pre-FEC (pre-forward-error-correction) BER (bit error rate) of 10^{-6}. With FEC, a near error free link is still achievable at this BER.

Different modulations schemes require different signal to noise ratios to achieve the same BER. For QAM (quadrature amplitude modulation) and PSK (phase shift keying) the required signal to noise ratio for the same BER increases and the spectral efficiency increases as the number of modulation levels increases.

Example LMDS receiver sensitivities for different modulations are shown in table 2.1 along with the corresponding theoretical E_{b}/N_{0}. The receiver sensitivity changes for different modulation schemes. This change is due to the increase in signal-to-noise ratio required to keep the same bit error rate at the modulation level increases.

** **

**Antenna Gain vs. Beamwidth**

In point-to-multipoint systems the antenna located at a subscriber site is typically a narrow beam parabolic dish antenna. The antenna located at a multi-point base station is generally a horn that allows coverage of a sector. The hub horn antenna can have different beamwidths in the horizontal and vertical directions. The horizontal beamwidths are typically 30, 45, or 90 degrees. The beamwidth in the vertical plane is typically much smaller as it is assumed that subscribers in the coverage area have similar elevations and anything radiated above building tops is wasted radiation. Typical values for the vertical beamwidth are 3 to 5 degrees.

The selection of the beamwidth is inversely proportional to the antenna gain and is an important selection in overall system design. Beamwidth selection becomes a tradeoff between the number of transmitters required to cover 360 degrees and the maximum link distance that can be achieved.

The vertical beamwidth geometry can limit both the maximum and minimum distances from the transmitter. The minimum and maximum distances can be found by simple trigonometry if the height (*h*) above the receiving antenna, the distance (*R*) from the base station, and the vertical beamwidth (*vbw*) are known. The downtilt angle (*t*) is typically specified as the angle below the level line to the horizon.

The beamwidth of the antenna is inversely related to the maximum gain of the antenna. The beamwidth can be varied in either the horizontal or the vertical dimension and the gain will vary inversely when either beamwidth is altered. For example, an antenna with a 30 degree beamwidth in the horizontal plane and a 3 degree beamwidth in the vertical plane has roughly the twice the gain when compared to an antenna with a 60 degree beamwidth in the horizontal plane and a 3 degree beamwidth in the vertical plane.

The following equation can be used to estimate antenna gain when given the horizontal and vertical beamwidths in degrees. The G is the antenna gain as a ratio, and the HP_{E}° and HP_{H}° are the half power bandwidths of the horizontal and vertical beamwidths.

Using a reference horn antenna we estimate its gain. The reference antenna with a measured gain of 22 dBi is specified to have a horizontal beamwidth of 30 degrees and a vertical beamwidth of 3 degrees. The estimated gain using this equation results in a gain of approximately 288.89 or 24.6 dB. It can also be seen that decreasing the beamwidth in a single dimension increases the gain by the same factor. Using the equation again we can find that an antenna with a 15 degree horizontal beamwidth and the same vertical beamwidth would have a gain of approximately 27.6 dB or twice the calculated gain of the reference antenna. This relationship results in a tradeoff between the antenna gain and the number of sectors required to cover 360 degrees.

**Free Space Loss**

As a radio signal travels through space the signal strength decreases at a rate of the square of the increase in distance. The equation to predict the power (*P** _{r}*) at the receiver is based upon the transmitted power (

*P*

*), wavelength of the signal (l), distance (*

_{t}*d*) between the transmitter and receiver, and the isotropic antenna gains of both the transmitter (

*G*

*) and receiver (*

_{t}*G*

*).*

_{r}**Rain Attenuation**

Organizations such as the ITU publish the amount of time a year that a particular rain rate is exceeded in a particular region [3]. This is the basis of calculating the needed margin when given the desired reliability.

This published rain rate data can then be turned into a probability distribution function that can show the probability of exceeding a particular rainfall rate during the entire year at a particular location. The link should be designed with enough link margin to continue to operate during this rain rate. The following equation can be used to calculate the amount of attenuation for a particular distance in kilometers. The *A* is the attenuation per kilometer due to rain and *r* is the rain rate in millimeters per hour.

Once the desired link reliability is chosen, data from rain measurements are used to determine the corresponding rain rate that is not exceeded for the same percentage of the time as the link reliability. This rain rate is converted into attenuation per kilometer using equation 2.7. The attenuation per kilometer is then multiplied by the effective link distance in kilometers to determine to attenuation due to rain at that rate. Links with a longer distance therefore require a higher margin to operate at the same reliability. The assumption that the effective link distance is equal to the actual link distance is used here. This assumption is valid for short links such as those considered here.

**Maximum Link Distance**

Once the desired reliability is known, it can be converted into a minimum required margin per kilometer. The transmitter power, receiver antenna gain, transmitter antenna gain, and receiver sensitivity can be used to iterate the maximum distance for the link to maintain that reliability. When rain margins are considered, the increase in radius gained from an increase in transmitter power is not as great. This is because as the link distance increases, the required margin also increases.

CHAPTER 1. INTRODUCTION

CHAPTER 2. THEORY

2.1 Link Margin

2.2 Amplifier Theory.

2.3 Predistortion Theory

CHAPTER 3. MEASUREMENT

3.1 Measurement Motivation

3.2 Measurement Procedure

3.3 Measurement Results

CHAPTER 4. SIMULATION

4.1 Simulation Overview

4.2 Simulation Design

4.3 Simulation Results

CHAPTER 5. APPLICATIONS TO LMDS

5.1 Proposed Multi-stage Implementation for LMDS

5.2 Implications of Predistortion for LMDS

5.3 Conclusions

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Adaptive Digital Predistortion with Applications for LMDS Systems