strength in complex environments
6.12 Noise and temperature effects
When it is considered to be operating as a receiver, an antenna is thought of as a device that gathers signal power. It is also, however, a device that gathers noise power. Just as it gathers a signal dependent on the direction in which it is pointing, so it gathers noise power dependent on its dir- ection. Every molecule radiates radio noise. The amount of radio noise any molecule radiates depends upon its temperature. The noise gathered by an antenna therefore depends on the temperature of whatever it is looking at. This makes analysis quite simple for terrestrial links from one point of the Earth’s surface to another: everything that the antenna can see is at approximately the same temperature. When calculating noise, temperatures are recorded in degrees Kelvin (or ‘kelvins’). Note that, to obtain the temperature in kelvins, you simply add 273 to the temperature in centigrade. The noise power gathered by an antenna is then found to be kTB watts where k is Boltzmann’s constant (1.38· 1023 joules per kelvin), T is the temperature in kelvins and B is the system bandwidth in hertz. For terrestrial systems, a standard temperature of 290 kelvins (17C) is used to estimate the noise power entering the antenna. For a bandwidth of 10 MHz, the noise power would then be 1.38· 1023· 290· 107¼ 4.0 · 1014watts or104 dBm. This is known as thermal noise. It is this thermal noise that determines the fundamental limit on all telecommunications systems.
All receivers will add internally generated noise to that gathered by the antenna. The receiver is characterised by its effective noise tem- perature, Te. The total noise at the input can then be regarded as k(Tþ Te)
B watts. Calculations can then be carried out as if the receiver were perfect.
Determining the noise temperature for satellite Earth stations, or radio telescopes, is more complicated. The antenna is looking at deep space, whose temperature is as low as perhaps 4 kelvins, but there will be some atmosphere at a much higher temperature in the way. The effect of the intervening atmosphere on the noise temperature can be determined if its loss is known. Clouds etc. therefore have a double effect on such systems: they attenuate the wanted signal and add to the noise. Wherever possible,
radio telescopes are situated at high altitudes to minimise the atmospheric effects.
6.12.1 Noise calculations on Earth–space systems
When a signal from a satellite is received by an Earth station, the ratio of the wanted signal power to any unwanted power is a crucial parameter in determining the quality of any received signal. Thermal noise is a sig- nificant contributor to the unwanted power. The Earth station’s main beam is directed into space. Deep space has a temperature of only per- haps 4 K. The minimum possible noise power that it will gather in a bandwidth of B Hz is therefore kTB with T equal to 4. However, as well as gathering noise power through the main beam, some power will be gathered by side lobes that are directed at the Earth, which will have a much higher temperature. The total noise power is an aggregate of all these losses. Whilst the effect of side lobes will increase the total noise power gathered, the overall noise temperature is substantially increased by losses in the system. These can take the form of resistive losses in the antenna and feeder system and atmospheric losses, especially higher losses produced by clouds and rain in the atmosphere.
To understand the effect of resistive losses on noise temperature, it is necessary to conduct a thought experiment. Let us compare two matched systems with all input components at the standard temperature of 290 K. The first system has a lossless input and the only noise at the input is therefore kTB watts. Now, the term noise temperature is a useful way of predicting the signal-to-noise ratio at the output of a receiver. It has no physical meaning as such and certainly cannot be taken as an indication of the actual temperature of any element of a communications link. The second system has an attenuator at the input. The system noise will be exactly the same but the signal will be attenuated and thus the signal-to-noise ratio will be lower. This effect can be described by attributing a noise temperature to the attenuator. Suppose that the attenuator produced 2 dB of loss. This will reduce the signal-to-noise ratio by 2 dB. The effect is equivalent to the total noise power being increased by 2 dB. Since 2 dB is a ratio of 1.68, the total
effective noise power is 1.68kTB watts. Thus the effect of the attenuator is to add 0.68kTB watts to the total noise power. Thus the effective noise temperature of the attenuator equals 0.68T, where T is 290 K in this case. The general formula is that the effective noise temperature of an attenuator, Te, is given by
Te¼ ðL 1ÞT, ð6:38Þ
where L is the loss of the attenuator as a ratio (rather than in dB) and T is the temperature of the attenuator in kelvins.
If the loss is at the input of a receiver with a very low noise temperature, the effect of a small amount of loss can be dramatic. Amplifiers of very low noise temperature can be produced by cooling the components to a very low temperature, perhaps using liquid helium. Suppose that an amplifier had a noise temperature of only 40 K. Now consider the effect on the signal-to-noise ratio if resistive losses at the input amounted to 1 dB and the components producing these losses were at room temperature, 290 K. Since 1 dB is a ratio of 1.25, the noise temperature of the lossy component will be 0.25· 290 ¼ 73 K. Thus the noise temperature of the system will have increased from 40 K to 113 K because of these losses. This is an increase by a ratio of 2.8, or 4.5 dB. Thus the insertion of only 1 dB of loss has reduced the signal-to-noise ratio by 4.5 dB. In reality, this figure of 4.5 dB represents the fact that the attenuator will do two things: it will attenuate the signal and it will actually generate extra noise by the motion of its molecules that are at a higher temperature than the rest of the system. The reduction of 4.5 dB in signal-to-noise ratio incorporates both of these effects.
Let us consider now a highly sensitive Earth station whose main beam is pointed at deep space with a noise temperature of only 4 K, but with side lobes pointed at the Earth. The overall noise gathered by the antenna corresponds to a temperature of 30 K. However, resistive losses in the reflective parabolic dish and the feed system amount to 0.5 dB. The dish and feed are at a temperature of 290 K. Since 0.5 dB is a ratio of 1.12, the noise temperature caused by the losses is 0.12· 290 ¼ 35 K. Thus the total effective noise temperature is now 65 K, an increase by a ratio of 2.18, or 3.4 dB.
Suppose now that this level of resistive loss is accepted and the antenna system is regarded as having a noise temperature of 65 K. Let us suppose that a rain storm introduces 4 dB of loss. Loss produced by a rain storm is a resistive loss (the water molecules will generate thermal noise). Since 4 dB equals 2.5 as a ratio, the effective noise temperature is 1.5· 290 ¼ 435 K. The total effective noise temperature is 435þ 65 ¼ 500 K. The increase from 65 K to 500 K constitutes an increase by a factor of 7.7, or 8.9 dB. Thus rain attenuation of 4 dB would make the signal-to-noise ratio 8.9 dB worse.
When dealing with extremely sensitive receivers such as those used for radio astronomy, gaseous attenuation can become a significant factor in determining the performance of the receiving system. For this reason it is often seen as desirable for radio telescopes to be situated at high altitudes in order to minimise the amount of atmosphere between them and the celestial object under investigation.
6.13 Summary
The structure of the atmosphere can have a significant effect on the nature of the received signal in a radio link. The two major effects are referred to as ‘multipath propagation’ and ‘ducting’. Under conditions where multipath propagation occurs the received signal power can drop very suddenly by tens of dB. The probability of such fading of the signal occurring can be estimated using parameters such as path length, fre- quency, path inclination and a further climatic factor that depends on the location on the Earth’s surface. Ducting produces enhancements of signal strength at large distances (the effects are most noticeable beyond the horizon, where the signal strength is normally very low). Ducting is responsible for many incidences of interference over long-distance paths.
The effect of multipath fading can be mitigated against by deploying a diversity system. One common example, space diversity, entails using a second receiving antenna in the expectation that a deep fade will not simultaneously affect both antennas. Diversity-based systems are widely used on long-distance, high-capacity, microwave links because these
suffer from selective fading whereby the spectrum of the received signal becomes distorted.
Another significant atmospheric effect is that of attenuation due to rain. Below about 10 GHz, rain fading is not very significant, but, at higher microwave frequencies, it becomes the major factor limiting path length, particularly in areas that experience high levels of rainfall. Additionally, the atmosphere itself is not perfectly lossless. Again the effect increases with frequency, with particularly high levels of loss occurring at about 60 GHz.
Thermal noise presents a limitation to all communication systems. In radio systems thermal noise is gathered alongside the wanted signal by the receiving antenna. The amount of noise depends on where the antenna is pointed and the loss of the atmosphere. Thermal noise levels are lower when the receiving antenna is pointed into space, but atmos- pheric and system losses then degrade the noise performance of the system.
management
The test of the usefulness of the knowledge gained can best be deter- mined by undertaking some practical exercises that give an insight into problems encountered by radio system designers in the ‘real world’. Firstly, the value of propagation studies in helping to identify the most appropriate frequency for various services is discussed. The system design of microwave links at 10 GHz (at which multipath fading will dominate) and at 23 GHz (at which rain fading will dominate) is explained in some detail. The fact that many thousands of microwave links will be required in an industrialised country leads to a need for interference management, so this topic is introduced. Next, attention is turned to the design of broadcasting systems with a view to obtaining maximum coverage whilst investigating methods of limiting interfer- ence at great distances. Additionally, an example of designing a link to a geostationary satellite is presented. Finally, special methods needed for providing and predicting the signal strength for in-building systems are presented.