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where US is the maximum power spectral density transmitted by S, GTS is the transmit gain of S in the direction of E, and GRE is the receive gain of E in the direction of S. It is assumed that the uplink and downlink propagation losses, LU and LD, are the same as those used for the interference signals. The transmission gain for network R is then defined as [ ] [URE] [URS] (13.16)
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Note that this is the same transmission gain shown in Fig. 12.9. Using the transmission gain, the interference I2 at the satellite may be referred to the earth-station receiver as I2, and hence the noisetemperature rise at the satellite receiver input may be referred to the earth-station receiver input as TS. This is illustrated in Fig. 13.9b. Expressed in decibel units, the relationship is [ TS
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[ TS]
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(13.17)
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13.4.3 Resulting noise-temperature rise
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The overall equivalent rise in noise temperature at earth-station E as a result of interference signals B1 and B2 is then T TS
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(13.18)
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In this final calculation the dBK values must first be converted to degrees, which are then added to give the resulting equivalent noisetemperature rise at the earth-station E receive antenna output.
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Example 13.6 Given that LU
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200 dB, LD 196 dB, GE G E 25 dB, GS G S 1 J, and U 10 J; 9 dB, GTE GRE 48 dB, GRS GTS 19 dB, US U S E calculate the transmission gain [ ], the interference levels [I1] and [I2], and the equivalent temperature rise overall. Using Eq. (13.14) gives [URS] 50 48 19 200
Solution
183 dBJ Using Eq. (13.15) gives [URE] 60 19 48 196
189 dBJ Therefore, [ ] 189 6 dB ( 183)
Interference
From Eq. (13.10), [I1] 60 9 25 196
222 dBJ From Eq. (13.12), [I2] 50 25 9 200
216 dBJ From Eq. (13.11), [ TE ] 222 6.6 dBK From Eq. (13.13), [ TS] 216 228.6 228.6 or TE 4.57 K
12.6 dBK From Eq. (13.17), [ TS
12.6 or TS
6.6 dBK
4.57 K
The resulting equivalent noise-temperature rise at the earth-station E receive antenna output is 4.57 4.57 9.14 K.
13.4.4 Coordination criterion
CCIR Report 454 3 (1982) specifies that the equivalent noise-temperature rise should be no more than 4 percent of the equivalent thermal noise temperature of the satellite link. The equivalent thermal noise temperature is defined in the CCIR Radio Regulations, App. 29. As an example, the CCIR Recommendations for FM Telephony allows up to 10,000 pW0p total noise in a telephone channel. The abbreviation pW0p stands for picowatts at a zero-level test point, psophometrically weighted, as already defined in connection with Table 13.1. The 10,000pW0p total includes a 1000-pW0p allowance for terrestrial station interference and 1000 pW0p for interference from other satellite links. Thus the thermal noise allowance is 10,000 2000 8000 pW0p. Four percent of this is 320 pW0p. Assuming that this is over a 3.1-kHz bandwidth, the spectrum density is 320/3100 or approximately 0.1 pJ0p (pW0p/Hz). In decibels, this is 130 dBJ. This is output noise, and to
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relate it back to the noise temperature at the antenna, the overall gain of the receiver from antenna to output, including the processing gain, discussed in Sec. 9.6.3, must be known. For illustration purposes, assume that the gain is 90 dB, so the antenna noise is 130 90 220 dBJ. The noise-temperature rise corresponding to this is 220 228.6 8.6 dBK. Converting this to kelvins gives 7.25 K.
13.4.5 Noise power spectral density
The concept of noise power spectral density was introduced in Sec. 12.5 for a flat frequency spectrum. Where the spectrum is not flat, an average value for the spectral density can be calculated. To illustrate this, the very much simplified spectrum curve of Fig. 13.10 will be used. The maximum spectrum density is flat at 3 W/Hz from 0 to 2 kHz and then slopes linearly down to zero over the range from 2 to 8 kHz. The noise power in any given bandwidth is calculated as the area under the curve, the width of which is the value of the bandwidth. Thus, for the first 2 kHz, the noise power is 3 W/Hz 2000 6000 W. From 2 to 8 kHz, the noise power is 3 (8 2) 1000/2 9000 W. The total power is therefore 15,000 W, and the average spectral density is 15,000/8000 1.875 W/Hz. The noise power spectral density over the worst 4-kHz bandwidth must include the highest part of the curve and is therefore calculated for the 0- to 4-kHz band. The power over this band is seen to be the area of the rectangle 3 W/Hz 4 kHz minus the area of the triangle shown dashed in Fig. 13.10. The power over the 0- to 4-kHz band is therefore (3 4000) (3 2) (4 2) 1000/2 11,000 W, and the spectral density is 11,000/4000 2.75 W/Hz. The units for spectral power density are often stated as watts per hertz (W/Hz). Expressed in this manner the units are descriptive of the way in which the power spectral density is arrived at. In terms of fundamental units, watts are equivalent to joules per second and hertz to cycles per second or simply seconds 1, since cycles are a dimensionless
Power spectrum density curve (see Sec. 13.4.5).
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