Cascade Calculation
Basic Conception Conception KT (heat noise density): it is the noise caused by electron motion inside the equipment, which is intrinsic and only related to the temperature. K: a constant, equal to 1.38*10-23J/K T: absolute temperature 1W=1J/S, 1W=1000mW [K×T]=10lg(1.38*10-23*103*293)=-174dBm Here we suppose the temperature is 20 , i.e. 293K EdoPL (effective path loss): it is the loss between the output port of BTS and the input port of repeater Grep: repeater’s gain NFrep: repeater’s noise figure, the value is 4dB in the latter calculations NFbs: base station’s noise figure, the value is 5dB in the latter calculations B: system bandwidth, the value is 100KHz in the latter calculations N: receiver’s equivalent heat noise level ROT: raise over thermal
Why downlink noise is not cared On one hand, we consider the most adverse circumstances for downlink: Environment Noise: N0=10lg[KTB] =10lg[1.38*10-23*103*293*100*103]= -124dBm Repeater Downlink Noise Figure: NFrep=5dB Repeater Downlink Gain: 100dB EdoPL: 70dB So, repeater downlink noise upon repeater’s access N: N=-124+5+100-70=-89dBm, this is very low for handset. Cascade calculation
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On the other hand, we consider the S/N (signal-noise ratio, supposed to be 33dB): S/N=(S/N)’-NFrep=33-5=28>9 So, the signal-noise ratio here satisfies the GSM requirement. To sum up, we only consider the uplink noise here for repeaters’ cascade.
Chain Calculation One Level The repeater’s noise and environment noise are amplified by the repeater’s uplink gain and attenuated by the effective path loss, then transmitted to the BS’s uplink receiver. The whole process can result in the rising of noise level of the receiver, and worsen the sensitivity of the receiver. Let’s consider the simplest situation first, and set a model as following:
NFbs
Bout=40dBm
R1out=33dBm
Grep1
Grep2 R2in
R1in
L1
Repeater1
L2
Repeater2
Base Station
At first, we calculate the interference of repeater2 to the repeater1. Using the noise conversion, we add repeater1’s noise to the BS. At last, the conclusion can be made. The values needed here are according to the practice: Bout=40dBm, R1out=33dBm, R2out=33dBm, NFbs=5dB, NFrep=4dB, B=100K. The equivalent noise level of repeater2 to repeater1: N2=K*T*B+NF2+G2–L2, according to the given value above, G2=L2 N2=K*T*B+NF2=-124dBm+4dB=-120dBm Cascade calculation
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ROT2=10lg[(10N2/10+10N1’/10)/10N1’/10]=10lg[10e(N2-N1’)/10+1]=3dB The equivalent noise level of repeater1 to BS: N1=K*T*B+NF1+G1–L1+ROT2, According to the given value above, L1=G1+7dB N1= -124dBm+4dB+3dB–7dB= -124dBm ROT1=10lg[10e(N1-Nbs’)/10+1]=10lg[10(-124-(-124+5))/10+1]=1.19dB Conclusion: the repeaters’ accession makes the noise level received by BS’s receiver increase 1.19dB, and leads to the receiver sensitivity decrease 1.19dB, which makes BS coverage area decrease approximate 6%. In practice, we usually make the first repeater’s downlink gain 5dB higher than its uplink gain, so: N1= -124dBm+4dB+3dB–7dB–5dB= -129dBm ROT1’=10lg(100.1+1)=0.41dB Conclusion: the receiver’s sensitivity decrease 0.41dB, and the coverage area reduces just a little.
More Than One Level Let’s set another model as following, and analysis this system in the same way
NFbs
Bout=40dBm
R1out=33dBm
Grep1 NF
Grep2 NF
Repeater1
Base Station L1
R2out=33dBm
Grep3 NF
Repeater2 L2
Cascade calculation
Repeater3 L3
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The equivalent noise level of repeater3 to repeater2: N3=K*T*B+NF3+G3–L3, similarly G3=L3 N3=K*T*B+NF3=-124dBm+4dB=-120dBm ROT3=10lg[(10N3/10+10N2’/10)/10N2’/10]=10lg[10e(N3-N2’)/10+1]=3dB The equivalent noise level of repeater2 to repeater1: N2=K*T*B+NF2+G2–L2+ROT3, similarly G2=L2 N2=-124dBm+4dB+3dB=-117dBm ROT2=10lg[(10N2/10+10N1’/10)/10N1’/10]=10lg(100.3+1)=4.76dB The equivalent noise level of repeater1 to BS: N1=K*T*B+NF1+G1–L1+ROT2, similarly L1=G1+7dB N1=-124dBm+4dB+4.76dB-7dB=-122.24dBm ROT1=10lg[(10N1/10+10Nbs’/10)/10Nbs’/10]=10lg(10-0.324+1)=1.69dB Conclusion: the repeaters’ accession makes the noise level received by BS’s receiver increase 1.69dB, and leads to the receiver sensitivity decrease 1.69dB, which makes BS coverage area decrease approximate 17%. That is unacceptable! We can make the repeater’s downlink gain 5dB higher than the uplink gain. Now we can set in three ways: set repeater3, set repeater2, or set repeater1. The results are: If set repeater3, ROT1=1.46, coverage area decreases approximate 12%. If set repeater2, ROT1=1.00, coverage area decreases approximate 5%. If set repeater1, ROT1=0.61, coverage area decreases just a little. The calculation about the relationship between ROT and the decrement of BS coverage range is very complex and beyond our discuss here, but we could give an experience table as following:
Cascade calculation
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Values
Items Increment of ROT (dB)
0.61
1.19
1.46
1.69
1.76
2.00
2.54
Decrement of coverage (%)
Little
6
12
17
20
30
40
Star Calculation Now it is the case of 1 front repeater and 4 back repeaters (assuming the output of front repeater is the same with above, and its downlink gain is 5dB higher than uplink gain), we set a model as following:
NFbs
Bout=40dBm
R1out=33dBm
B
Grep1
Grep21 R2in
R1in
L1
Repeater1
L21
Repeater21
Base Station
L21
L21
L22
Grep24
Grep23
Grep22
Repeater2
Repeater2
Repeater22
The equivalent noise level of 4 back repeaters to 1 front repeater: N2’=N2+10lg4=-114dBm (assuming the four back repeaters are just the same) Cascade calculation
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ROT2’=10lg[(10N2’/10+10N1’/10)/10N1’/10]=6.97dB The equivalent noise level of front repeater to BS: N1’=K*T*B+NF1+ROT2’+Grep1-EdoPL=-124+4+6.97-7=-120dBm ROT1’=10lg[(10N1’/10+10Nbs’/10)/10Nbs’/10]=2.54dB Conclusion: the repeaters’ accession makes the noise level of BS increase 2.54dB, and its coverage area reduce as much as 40%. Obviously, it is unacceptable! We can make every back repeater’s uplink gain reduce 5dB, in this case: The equivalent noise level of 4 back repeaters to 1 front repeater: N2’=N2+10lg4-5=-119dBm ROT2’=10lg[(10N2’/10+10N1’/10)/10N1’/10]=3.54dB The equivalent noise level of front repeater to BS: N1’=K*T*B+NF1+ROT2’+Grep1-EdoPL=-124+4+3.54-7=-123.46dBm ROT1’=10lg[(10N1’/10+10Nbs’/10)/10Nbs’/10]=1.33dB Conclusion: the repeaters’ accession makes the noise level of BS increase 1.33dB, and its coverage area reduce approximate 10%. Attention: in the case of cascading many back repeaters, to avoid the uplink interference, we can set the repeaters’ downlink gain higher than the uplink gain. But the difference between downlink and uplink must be less than 10dB. If the back repeaters are not the same, we should re-analyze. And the discursion process will be the same.
Cascade calculation
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