ECS455 Chapter 2 Cellular Systems

Transcription

1 ECS455 Chapter 2 Cellular Systems 2.2 Co-Channel Interference r.rapun Suksompong prapun.com/ecs455 Office Hours: BK Tuesday 9:30-0:30 Tuesday 3:30-4:30 Thursday 3:30-4:30

2 Co-Channel Cells: Ex. N = 3 2

3 Co-Channel Cells: Ex. N = 3 We can locate its co-channel cells by using the recipe in the previous section. These cells are called cochannel cells in the first tier. 3

4 Co-Channel Cells: Ex. N = 3 The recipe can be applied to each cell in the first tier to find even more co-channel cells. These additional cells are called co-channel cells in the second tier. 4

5 Co-Channel Cells: Ex. N = 3 5 The recipe can be applied to each cell in the first tier to find even more co-channel cells. These additional cells are called co-channel cells in the second tier.

6 Co-Channel Cells: Ex. N = 3 6

7 Co-Channel Cells: Ex. N = 3 7

8 (Intercell) Co-Channel Interference Frequency reuse co-channel interference Consider only nearby interferers. B ower decreases rapidly as the distance increases. In a fully equipped hexagonal-shaped cellular system, there are always K = 6 cochannel interfering cells in the first tier. C C B B C C C B B C C B B 8

9 Three Measures of Signal Quality For noise-limited systems, SNR Consider both noise & interference: r noise SINR r interference noise 9 The best cellular system design places users that share the same channel at a separation distance (as close as possible) where the intercell interference is just below the maximum tolerable level for the required data rate and BER. Good cellular system designs are interference-limited, meaning that the interference power is much larger than the noise power. SIR r interference

10 Reliable vs. tolerable? (Why not as far as possible?) Co-channel cells, must be spaced far enough apart so that interference between users in co-channel cells does not degrade signal quality below tolerable levels. Subjective tests found that people regard an FM signal using a 30 khz channel bandwidth to be clear if the signal power is at least sixty times higher than the noise/interference power. 0log db 0 [Klemens, 200, p 54] 0 We will soon revisit and use these numbers for some more specific calculations

11 Review: Simplified ath Loss Model r t d0 K d 0 K is a unitless constant which depends on the antenna characteristics and the average channel attenuation d 0 is a reference distance for the antenna farfield Typically -0 m indoors and 0-00 m outdoors. γ is the path loss exponent. 2 in free-space model 4 in two-ray model [Goldsmith, 2005, eq. 2.7] r Kd t d d Captures the essence of signal propagation without resorting to complicated path loss models, which are only approximations to the real channel anyway! [Goldsmith, 2005, Table 2.2]

12 Caution: Not the same as the K shown on the previous slide SIR (S/I): efinition/calculation K = # co-channel interfering cells The signal-to-interference ratio (S/I or SIR) for a mobile receiver which monitors a forward channel can be expressed as SIR r interference of the i interferer r = the desired signal power from the desired base station i = the interference power caused by the ith interfering cochannel cell base station. Often called the carrier-to-interference ratio: CIR. K i r th 2 [Rappaport, 2002]

13 3 SIR: N = 3

14 SIR: N = 3 3R 2 7R 3 2R 4R 7R 3R R 2 Consider only cells in first tier. Worse-case distance k R SIR k i i i i i R i R (Ignore co-channel cells that are too far away) R 2 If N = 9, will the SIR be better or worse? 4

15 SIR: N = 3 SIR d = distance between MS and BS k d k i i i i i d i d SIR: N = Observe that the SIR value is smallest when MS is at any of the corners of the hexagonal cell. t such locations, d = R (the cell radius) Centers of cochannel cells when N = 3 5

16 SIR: N = 3 vs. N = 7 SIR: N = SIR: N = SIR: N = SIR: N = Centers of cochannel cells when N = 3 Centers of cochannel cells when N = 7

17 pproximation Consider only first tier. Worse-case distance SIR i i R Use the same for i 7

18 pproximation 8 Consider only first tier. Worse-case distance Use the same for i IR S i K R K R R Notice that /R is an important quantity! SIR i i R

19 Center-to-center distance () cos20 i R j R i R j R 2 2 R 3 i j ij R 3N j 3R 20 B i 3R This distance,, is called reuse distance. 9 2Bcos B ; cos Co-channel reuse ratio Q 3 N. R

20 Q and N Co-channel reuse ratio Q 3 N. R 20

21 pproximation: Crude formula 2 s the cell cluster size (N) increases, the spacing () between interfering cells increases, reducing the interference. interference of the interfer r e SIR 3 th K r r i i i i K R R R K N K

22 Summary: Quantity vs. Quality S = total # available duplex radio channels for the system ath loss exponent Capacity S total C cell N Tradeoff SIR K 3N Frequency reuse with cluster size N m = # channels allocated to each cell. 22

23 SIR: N = 7 Better approximation R SIR 2 R 2 R 2 2 Q 2 Q 2Q gain, Q 3 N. R 23

24 Comparison 28 SIR [db] SIR 6 i i R SIR Q N i SIR Q 2Q Q 24 Q R

25 SIR Threshold [Schwartz, 2005, p 64] The SIR should be greater than a specified threshold for proper signal operation. In the G MS system, designed for voice calls, the threshold for acceptable voice quality is SIR equal to 8 db. For the 2G digital MS system (-MS or IS-54/36), a threshold of 4 db is deemed suitable. For the GSM system, a range of 7 2 db, depending on the study done, is suggested as the appropriate threshold. The probability of error in a digital system depends on the choice of this threshold as well. 25