ECS455 Chapter 2 Cellular Systems 2.2 Co-Channel Interference r.rapun Suksompong prapun.com/ecs455 Office Hours: BK 360-7 Tuesday 9:30-0:30 Tuesday 3:30-4:30 Thursday 3:30-4:30
Co-Channel Cells: Ex. N = 3 2
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
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
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.
Co-Channel Cells: Ex. N = 3 6
Co-Channel Cells: Ex. N = 3 7
(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
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
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 60 7.78 8 db 0 [Klemens, 200, p 54] 0 We will soon revisit and use these numbers for some more specific calculations
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]
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]
3 SIR: N = 3
SIR: N = 3 3R 2 7R 3 2R 4R 7R 3R 5 6 4 3R 2 Consider only cells in first tier. Worse-case distance k R SIR k i i i i i R i R 2 7 2 3 2 4 (Ignore co-channel cells that are too far away) R 2 If N = 9, will the SIR be better or worse? 4
SIR: N = 3 SIR d = distance between MS and BS k d k i i i i i d i d 30 28 40 30 20 0 SIR: N = 3 0-2 -4 26 24 22 20 8 6 4 2 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). 0 3 2 0 - -2-3 4 2 0 Centers of cochannel cells when N = 3 5
SIR: N = 3 vs. N = 7 SIR: N = 7 40 40 35 30 25 SIR: N = 3 20 5 50 0 - -0.5 30 25 20 5 SIR: N = 7 35 30 0 0.5 0-0.5-0.5 40 0 SIR: N = 3 25 30 20-5 -0 20 0 0 5 0 6 4 2 0-2 -4-6 0 5 0 6 Centers of cochannel cells when N = 3 Centers of cochannel cells when N = 7
pproximation Consider only first tier. Worse-case distance SIR i i R Use the same for i 7
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
Center-to-center distance () 2 2 3 3 2 3 3 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 20 2 2 2 2 Co-channel reuse ratio Q 3 N. R
Q and N Co-channel reuse ratio Q 3 N. R 20
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
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
SIR: N = 7 Better approximation R SIR 2 R 2 R 2 2 Q 2 Q 2Q gain, Q 3 N. R 23
Comparison 28 SIR [db] 26 24 22 20 8 6 SIR 6 i i R SIR Q 6 4 2 0 8 2 4 6 8 0 2 4 6 8 20 N i SIR Q 2Q +- 2 2Q 24 Q R
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