Analysis of Uplink Power Control in Cellular Mobile Systems

Transcription

1 University Comnet A!Aalto Wireless Networks Research Seminar-NETS 2020 Analysis of Uplink Power Control in Cellular Mobile Systems U. Oruthota, P. Dharmawansa and O. Tirkkonen Aalto, Department of Communications and Networking University of Oulu

2 A! Outline Introduction Fractional power control model Objective System model SINR of a user Average inverse interference and bounds Average interference of a cell Rate approximation Selection of FPC parameters Conclusion FPC 2 (18) University of Oulu

3 A! Introduction: Why Uplink Power Control? To determine the appropriate transmit power to achieve acceptable link performance while minimizing inter-cell/intra-cell interference and preserving mobile terminal battery power 3GPP has approved the use of Fractional Power Control (FPC) which compensates a fraction of the path-loss to makes users with a higher path-loss operate at a lower SINR while minimizing the interference to neighbours. Baseline Research study: Coupechoux and Kelif 1 derived an analytical expression for the average interference caused by neighbouring rings of interfering cells with uniform user distribution by assuming homogeneity in the angular domain, when seen from the center cell. Our Attention: Analysing the SINR of a user in a cell which suffers from random interference sources from neighbouring cells in a network without angular homogeneity. 1 M. Coupechoux and J. M. Kelif, How to set the fractional power control compensation factor in LTE?, Sarnoff Symposium, th IEEE, May FPC 3 (18) University of Oulu

4 A! FPC Model We consider simplified per PRB Fractional Power Control { } P t = min P m, P 0 + αl P m maximum allowed transmit power of an UE, depends on UE class P 0 cell specific initial power assignment α fractional power control parameter L is downlink path loss estimated at UE in dbm P 0 and α are cell specific parameters assigned by upper layers. Single slope path-loss model L = K λ log 10 r where K 0 is the path-loss at cell radius R = 1km, λ is the path-loss exponent and r is the normalized distance to user from its serving base station. FPC 4 (18) University of Oulu

5 A! Objective In this study: Derive an approximation for the average rate. For this, distributions of inverse interference have to be treated Target: Control of fractional control parameters (P 0, α) for individual cells to handle their current loads. Deliverable: U. Oruthota, P. Dharmawansa and O. Tirkkonen, Analysis of Uplink Power Control in Cellular Mobile Systems, Accepted for VTC-Spring, June FPC 5 (18) University of Oulu

6 A! System Model I 1 I 2 BS 0 R ~ BS n i r~ i d ~ i user i x~ i r~j user j i Received SINR at BS 0 corresponding to the user j is of interest. FPC 6 (18) University of Oulu

7 A! SINR of User j Received SINR at BS 0 corresponding to the user j η 1 γ j = N n=1 I n(r i, θ i ). r (1 α)λ j where η = p 0 ko α 1 p 0 is the cell-specific minimum power in linear domain k 0 is the path loss at reference distance (cell edge) linear domain Interference from neighbour n due to user i is I n (r i, θ i ) = ηr αλ i ( d 2 + r 2 i 2r id cos θ i ) λ/2. Aggregate interference at BS 0 is N n=1 I n(r i, θ i ) Interference caused by the N neighbouring cells is assumed i.i.d. Assumptions: 1st tier of cells create dominant interference to the center cell. Hexagonal cell approximated by circular cell with same radius. Distances are normalised w.r.t cell radius. Network is designed such that the cell edge users never reach P m. FPC 7 (18) University of Oulu

8 A! Average SINR of User We are interested in the expected SINR of the user, conditioned on knowing the path loss of the user averaged over all possible interference scenarios Complicated nature of I n (r i, θ i ) prevents derivation of exact answers to the statistical properties of γ j Approximately characterize by upper and lower bounds. Statistical quantity of interest is { } η 1 E {γ j r j } = J, where J = E N n=1 I n(r i, θ i ) r (1 α)λ j FPC 8 (18) University of Oulu

9 A! Upper Bound From geometric-arithmetic inequality we have ( 1 N n=1 I n(r i, θ i ) 1 N ) I n (r i, θ i ) 1/N N Which leads to { J 1 N } N E I n (r i, θ i ) 1/N n=1 n=1 = 1 N [ E {I n (r i, θ i ) 1/N }] N Upper bound for average inverse interference J U = 1 [ { }] N E I(r i, θ i ) 1/N. N Depends on the average on the inverse interference which can be modeled as the average interference at path loss exponent λ/n of a single cell., FPC 9 (18) University of Oulu

10 A! Lower Bound From Jensen s inequality, J 1 N n=1 E {I n (r i, θ i )} = 1 N [E {I n(r i, θ i )}] 1, Lower bound for average inverse interference J L = 1 N [E {I(r i, θ i )}] 1. Depends on the average interference generated by a single cell, E {I(r, θ}. FPC 10 (18) University of Oulu

11 A! Average Interference/Cell Average interference experience at BS 0 due to uniformly distributed users of a single cell (r i [0, 1] and θ i [0, 2π)) Ī(α, λ) = E {I(r i, θ i )} = 2η π 1 0 r αλ+1 i π Average Interference is Ī(α, λ) = 2η a k (λ) B[b 1, 1] d λ+k k=0 0 dθ i (d 2 + r 2 i 2r id cos θ i ) λ 2 dr i. 2F 1 [a 1, b 1, ; c 1 ; 1/d] where a k (λ) = (λ/2) k(1/2) k (1) k k! 4 k with (z) k = z(z + 1))... (z + k 1) denoting the Pochhammer symbol. Parameters of the Gauss hypergeometric function 2 F 1 [a 1, b 1 ; c 1 ; z 1 ] are a 1 = 2k + λ, b 1 = αλ + k + 2 and c 1 = b B[a, b] is a beta function. FPC 11 (18) University of Oulu

12 A! Interference Boundaries Average Interference is bounded by where J U = J L J J U 1 Nη N+1 [ ( Ī α, λ )] N N and J L = 1 N [Ī (α, λ) ] 1. Average of the upper and lower bound provides a good approximation. { J 1 [ ( 1 Ī α, λ )] N + [ Ī (α, λ) ] 1}. 2N η N+1 N FPC 12 (18) University of Oulu

13 A! Fitness of Approximation 220 Average Inverse Interference (dbm) Actual at λ=2 Approx. at λ=2 Actual at λ=3.76 Approx. at λ= α Actual and approximate average inverse interference for typical cellular network (N = 6) with α for P 0 = 78dBm and λ = [2, 3.76]. FPC 13 (18) University of Oulu

14 A! Rate Approximation (1) Achievable average rate of a cell, ( )} R = E {log ηr (1 α)λ 1 j N n=1 I. n(r i, θ i ) Random variables (r i, θ i ), i = 1,.., N and (r j ) are independent. Jensen s inequality leads to ( { }) 1 R 2 r j log ηr (1 α)λ 1 j E N 0 n=1 I dr j n(r i, θ i ) [ = 1 ln( ln(2) J + 1) B[b 3, 1] 2 F 1 [a 3, b 3 ; c 3 ; 1/ J] ] + α J here J = ηj, α = (1 α)λ/2, a 3 = 1, b 3 = 1/ α + 1, and c 3 = b Upper bound on average rate depends on J for which we do not have a closed form solution. Approximation of J may be used. FPC 14 (18) University of Oulu

15 A! Rate Approximation (2) Actual average Jensen's bound Approximation 1.8 Average rate (bps/hz) α Actual average rate with the derived approximation, free space path-loss. Jensen s upper bound is also simulated for the comparison. FPC 15 (18) University of Oulu

16 A! Select FPC parameters (1) Typical cellular system, FPC is implemented with a single (P 0, α) pair for the whole network. Different cells may have different distributions of services to provide to the users, and accordingly different fairness requirements. React to this, it would be preferable to tune the power control parameters on a per-cell basis. P 0 and α can be independently selected in each cell, according to the current user distribution and their needs Network planning may set the tolerable interference levels. Each cell selects P 0 and α keeping interference constant. FPC 16 (18) University of Oulu

17 A! Select FPC parameters (2) Average Interference/Cell (dbm) for λ= P 0 =-38 dbm P 0 =-48 dbm P 0 =-58 dbm P 0 =-68 dbm P 0 =-78 dbm P 0 =-88 dbm I FIXED =-127 dbm α Overall interference is evenly distributed among the N interference originating cells and the average interference for different P 0 values are depicted for free space. FPC 17 (18) University of Oulu

18 A! Conclusion New approximation for average inverse interference provided Approximation is tight at low values of α irrespective of λ. Slight discrepancy is visible at large values of α when λ increases. Resulting rate approximation is rather tight at small values of α and Jensen s bound becomes tighter when α goes to one. Parameters P 0 and α may be separately selected for each cell depending on current user population and their needs, keeping the interference constant. FPC 18 (18) University of Oulu