A New Analysis of the DS-CDMA Cellular Uplink Under Spatial Constraints

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1 A New Analysis of the DS-CDMA Cellular Uplink Under Spatial Constraints D. Torrieri M. C. Valenti S. Talarico U.S. Army Research Laboratory Adelphi, MD West Virginia University Morgantown, WV June, 3 the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 / 3

2 Outline Introduction Network Model 3 Conditional Outage Probability 4 Network Policies 5 Performance Analysis 6 Conclusion the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 / 3

3 Outline Introduction Introduction Network Model 3 Conditional Outage Probability 4 Network Policies 5 Performance Analysis 6 Conclusion the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 3 / 3

4 Introduction Introduction A cellular network is currently modeled by: Classic approach (regular grid): The analysis often focuses on the worst case-locations (cell edge) Using stochastic geometry: Assumes infinite network; A random point process with no constraint on the minimum separation is used to deploy the base stations. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 4 / 3

5 Introduction Actual Vs Simulated Base-Station Locations distance in km distance in km Figure: Actual base-station locations from a current cellular deployment in a small city with a hilly terrain Figure: Simulated base-station locations when the minimum base-station separation is r bs =.5. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 5 / 3

6 Introduction Actual Vs Simulated Base-Station Locations distance in km distance in km Figure: Actual base-station locations from a current cellular deployment in a small city with a hilly terrain Figure: Simulated base-station locations when the minimum base-station separation is r bs =.5. Cell boundaries are indicated. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 5 / 3

7 Introduction Actual Vs Simulated Base-Station Locations distance in km distance in km Figure: Actual base-station locations from a current cellular deployment in a small city with a hilly terrain Figure: Simulated base-station locations when the minimum base-station separation is r bs =.5. Cell boundaries are indicated, and the average cell load is 6 mobiles. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 5 / 3

8 Introduction Actual Vs Simulated Base-Station Locations distance in km distance in km Figure: Actual base-station locations from a current cellular deployment in a small city with a hilly terrain Figure: Simulated base-station locations when the minimum base-station separation is r bs =.5. Cell and sector boundaries are indicated, and the average cell load is 6 mobiles. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 5 / 3

9 Outline Network Model Introduction Network Model 3 Conditional Outage Probability 4 Network Policies 5 Performance Analysis 6 Conclusion the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 6 / 3

10 Network Model Network Model The Network comprises: C cellular base stations {X,..., X M } with an exclusion zone of radius r bs ; 3C sectors {S,..., S 3C}, assuming there are three ideal sector antennas per base station, each covering π/3 radians. M mobiles {Y,..., Y K} with an exclusion zone of radius r m. Finite circular network with area A net = πr net. DS-CDMA is considered. Both intracell and intercell interference within the coverage angle of the sector are considered. Let A j denote the set of mobiles covered by sector antenna S j. A mobile X i A j will be associated with S j if the mobile s signal is received at S j with a higher average power than at any other sector antenna in the network. Let X j A j denote the set of mobiles associated with sector antenna S j. Let X r X j denote a reference mobile that transmits a desired signal to S j. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 7 / 3

11 Network Model Despread Instantaneous Power The despread instantaneous power of X i received at S j is P rg r,j ξ r,j / f ( S j X r ) from the reference mobile X r ( h ) ρ i,j = G Pig i,j ξ i,j / f ( S j X i ) from the other mobiles X i covered by S j where from all other mobiles, i : X i / A j P i is the power transmitted by X i; g i,j is the power gain due to Nakagami fading; ξ i,j is a shadowing factor and ξ i,j N (, σ s) ; f( ) is a path-loss function: ( d f (d) = α is the path loss exponent; d d ; h is the chip factor; G is the common spreading factor. d ) α the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 8 / 3

12 Network Model Despread Instantaneous Power The despread instantaneous power of X i received at S j is P rg r,j ξ r,j / f ( S j X r ) from the reference mobile X r ( h ) ρ i,j = G Pig i,j ξ i,j / f ( S j X i ) from the other mobiles X i covered by S j where from all other mobiles, i : X i / A j P i is the power transmitted by X i; g i,j is the power gain due to Nakagami fading; ξ i,j is a shadowing factor and ξ i,j N (, σ s) ; f( ) is a path-loss function: ( d f (d) = α is the path loss exponent; d d ; h is the chip factor; G is the common spreading factor. d ) α the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 8 / 3

13 Network Model Despread Instantaneous Power The despread instantaneous power of X i received at S j is P rg r,j ξ r,j / f ( S j X r ) from the reference mobile X r ( h ) ρ i,j = G Pig i,j ξ i,j / f ( S j X i ) from the other mobiles X i covered by S j where from all other mobiles, i : X i / A j P i is the power transmitted by X i; g i,j is the power gain due to Nakagami fading; ξ i,j is a shadowing factor and ξ i,j N (, σ s) ; f( ) is a path-loss function: ( d f (d) = α is the path loss exponent; d d ; h is the chip factor; G is the common spreading factor. d ) α the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 8 / 3

14 Network Model Despread Instantaneous Power The despread instantaneous power of X i received at S j is P rg r,j ξ r,j / f ( S j X r ) from the reference mobile X r ( h ) ρ i,j = G Pig i,j ξ i,j / f ( S j X i ) from the other mobiles X i covered by S j where from all other mobiles, i : X i / A j P i is the power transmitted by X i; g i,j is the power gain due to Nakagami fading; ξ i,j is a shadowing factor and ξ i,j N (, σ s) ; f( ) is a path-loss function: ( d f (d) = α is the path loss exponent; d d ; h is the chip factor; G is the common spreading factor. d ) α the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 8 / 3

15 SINR Network Model The performance at the sector S j when the desired signal is from X r X j is characterized by the signal-to-interference and noise ratio (SINR), given by: γ r,j = Γ + h G g r,jω r,j () M g i,jω i,j i= i r where Γ is the signal-to-noise ratio (SNR) at a mobile located at unit distance when fading and shadowing are absent; Ω i,j = P i P r ξ i,j / S j X i α is the normalized power of X i received by S j before despreading. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 9 / 3

16 Outline Conditional Outage Probability Introduction Network Model 3 Conditional Outage Probability 4 Network Policies 5 Performance Analysis 6 Conclusion the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 / 3

17 Definition Conditional Outage Probability An outage occurs when the SINR is below a threshold β. β depends on the choice of modulation and coding. The outage probability of a desired signal from X r X j at the sector antenna S j conditioned over the network is Substituting () into (), from [8]: ɛ r = e β Γ m r,j n= ɛ r = P [ γ r,j β r Ω j ]. () ( ) n β n Γ k= Γ k (n k)! l i Mi= l i =k M G li (Ψ i) (3) i= i r where β = βm r,j/ω, G l (Ψ i) = Γ(l + mi,j) l!γ(m i,j) ( Ωi,j m i,j ) l ( ) mi,j l βhω i,j +. (4) Gm i,j [8] D. Torrieri and M.C. Valenti, The outage probability of a finite ad hoc network in Nakagami fading, IEEE Trans. Commun., Nov.. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 / 3

18 Conditional Outage Probability Distance-Dependent Fading Model In (3) non-identical Nakagami-m parameters can be chosen to characterize the fading from the mobile X i to the sector antenna S j and a distance-depending fading model can be adopted: 3 if S j X i r bs / m i,j = if r bs / < S j X i r bs. (5) if S j X i > r bs The distance-dependent-fading model characterizes the situation where a mobile close to the base station is in the line-of-sight (LOS), while mobiles farther away tend to be non-los. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 / 3

19 Outline Network Policies Introduction Network Model 3 Conditional Outage Probability 4 Network Policies 5 Performance Analysis 6 Conclusion the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 3 / 3

20 Resource Allocation Network Policies Power control: Rate control: The transmit power {P i} for all mobiles in the set X j is selected such that, after compensation for shadowing and power-law attenuation, each mobile s transmission is received at sector antenna S j with the same power P : P i ξ i,j / f ( S j X i ) = P, X i X j. Let R j = C(β j) represent the relationship between R j and β j. For modern cellular systems, it is reasonable to assume the use of a capacity-approaching code, two-dimensional signaling over an AWGN channel, and Gaussian interference, and in this case: C(β j) = log ( + β j). Let T i indicate the throughput of the i th uplink. The throughput represents the rate of successful transmissions and is found as T i = R i( ɛ i). (6) the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 4 / 3

21 T Policies Average Individual uplinks R (a) Throughput vs the rate R. Network Policies ε Average Individual uplinks R (b) Outage probability vs the rate R. Example: C = 5. M = 4. r net =. r bs =.5. r m =.. G = 6. h = /3. Γ = db. α = 3. σ s = 8 db. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 5 / 3

22 T Policies Average Individual uplinks R (a) Throughput vs the rate R. Policies: Network Policies ε Average Individual uplinks R (b) Outage probability vs the rate R. maximal-throughput fixed rate (MTFR) policy; Example: C = 5. M = 4. r net =. r bs =.5. r m =.. G = 6. h = /3. Γ = db. α = 3. σ s = 8 db. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 5 / 3

23 T Policies Average Individual uplinks R (a) Throughput vs the rate R. Policies: Network Policies ε Average Individual uplinks R (b) Outage probability vs the rate R. maximal-throughput fixed rate (MTFR) policy; maximal-throughput variable-rate (MTVR) policy; Example: C = 5. M = 4. r net =. r bs =.5. r m =.. G = 6. h = /3. Γ = db. α = 3. σ s = 8 db. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 5 / 3

24 T Policies Average Individual uplinks R (a) Throughput vs the rate R. Policies: Network Policies ε Average Individual uplinks R (b) Outage probability vs the rate R. maximal-throughput fixed rate (MTFR) policy; maximal-throughput variable-rate (MTVR) policy; 3 outage-constrained fixed rate (OCFR) policy (E[ɛ] = ζ); Example: C = 5. M = 4. r net =. r bs =.5. r m =.. G = 6. h = /3. Γ = db. α = 3. σ s = 8 db. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 5 / 3

25 T Policies Average Individual uplinks R (a) Throughput vs the rate R. Policies: Network Policies ε Average Individual uplinks R (b) Outage probability vs the rate R. maximal-throughput fixed rate (MTFR) policy; maximal-throughput variable-rate (MTVR) policy; 3 outage-constrained fixed rate (OCFR) policy (E[ɛ] = ζ); 4 outage-constrained variable-rate (OCVR) policy (ɛ i = ζ). Example: C = 5. M = 4. r net =. r bs =.5. r m =.. G = 6. h = /3. Γ = db. α = 3. σ s = 8 db. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 5 / 3

26 Outline Performance Analysis Introduction Network Model 3 Conditional Outage Probability 4 Network Policies 5 Performance Analysis 6 Conclusion the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 6 / 3

27 Transmission Capacity Performance Analysis The performance metric used is the transmission capacity, defined as τ = λe[t ] = λe [( ɛ) R] (7) where λ = M/A net is the density of transmissions in the network; E[T ] is computed using a Monte Carlo approach as follows: Draw a realization of the network; Compute the path loss from each base station to each mobile; 3 Determine the set of mobiles associated with each base station; 4 Determine the set of mobiles associated with each cell sector; 5 Apply a denial policy if there are more than G mobiles in a cell sector; 6 Apply at sector antenna the power-control policy and the rate-control; 7 Determine the outage probability conditioned over the topology ɛ j by (3); 8 By applying the function R j = C(β j), find the rate for the mobile; 9 Compute the throughput by (6); Repeat this process for a large number of networks. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 7 / 3

28 Performance Analysis Example: Policy Comparison τ σ s = 8 db No Shadowing MTVR MTFR OCVR OCFR M/C Figure: Transmission capacity for the four network policies as function of the load M/C for distancedependent fading and both shadowed (σ s = 8 db) and unshadowed cases. Example: Recall: M = 5 base stations; Circular arena with r net = ; r bs =.5; r m =.; α = 3; Γ = db; h = /3; G = 6; ζ =. for OCFR and OCVR. MT = Maximal-throughput; OC = Outage-constrained; FR = Fixed-rate; VR = Variable-rate. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 8 / 3

29 Performance Analysis Example: Spreading Factor τ MTVR, M/C=G MTVR, M/C=G/ MTFR, M/C=G MTFR, M/C=G/ OCVR, M/C=G OCVR, M/C=G/ OCFR, M/C=G OCFR, M/C=G/ G Example: M = 5 base stations; Circular arena with r net = ; r bs =.5; r m =.; α = 3; Γ = db; h = /3; ζ =. for OCFR and OCVR; σ s = 8 db. Recall: Figure: Transmission capacity as function of spreading factor G for two values of system load, distance- MT = Maximal-throughput; OC = Outage-constrained; dependent fading, and shadowing with σ s = 8 db. FR = Fixed-rate; VR = Variable-rate. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 9 / 3

30 Performance Analysis Example: Minimum Distance between Base-Stations τ MTVR, α = 4 MTVR, α = 3 MTFR, α = 4 MTFR, α = 3 OCVR, α = 4 OCVR, α = 3 OCFR, α = 4 OCFR, α = r bs Figure: Transmission capacity as a function of the base-station exclusion-zone radius r bs for four policies and two values of path-loss exponent α. Example: Recall: M = 5 base stations; Circular arena with r net = ; r m =.; Γ = db; h = /3; G = 6; ζ =. for OCVR and OCFR; σ s = 8 db. MT = Maximal-throughput; OC = Outage-constrained; FR = Fixed-rate; VR = Variable-rate. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 / 3

31 Outline Conclusion Introduction Network Model 3 Conditional Outage Probability 4 Network Policies 5 Performance Analysis 6 Conclusion the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 / 3

32 Conclusion Conclusions The new approach for modeling and analyzing the DS-CDMA cellular uplink has the following benefits: the model allows constraints to be placed on the distance between base stations, the geographic footprint of the network, and the number of base stations and mobiles; a flexible channel model, accounting for path loss, shadowing, and Nakagamim fading with non-identical parameters, is considered. The approach is general enough and it can be extended: to compare various access and resource allocation techniques; to analyze reselection schemes; to model other types of access, such as orthogonal frequency-division multiple access (OFDMA). See journal version for more details: D. Torrieri, M.C. Valenti and S. Talarico, An Analysis of the DS-CDMA Cellular Uplink for Arbitrary and Constrained Topologies, IEEE Trans. Commun., to appear. the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 / 3

33 Conclusion Thank You the DS-CDMA Cellular Uplink Under Spatial Constraints June, 3 3 / 3

Multihop Routing in Ad Hoc Networks

Multihop Routing in Ad Hoc Networks Dr. D. Torrieri 1, S. Talarico 2 and Dr. M. C. Valenti 2 1 U.S Army Research Laboratory, Adelphi, MD 2 West Virginia University, Morgantown, WV Nov. 18 th, 20131 Outline