Basics of Cellular Communications Grade of Service, Interference, & Capacity

The Cellular Concept Early Mobile Communications The Cellular Concept Single, high powered transmitter with an antenna mounted on a tall tower The Cellular Concept Replace a single high power transmitter (large cell) with many low power transmitters (small cells) each providing coverage to only a small portion of the service area

Frequency Reuse Cluster Cluster Each base station is allocated a group radio channels to be used within a small geographic area Base station in adjacent cells are assigned channel groups which contain completely different channels than neighboring cells E D F A G B C Cluster Total Number of Channels in the System: C=MkN=MS M: Number of clusters within the system K: Number of channels per cell N: Cluster Size S: Number of available physical channels A Cluster: A Group of N cells that which collectively use the complete set of available frequencies

Locating Co-channel Cells Number of Cells per Cluster N = i2+ij+j2, i, j are non-negative integers To find nearest co-channel neighbor of a given cell Move i cells along any chain of hexagons Turn 600 counter clockwise and move j cells i=3, j=2, N=19

Grade of Service and Capacity (i.e., Blocking Probability)

Trunking & Grade of Service Trunked Radio System: Each user is allocated a channel on per call basis, and upon termination of the call, the previously occupied channel is immediately returned to the pool of available channels. Grade of Service: A measure of the ability of a user to access the trunked system GOS measures in cellular networks Probability that a call is blocked Probability a call experiences a delay greater than a certain queuing time

Traffic Intensity Traffic intensity generated by each user: Au Erlangs Au = H H : average duration of the call λ : average number of call requests per unit time For a system containing U users and unspecified number of channels, Total offered traffic intensity: A Erlangs A = UAu In C channel trunked system, if the traffic is equally distributed among the channels, Traffic intensity per channel : Ac Erlangs Ac = UAu/C

Types of Trunked Systems Calls Blocked Cleared Trunking System No queuing provided for call requests and calls are blocked if no available channels Calls Blocked Delayed Trunking System Queuing is provided to hold call requests. Calls are blocked if no available channels for a certain delay Assumptions: Calls arrive as determined by Poisson distribution Infinite number of users Memoryless arrivals of requests : all users can request channel at any time Probability of user occupying a channel is exponentially distributed Finite number of channels available in the trunking pool

Erlang B Formula M/M/C/C Queuing System Queue Size C Servers and Exponential Service Times Inter-arrival time distribution Service time distribution Number of Servers Exponential Interarrival Time (Poisson Arrival Process)

Erlang B Curves

Erlang C Formula

Erlang C Curves Pr[delay>0]

Interference and Capacity in Cellular Systems

Interference & System Capacity The wireless environment constitutes a shared medium Interference is the major limiting factor in performance of wireless systems in general Types of Interference: Co-channel interference Adjacent channel interference

Co-channel Interference Frequency reuse implies that several cells use the same set of channels E D F A G B C E D F A G B C E D F A G B C E D F A G B C E D F A G B C Frequency reuse = 7 Co-channel interfering cells for cell allocated with channel group A

Co-channel Interference, SIR & System Capacity Co-channel Interfering Cells P2 H21 BS 2 H12 P1 H22 H11 R D MT 2 BS 1 R MT 1 BS: Base Station MT: Mobile Terminal Px: Transmitter power by base station x Hxy: Small-scale & Large-scale channel between base station x and mobile terminal y SIRy: Signal-to-Interference Ratio at mobile terminal y Improving SIR1 by increasing P1 would result in a decrease in SIR2 Improving BOTH SIR1 & SIR2 is possible by increasing the distance separation between BS1 and BS2

Distance Separation between Base Stations j(2R’) i(2R’) Q: Co-channel reuse Ratio

SIR Computations Assume interference from first tier (ring) of co-channel interferers D D D X R D D D Di: interfering distance from ith co-channel interference NB No. of co-channel interfering sites

SIR Computations X Worst Case SIR Assume interference from first tier (ring) of co-channel interferers D+R D+R D R X Worst Case SIR D-R D D-R Di: interfering distance from ith co-channel interference NB No. of co-channel interfering sites

SIR & System Capacity Improving SIR means increasing cluster size, which corresponds to a decrease in system capacity Decreasing the cell size does not affect the SIR as Q=D/R remains constant. A decrease in cell size corresponds to an increase in system capacity

 Capacity reduction = 7/9 Example In First Generation cellular systems, sufficient voice quality is achieved when SIR = 18 dB N=7Q=4.6. Worst Case SIR = 49.56 (17 dB) To design cellular system with worst performance better than 18 dB, N=9  Capacity reduction = 7/9

Adjacent Channel Interference Adjacent channel interference results from imperfect receiver which allows nearby frequencies to leak into the passband Adjacent channel interference can be minimized through careful filtering and channel assignments

Improving Coverage and Capacity in Cellular Systems: Cell Splitting Subdividing a congested cell into smaller cells, each with its own base station and a corresponding reduction in antenna height and transmitter power Cell splitting Increasing system capacity by increasing the number of clusters in a given area Decreasing Transmitter Power The SIR is independent of transmitted power as long as it is the same for all base stations Why not make Transmitter Power as low as possible? The SNR must be a above a minimum threshold controlled by Pr