Cellular Systems Cellular Concepts The cellular concept was a ...

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EE5401 Cellular Mobile Communications EE5401 Cellular Mobile Communications P 0 = C ∑ − 1 n= 0 1 ⎛ λ ⎞ ⎜ ⎟ n! ⎝ µ ⎠ n 1 1 ⎛ λ ⎞ + ⎜ ⎟ C! ⎝ µ ⎠ C 1 ⎛ λ ⎞ ⎜1 − ⎟ ⎝ µ C ⎠ The probability that the call will not have immediate access to a channel (i.e. having nonzero delay) Pr( delay > 0) = ∑ ∞ P = k k C C A 1 = P C! A 1− C where A = λ / µ . This is the Erlang C formula. - This probability of non-zero delay that can be tolerated is also known to be the GoS parameter of the Erlang C system. - If no channels are immediately available, the call is delayed, and the probability that the delayed call is forced to wait more than t seconds is given by the probability that a call is delayed, multiplied by the conditional probability that the delay is greater than t seconds (the delay threshold). Pr(delay > t) = Pr(delay > 0) Pr(delay > t delay > 0) = Pr(delay > 0) exp[ −( C − A) t / H ] - The average delay D for all calls in a queued system is given by ∞ H D = ∫ Pr(delay > t) dt = Pr(delay > 0) 0 C − A or the average delay for those calls which are queue is given by H /( C − A) . 0 Note: Proof for Pr( delay > t delay > 0) = exp[ −( C − A) t / H ] Consider C=1, this corresponding to the M/M/1 queue model. The waiting time W consists of the service times of the existing N customers in the system, ie., W = S1 + S2 + L+ S N where S i follows exponential distribution fS ( t) = µ exp( − µ t) and W is the sum of these N i independent random variables. Note that implicity we assume that N > 0 . λ λ n Also can easily show that P n = (1 − )( ) , i.e. n follows a µ µ geometric distribution (memoryless property). The pdf of W is then given by Erlang( n+ 1, µ ) 64748 4 ∞ ∞ n ( µ t) −µ t λ λ n fW ( t) = ∑ f W | n ( t, n) Pn = ∑ µ e ⋅ (1 − )( ) n= 0 n= 0 n! µ µ −( µ −λ) t = ( µ − λ) e Note that µ = 1/ H , A = λH , integrate this from t to ∞ will obtain Pr( delay > t delay > 0) For M/M/C queue, the system behaves as an M/M/1 queue with higher service rate C µ (rather than µ ). Institute for Infocomm Research 69 National University of Singapore Institute for Infocomm Research 70 National University of Singapore
EE5401 Cellular Mobile Communications EE5401 Cellular Mobile Communications Channel Assignment Strategies Channel allocation schemes can affect the performance of the system. Fixed Channel Allocation (FCA) : • Channels are divided in sets. • A set of channels is permanently allocated to each cell in the network. Same set of channels must be assigned to cells separated by a certain distance to reduce co-channel interference. • Any call attempt within the cell can only be served by the unused channels in that particular cell. The service is blocked if all channels have used up. • Most easiest to implement but least flexibility. • An modification to this is ‘borrowing scheme’. Cell (acceptor cell) that has used all its nominal channels can borrow free channels from its neighboring cell (donor cell) to accommodate new calls. • Borrowing can be done in a few ways: borrowing from the adjacent cell which has largest number of free channels, select the first free channel found, etc. Institute for Infocomm Research 71 National University of Singapore • To be available for borrowing, the channel must not interfere with existing calls. The borrowed channel should be returned once the channel becomes free. Dynamic Channel Allocaton (DCA) : • Voice channels are not allocated to any cell permanently. All channels are kept in a central pool and are assigned dynamically to new calls as they arrive in the system. • Each time a call request is made, the serving BS requests a channel from the MSC. It then allocates a channel to the requested cell following an algorithm that takes into acount the likelihood of future blocking within the cell, the reuse distance of the channel and other cost functions ⇒ increase in complexity • Centralized DCA scheme involves a single controller selecting a channel for each cell. Distributed DCA scheme involves a number of controllers scattered across the network. • For a new call, a free channel from central pool is selected based on either the co-channel distance, signal strength or signal to noise interference ratio. Flexible channel assignment Institute for Infocomm Research 72 National University of Singapore
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