Analysis of Code-expanded Random Access

Transcription

1 Analysis of Code-expanded Random Access J.Y. Park Wireless and Mobile Communication Lab. 1

2 Introduction(Random Access Procedure) When a device want to access Base Station, Random Access Procedure is processed In this paper, Message 1 is the main issue A device should transmit a preamble at a specific subframe There are 64 different preambles For M2M, H2H Devices randomly select preambles If more than 2 devices select same preamble, collision occur, and collided devices try Random Access again at next opportunity If large number of devices try random access simultaneously, the probability of collision will be increased 2

3 Introduction[1] By utilizing code-expanded random access, collision probability can be decreased M: # of preamble used for M2M, L: length of codeword Codeword: combination of preamble by virtual frame Play a role as a preamble Number of codeword: (M+1) L 1 If preamble p a, p b, and length= 2, possible codewords: (p a, idle), (p a, p b ), (p a, p a ), (p b, idle), (p b, p a ), (p b, p b ), (idle, p a ), (idle, p b ) 3

4 Introduction Consider if (# of codeword) >>> (# of devices) # of codeword = (M+1) L 1 M: # of preamble to use, L: length of codeword To increase the number of codeword, M or L should be larger # of preamble for M2M is restricted Length of codeword can be infinitely long, however it can cause long access time Access time constraint Phantom-codeword It reduces the resource for data transmission Codewords that are not used are candidate for phantom-codeword Reduce the number of codewords that are not used P idle : # of not used codewords total # of codewords = # of candidate for codewords total # of codewords constraint 4

5 Introduction[1] Consider there are 2 preambles available: A, B user1 sends codeword (B, I) user2 sends codeword (I, A) user3 sends codeword (A, A) Phantom codeword (B, A) Codeword that is not used but perceived by Base Station Base station perceive that there is a device sending codeword (B, A) Base Station sends message2 to non-exist device Decrease of downlink resource for data transmission Base Station allocate a certain uplink resource to non-exist device to get message3 Decrease of uplink resource for data transmission Shortcoming of Code-expanded random access 5

6 Introduction In [1] Efficiency = # of uncollided codewords # of total codewords = # of codewords selected by a device # of total codewords where CW = (M + 1) L 1 and N: number of device = N 1 CW (1 1 CW )N 1 CW Compare efficiency of code-expanded with reference for specific M, L Does not give algorithm to get optimal # of preamble (M) and length of codeword (L) Does not consider access time 6

7 Proposed Optimization Problem Goal Minimize the collision probability while guaranteeing idle codeword ratio requirement and average access time of devices requirement Solution: (M*, L*) M*: # of preamble used for M2M L*: length of codeword For given M, As length of codeword longer # of codeword increase; collision probability, codeword usage ratio Average access time 7

8 Proposed Optimization Problem (M*, L*) = argmin P collision s. t. C1: P idle < P req C2: F Areq < α Access time : time difference between the first subframe after its arrival and the subframe at which it successfully transmit codeword P idle : # of not used codewords total # of codewords = # of candidate for phantom codewords total # of codewords C1: codeword idle ratio requirement should be satisfied C2: Fail to access until A req ratio requirement should be satisfied α: fail rate requirement 8

9 Assumption At each frame, N new devices arrive with the rate of λ Uniformly distributed arrivals over a fixed time interval [0, T] Uniformly distributed arrival model can be a realistic scenario in which MTC devices access the network uniformly over a period of time. [2] There may be remaining unsuccessful devices from the prior Random Access There is single subframe for Random Access per frame 9

10 Proposed Optimization Problem(obj func) Collision probability (P collision )= # of collision devices total # of attemping devices [6] Total random access arrival rate in the i-th virtual frame slot : λ T [i](new+backlogged) [5] λ T [i] = λt + P collision λ T [i-1] P collision : collision probability T: period of subframe for preamble transmission (10ms) In steady state, drop slot index i λ T = λt + P collision λ T λ T = λt 1 P collision Collision probability p can be estimated by P collision = 1 Pr[no device select a given codeword] Pr[one device select a given codeword] = 1 - (1 1 CW )λ T - λ T CW (1 1 CW )λ T 1 Where # of codewords(cw) : (M+1) L 1 1 W[ln 1 P collision = 1 e CW ]λt, where W[.] is a lambert W function [5] 10

11 Proposed Optimization Problem(C1) P idle : # of not used codewords total # of codewords = # of candidate for phantom codewords total # of codewords let X be a random variable that is # of MNs selecting per codeword Probability that a given codeword is selected by k MNs among N devices Pr[X = k] = N k ( 1 CW )k (1 # of codewords(cw): (M+1) L 1 1 CW )N k [1] Probability that a given codeword is not selected Pr[X = 0] = (1 1 CW )N # of idle codewords in a cycle = Pr[X=0] * CW Total # of codewords in a cycle CW = (M+1) L 1 M: # of preamble, L: length of codeword P idle = Pr X=0 CW CW = Pr[X=0] = (1 1 CW )N = (1 1 (M+1) L 1 )N 11

12 Proposed Optimization Problem(C2) Access time requirement New devices arrive to the channel at the following uniform rate λ = N T 0 < t < T = 10ms (1 frame) 0 otherwise 12

13 Proposed Optimization Problem(C2) N i = total number of devices trying to access base station at i-th virtual frame N 1 = N P i = collision probability at i-th virtual frame N i = P i-1 N i-1 + N 1 W ln 1 P i = 1 e CW N i, where W[.] is a lambert W function [5] # of codewords(cw): (M+1) L 1 13

14 Proposed Optimization Problem(C2) Acess time requirement: A req Access time requirement Time ( 횟수 ) limit (T limit ) to satisfy A req : = A req time length of a virtual frame L: length of codeword, T: time length of a frame(10ms) Ratio of devices fail to access base station among N devices after T limit virtual frame T F Areq = limit i=1 P i Constraint 2 F Areq < α α: fail rate requirement L T 14

15 Performance (Environment) λ = arrivals/10sec [7] Max number of preamble for M2M: 30 A req : 22ms(delay sensitive), 60ms(delay nonsensitive) [9] Fail rate requirement (α): 0.2, 0.05 Time between subframes for preamble transmission T = 10ms There are one subframe for preamble transmission per frame Codeword idle ratio P idle = 0.5,

16 Performance (GA) (M*, L*) = argmin P collision = argmin (1 e W[ln(1-1 CW )]λt ) s.t. C1: (1 1 (M+1) L 1 )N < P req T C2 : limit i=1 P i < α 1 W ln 1 Where P i = 1 e CW N i Mixed Integer Nonlinear Programming The optimization of such model is typically difficult due to their combinatorial nature and potential existence of multiple local minima in the search space GAs are powerful tools for solving MINLP problems [8] 16

17 Performance (GA) Chromosome format: (X 1, X 2 ) X 1 : number of preamble, X 2 : length of codeword Fitness function f = P collision + 10*max(0, P idle P req ) + 10*max(0, F Areq - α) Penalty when constraints are not met Population size: 500 Mutation rate: 0.01 Elitist one per generation was keeped (no mutation) Natural Selection Chromosome which has function value bigger than average function value is discarded Binary tournament selection Stopping criteria : F best, n F best, (n+1) <

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23 reference [1] Nuno K. Paratas, Henning Thomsen, Code-Expanded radio access protocol for machine-to-machine communications TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES [2] 3GPP Generation Partnership Project; 3GPP TR v ( ) Technical Report [3] Nuno K. Paratas, Henning Thomsen, Code-Expanded Random Access for Machine-Type Communications [4] Mehmet Koseoglu, Lower bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals IEEE TRANSACTIONS ON COMMUNICATIONS [5] Dan Keun Sung, Spatial Group Based Random Access for M2M Communications IEEE COMMUNICATIONS LETTERS, VOL. 18, NO 6, JUNE 2014 [6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine Communications [7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals [8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint Approximations [9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices 23