Outline • Background • System Model • Transmission Probability Scheduling (TPS) Scheme • Hidden Markov Model (HMM) Based Predictor • Simulations • Conclusions

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Background

Spectrum Holes for Secondary User

Primary Packets

Time

• Opportunistic spectrum access • Fundamental challenges: – Protect the primary transmissions – Improve the spectrum efficiency as much as possible 2010/8/27

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System Model Collision Occurs

L Primary Packets

Time Sensing sub-slot

Secondary Packets

• Network elements: – Primary user: • ON-OFF alternative process (ON-busy, OFF-idle)

– Secondary user: • Slotted transmission • The sensing capability is perfect 2010/8/27

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Slot boundary

System Model (cont’d) • Performance metrics: – Average packet collision ratio (APCR) of the primary user NC

RC = lim

U →+∞

NP

– Normalized throughput of the secondary user

NS T = lim U →+∞ N IDLE

• Optimization aim: maximize T while keep RC under a preset threshold RTH NP NC NS N IDLE

--the number of the primary user’s packets during U --the number of collision events during U --the number of idle slots successfully utilized by the secondary user during U --the total number of idle slots during U

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TPS Scheme Spectrum Hole Identified

X (k − 1) = 1 X (k ) = 0

slot k-1

Primary Packets

step 1

step 2

PkT (0)

PkT (1)

slot k

slot k+1

step N-1

...

Sensing sub-slot

step N

PkT ( N − 1)

Time Slot boundary

• Calculate the transmission probabilities PkT (0), PkT (1),..., PkT ( N − 1)

at the N following data sub-slots according to the optimization aim. 2010/8/27

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TPS Scheme (cont’d) • The definition of two probabilities – the probability that the primary user accesses the channel during the (k + i)-th data sub-slot 1) 1), = i 0 Pr( X (k + i + = Bk (i ) = (1) Pr( X (k += 1) 0,..., X (k += i ) 0, X (k + i += 1) 1), 0

– The probability that the primary user would not access the channel from the k-th to the (k + i)-th data sub-slot 1) 0),= i 0 Pr( X (k + i += I k (i ) = (2) Pr( X (k += 1) 0,..., X (k += i ) 0, X (k + i += 1) 0), 0

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TPS Scheme (cont’d) • The formulation of performance metrics – the collision probability for the coming primary packet PkC =

N −1

∑ B (i) ⋅ P

T k

k

i =0

PkC ⇔ RC

(i )

– the expected normalized throughput of the secondary N −1 user T Tk =

∑I i =0

k

(i ) ⋅ Pk (i )

Tk ⇔ T

N −1

∑I i =0

k

(i )

Max. Tk

Optimization problem

PkC ≤ RTH

s.t.

0 ≤ PkT (i ) ≤ 1, = i 0,1,..., N − 1. 2010/8/27

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HMM-Based Predictor Make prediction

Train HMM

…

Primary Packets

Sensing sub-slot

Secondary Packets

Time

X (k − 1) X (k )

Slot boundary

• Make prediction based on the sensing history Z ( k= ) [ X (k − W + 1),..., , X (k − 1), X (k )]

• The channel usage pattern of the primary user is generated by a HMM, which is denoted as ξ 2010/8/27

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HMM-Based Predictor (cont’d) • The process of making prediction Z(k ), ξ 0

Baum-Welch Algorithm (Expectation Maximization)

max . Pr(Z(k ) ξ j )

Forward-backward procedure

ξ∗

Pr( ⋅ ξ ∗ ) 2010/8/27

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HMM-Based Predictor (cont’d) • The prediction of the two probabilities Pr( X (k + i + 1) = 1, Z(k ) ξ ) , i=0 Pr(Z(k ) ξ ) Bˆ k (i ) = (3) Pr( X (k += i ) 0, X (k + i += 1) 0,..., X (k += 1) 1, Z(k ) ξ )) , 0

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Simulations Parameters: •The primary packet length is fixed to 4 slots •The mean duration of the primary user’s idle period is 8 slots •The prediction steps number is set to 40 •The training sequence length is set to 3000

• Case 1: Exponential distributed idle period baseline TPS(HMM)

0.2

Normalized Troughput

0.2

APCR

0.15

0.1

0.05

0 0

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0.05

0.1 APCR Threshold

0.15

f (t ) = e − λt

baseline TPS(HMM)

0.15

0.1

0.05

0.2

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0 0

0.05

0.1 APCR Threshold

0.15

0.2

Simulations (cont’d) • Case 2: Hyper-Erlang-2-2 distribution idle period (k1λ1 ) k1 t k1 −1 − k1λ1t (k2 λ2 ) k2 t k2 −1 − k2 λ2t f (t ) α1 e e + α2 (k1 − 1)! (k2 − 1)! 0.35

0.2 baseline TPS(HMM)

0.3

Normalized Troughput

APCR

0.15

0.1

0.05

baseline TPS(HMM)

0.25 0.2 0.15 0.1 0.05

0 0

0.05

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0.1 APCR Threshold

0.15

0 0

0.2

13

0.05

0.1 APCR Threshold

0.15

0.2

Conclusions • The TPS scheme could maximize the throughput of the secondary user while constraining the APCR of the primary packet under a required threshold. • The maximum achievable throughput of the secondary user has a relationship with the distribution of the primary user’s idle period. • The accuracy of the HMM-based predictor is satisfactory.

Thanks for your time! Any questions? 2010/8/27

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