Throughput Maximization for Opportunistic Spectrum Access via Transmission Probability Scheduling Scheme Yang Cao, Daiming Qu, Guohui Zhong, Tao Jiang Huazhong University of Science and Technology, Wuhan, China
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
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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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