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![Page 1: PhD_presentation](https://reader031.fdocuments.in/reader031/viewer/2022032300/55ce1875bb61ebe4158b47b6/html5/thumbnails/1.jpg)
Dynamic spectrum access in large scale cognitive networks
Oshri Naparstek
Thesis directed by Prof. Amir LeshemFaculty of Engineering, Bar-Ilan University,
Ramat-Gan, Israel
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2
List of Publications• O. Naparstek and A. Leshem, “Fully distributed optimal
channel assignment for open spectrum access,” Signal Processing, IEEE Transactions on, 2013.
• O. Naparstek and A. Leshem, “Expected time complexity of the auction algorithm and the push-relabel algorithm for maximal bipartite matching on random graphs,” Submitted to Random Structures & Algorithms, 2014.
• O. Naparstek ; A. Leshem and E. Jorswieck, " Distributed medium access control for energy efficient transmission in cognitive radios," Submitted to IEEE Transactions on wireless Communications.
• Naparstek, O; Cohen, K.; Leshem, A., "Parametric Spectrum Shaping for Downstream Spectrum Management of Digital Subscriber Lines," Communications Letters, IEEE , vol.16, no.3, pp.417,419, March 2012.
April 15, 2023
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3
Spectrum scarcity problem
April 15, 2023
No channels left!
Really?
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4
Spectrum underutilization
April 15, 2023
Planty of spectrum.
Inefficient use!
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5
Dynamic spectrum access
• Rigid allocation
• No sharing• Rigid usage
requirements
April 15, 2023
• Flexible allocation
• Shared resources
• Flexible usage
Current Policy DSA
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6
Dynamic spectrum access
April 15, 2023
Dynamic Spectrum
Access
Exclusive use
model
Open sharing model
Hierarchal access
model
Property rights
Dynamic allocation
Overlay Underlay
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7
Channel assignment problem
April 15, 2023
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8
Related work• K. Kim, Y. Han, and S.-L. Kim, “Joint subcarrier and power
allocation in uplink OFDMA systems,” Communications Letters, IEEE, vol. 9, pp. 526 – 528, jun 2005.
• L. Gao and S. Cui, “Efficient subcarrier, power, and rate allocation with fairness consideration for OFDMA uplink,” Wireless Communications, IEEE Transactions on, vol. 7, pp. 1507 –1511, may 2008.
• Z. Tang and G. Wei, “An efficient subcarrier and power allocation algorithm for uplink OFDMA-based cognitive radio systems,” in Wireless Communications and Networking Conference, 2009. WCNC 2009. IEEE, pp. 1 –6, april 2009.
• A. Leshem, E. Zehavi, and Y. Yaffe, “Multichannel opportunistic carrier sensing for stable channel access control in cognitive radio systems,” JSAC special issue on application of game theory to communication, 2012.
April 15, 2023
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April 15, 2023
Assignment problem formulation
1 1
1
1
,
Subject to:
1 1..
1 1.
max
{0,1}
.
, 1. .
N N
i j
N
i
N
j
ij iji j
ij
ij
ij
c x
x j N
x i N
x i j N
1
2
3
1
3
2
Users Channels
1,1c
1,2c
1,3c
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April 15, 2023
The auction algorithm (Bertsekas 1979)
Let be a nonempty subset of persons that are unassigned.
Bidding phase:
Each person finds an object which offers maximal profit,
And compute bidding increment
Where is the best object profit
and is the second best object profit
I
i I ij
arg maxi i jjj
j a p
,i i i òi
maxi ij jj
a p
i
maxi
i ij jj j
a p
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April 15, 2023
The auction algorithm (Bertsekas 1979)
Assignment phase:Each object that is selected as best object by a nonempty subset of persons in , determines the highest bidder
raises its prices by the highest bidding increment and gets assigned to the highest bidder ; the person that was assigned to j at the beginning of the iteration (if any) becomes unassigned.
The algorithm continues with a sequence of iterations until all persons have an assigned object.
Note: there is a freedom of picking how many users from I get assigned in each iteration.
j( )p j I
( )arg maxj i
i p ji
( )max i p j i
ji
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12
Properties
• Solution is within from the optimum.
• Worst case time complexity is
April 15, 2023
Nò
2NO
ò
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April 15, 2023
Example
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
Bidder 1
Bidder 2
Bidder 3
Bidder 4
Obj
ect 1
Obj
ect 2
Obj
ect 3
Obj
ect 4
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April 15, 2023
Example (Cont.)
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
Profit matrix
0 0 17 0
0 8 0 0
20 0 0 0
0 7 0 0
Bids
Bidding phase:0+65-51+3=17
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April 15, 2023
Example (Cont.)
31 24 48 7
44 74 25 77
76 71 23 68
25 78 65 72
Profit matrix
0 0 17 0
0 8 0 0
20 o 0 0
0 0 0 0
Bids
Assignment phase:
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April 15, 2023
Example (Cont.)
31 24 48 7
44 74 25 77
76 71 23 68
25 78 65 72
Profit matrix
0 0 0 0
0 0 0 0
0 0 0 0
0 9 0 0
Bids
Assignment phase:
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April 15, 2023
Example (Cont.)
31 15 48 7
44 65 25 77
76 62 23 68
25 69 65 72
Profit matrix
0 0 17 0
0 0 0 0
20 0 0 0
0 17 0 0
Bids
Assignment phase:
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April 15, 2023
Example (Cont.)
31 15 48 7
44 65 25 77
76 62 23 68
25 69 65 72
Profit matrix
0 0 0 0
0 0 0 15
0 0 0 0
0 0 0 0
Bids
Assignment phase:
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April 15, 2023
Example (Cont.)
31 15 48 -8
44 65 25 62
76 62 23 53
25 69 65 57
Profit matrix
0 0 17 0
0 0 0 15
20 0 0 0
0 17 0 0
Bids
Assignment phase:
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April 15, 2023
Example (Cont.)
Total profit is 324 and is optimal in that case
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72Great!!!
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April 15, 2023
ButThere is
A Small
Problem
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22 April 15, 2023
The auction algorithm requires a knowledge of all the bids on each stage
Sometimes it is not possible
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23
Distributed auction algorithm
• Same as the auction algorithm with one important difference.
• Each user raises his bids only according his own bids.
• No message passing is needed!!
April 15, 2023
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24
Properties
• Solution is within from the optimum (Just like the original auction algorithm).
• Worst case time complexity is
April 15, 2023
Nò
3NO
ò
Not so good…
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April 15, 2023
Distributed access via opportunistic carrier sensing (Zhao et al.)
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April 15, 2023
Auction algorithm using Opportunistic CSMA
• The auction algorithm could be implemented by Opportunistic CSMA• At each iteration, each unassigned
user computes the increment of his bid and maps it to a back –off time
• Each user get assigned to a channel using Opportunistic CSMA
1
oldi i i i
ii
ò
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Example
April 15, 2023
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
User 1
User 2
User 3
User 4
Cha
nnel
1C
hann
el 2
Cha
nnel
3C
hann
el 4
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Example
April 15, 2023
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
Time slot 1 Time slot 2 Time slot 3 Time slot 4
Channel 1
Channel 2
Channel 3
Channel 4
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 17 0
0 8 0 0
20 0 0 0
0 7 0 0
0 0 17 0
0 8 0 0
20 0 0 0
0 7 6 0
0 0 17 0
0 8 0 0
20 0 0 0
0 13 6 0
0 0 17 0
0 8 0 6
20 0 0 0
0 13 6 0
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
51 32 48 7
64 74 42 77
76 79 40 68
45 79 82 72
51 32 48 7
64 74 42 77
76 79 40 68
45 79 82 72
51 32 48 7
64 74 42 77
76 79 40 68
45 79 76 72
51 32 48 7
64 74 42 77
76 79 40 68
45 79 76 72
51 32 48 7
64 74 42 77
76 79 40 68
45 73 76 72
51 32 48 7
64 74 42 77
76 79 40 68
45 73 76 72
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Worst case time complexity
• For an i.i.d matrix with common random variable X. The worst case time complexity is :
• And the worst case time complexity to get the optimum solution with quantization q is:
April 15, 2023
N N
2 ( )NO
E X ò
3 ( )NO
q
E X
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Simulations
April 15, 2023
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Simulations
April 15, 2023
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April 15, 2023
The convergence might be too
slowWe need something
FasterAnd Simpler
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33
Truncated auction
Lets ignore the bad channels
April 15, 2023
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
51 0 65 0
0 82 0 77
96 79 0 0
0 86 82 0
How many can we ignore?
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Truncated auction
Theorem: Let be a bounded random variable such that and let A be an i.i.d random matrix with common variable X. The probability that a channel which is not part of the best channels of a user is user is used in the optimal assignment is less than
April 15, 2023
[0, ]X a( ) 0Xf a
2 )log (N
1
1
N
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35
Truncated auction
Proof:
April 15, 2023
Just kiddingWe got a real
proof… In our paper.
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36
Truncated auction
• So, if we ignore all the channels but the best
channels then the worst case time complexity is w.h.p
• We also conjecture that this is the complexity of the auction algorithm
April 15, 2023
2log ( )N
2 log( )O N N
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37 April 15, 2023
Can we go even faster?
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38
Fast auction
Lets ignore the bad channels
April 15, 2023
51 0 65 0
0 82 0 77
96 79 0 0
0 86 82 0
1 0 1 0
0 1 0 1
1 1 0 0
0 1 1 0
Equivalent to finding a perfect matching on a
bipartite graph
And actual rates
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39
Bipartite graph
April 15, 2023
1
3
2
1
2 3
1 0 1 0
0 1 0 1
1 1 0 0
0 1 1 04
4 1 1
2
3
4
2
3
4
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Matching on bipartite graphs
April 15, 2023
MatchingPerfect
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Random bipartite graphs
April 15, 2023
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Matching on random bipartite graphs
April 15, 2023
(
| | | |
2 Erd
, )
ős and Rényi 1959(
be the set of all bipartite graphs
with vertex sets U V N and an edge set E where
the edges in E are independently chosen with probability p.
: Let B N p
Theorem
Definition
2
(1 ) log( )Let and a bipartite graph ( , )
)
contains a pe
the
rfec
n
lim t matching 0N
NP
Np G
G
N pN
e
B
ò
ò
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43
Fast auction
Theorem: The worst case time complexity of the fast auction for NxN i.i.d random matrices is:
The expected time complexity of the fast auction is:
April 15, 2023
2O N
log( )O N NTook us a whole paper to prove this one…
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44
Simulations
April 15, 2023
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45
Simulations
April 15, 2023
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46 April 15, 2023
OK, it is fast!
ButIs the solution
GOOD?
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Asymptotical optimality
Theorem: Let R be light tailed or bounded random variable and let R be an i.i.d random matrix with
Let be the maximal sum rate obtained by solving the assignment problem on R and let be the sum rate obtained by the matching algorithm for the thresholded matrix
then April 15, 2023
The short answer is
YES!!
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48
Simulations
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50 April 15, 2023
Faster approaches?
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51
Greedy assignment
Related work, stable marriage algorithm:
A. Leshem, E. Zehavi, and Y. Yaffe, “Multichannel opportunistic carrier sensing for stable channel access control in cognitive radio systems,” JSAC special issue on application of game theory to communication, 2012.
• The algorithm converge within one iteration• This algorithm is probably asymptotically optimal
for i.i.d Rayleigh channels but we don’t know how to prove it.
April 15, 2023
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52
Greedy assignment
• Randomly choose a free user.
• Assign him with his best available channel.
• Repeat until all users are assigned
April 15, 2023
It goes like this: 51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
51 32 65 7
64 82 42 77
96 79 40 68
45 86 82 72
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53
Greedy assignment
Theorem: The greedy assignment is asymptotically optimal for i.i.d Rayleigh channels.
April 15, 2023
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54
Simulations
April 15, 2023
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55
Simulations
April 15, 2023
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56
Simulations
April 15, 2023
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57 April 15, 2023
We can apply the same methods for
GreenCommunications
O. Naparstek ; A. Leshem and E. Jorswieck, " Distributed medium access control for energy efficient transmission in cognitive radios," Submitted to IEEE Transactions on wireless Communications.
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58 April 15, 2023
And much more!
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59 April 15, 2023
Thank you!