Dynamic spectrum access in large scale cognitive networks

Oshri Naparstek

Thesis directed by Prof. Amir LeshemFaculty of Engineering, Bar-Ilan University,

Ramat-Gan, Israel

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.

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Spectrum scarcity problem

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No channels left!

Really?

4

Spectrum underutilization

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Planty of spectrum.

Inefficient use!

5

Dynamic spectrum access

• Rigid allocation

• No sharing• Rigid usage

requirements

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• Flexible allocation

• Shared resources

• Flexible usage

Current Policy DSA

6

Dynamic spectrum access

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Dynamic Spectrum

Access

Exclusive use

model

Open sharing model

Hierarchal access

model

Property rights

Dynamic allocation

Overlay Underlay

7

Channel assignment problem

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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.

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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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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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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

12

Properties

• Solution is within from the optimum.

• Worst case time complexity is

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Nò

2NO

ò

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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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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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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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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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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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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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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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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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ButThere is

A Small

Problem

22 April 15, 2023

The auction algorithm requires a knowledge of all the bids on each stage

Sometimes it is not possible

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!!

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24

Properties

• Solution is within from the optimum (Just like the original auction algorithm).

• Worst case time complexity is

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Nò

3NO

ò

Not so good…

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Distributed access via opportunistic carrier sensing (Zhao et al.)

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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

Example

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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

Example

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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

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:

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N N

2 ( )NO

E X ò

3 ( )NO

q

E X

Simulations

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Simulations

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The convergence might be too

slowWe need something

FasterAnd Simpler

33

Truncated auction

Lets ignore the bad channels

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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?

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

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[0, ]X a( ) 0Xf a

2 )log (N

1

1

N

35

Truncated auction

Proof:

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Just kiddingWe got a real

proof… In our paper.

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

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2log ( )N

2 log( )O N N

37 April 15, 2023

Can we go even faster?

38

Fast auction

Lets ignore the bad channels

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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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Bipartite graph

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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

Matching on bipartite graphs

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MatchingPerfect

Random bipartite graphs

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Matching on random bipartite graphs

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(

| | | |

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

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:

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2O N

log( )O N NTook us a whole paper to prove this one…

44

Simulations

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45

Simulations

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46 April 15, 2023

OK, it is fast!

ButIs the solution

GOOD?

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!!

48

Simulations

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50 April 15, 2023

Faster approaches?

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.

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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

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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

53

Greedy assignment

Theorem: The greedy assignment is asymptotically optimal for i.i.d Rayleigh channels.

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54

Simulations

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55

Simulations

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56

Simulations

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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.

58 April 15, 2023

And much more!

59 April 15, 2023

Thank you!