Cognitive Radio Maximizing SU throughput via optimal sensing

Faizan Ahmed Hashmi 7/8/2011

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Contents Introduction: ........................................................................................................................................... 3

Background: ........................................................................................................................................ 3

Cognitive Radio: .................................................................................................................................. 3

The Standard: .................................................................................................................................. 4

Cognitive Tasks: ............................................................................................................................... 4

The Optimal Sensing Problem: ................................................................................................................ 7

Solution to the OSP: ............................................................................................................................ 8

Assumptions: ................................................................................................................................... 8

Solution: .......................................................................................................................................... 9

An outline of POMDP: ....................................................................................................................... 11

Results and Interpretation: ................................................................................................................... 13

Ideas for further extention: .................................................................................................................. 16

Acknowledgements:.............................................................................................................................. 17

References: ........................................................................................................................................... 18

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Introduction:

Background: The frequency spectrum is a scarce natural resource most of which is licensed. Only very

few bands in the spectrum are unlicensed and open for use to anyone. These unlicensed

frequencies are also called ISM bands. An example of one such commonly used ISM band is

2.4-2.4835GHz [1]. Any wireless personal devices (PDs) if operating must use these free

bands. But with the development of technology the number of wireless PDs have increased

to a huge extent hence these free bands are becoming overcrowded and many PDs are

interfering with each other. Hence it is putting a limit on the number of such devices that

can be operated.

On the other hand, according to the report published in November 2002 by the Federal

Communications Commission (FCC) [2], the licensed band frequencies are not utilised all the

times. Some frequency bands are largely unoccupied most of the time whereas some are

only partially occupied and only the rest are heavily used.

Cognitive Radio: To overcome the problem of spectrum under utilization a new approach was thought in

which the unlicensed users called as secondary users (SUs) could use the licensed spectrums

when the license holder called the primary user (PU) was not using its band. The technology

being developed to implement this approach is called cognitive radio. The idea of cognitive

radio was first presented by Joseph Mitola III in a seminar at KTH, The Royal Institute of

Technology, in 1998. Cognitive radio can be thought of as a radio with brains which has the

capacity to be sensitive and adapt. It is well aware of its surrounding environment and

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changes its transmission or reception parameters to communicate more efficiently while

not crossing the interference limit of PUs. More formally it is defined as [3],

Cognitive radio is an intelligent wireless communication system that is aware of its

surrounding environment (i.e., outside world), and uses the methodology of understanding-

by-building to learn from the environment and adapt its internal states to statistical

variations in the incoming RF stimuli by making corresponding changes in certain operating

parameters (e.g., transmit-power, carrier-frequency, and modulation strategy) in real-time,

with two primary objectives in mind:

• Highly reliable communications whenever and wherever needed

• Efficient utilization of the radio spectrum.

The Standard: IEEE 800.22 is the standard in development of cognitive wireless regional area networks

(WRANs). It aims at using the licensed TV bands for serving denser areas and providing

wireless broadband access to rural and remote areas. For these cognitive tasks FCC has told

that TV channels 5-13 in VHF band and 14-51 in UHF band are to be used [4]. There

corresponding frequency bands are 76MHz-216MHz in the VHF range and 470 to 698 MHz

in the UHF range with each channel having a bandwidth of 6MHz [5]. TV bands were

specifically selected because of their favourable propagation characteristics which allow far

out users also to be serviced. This will provide suitable business for the wireless internet

service providers. Also it was due to the fact that many TV channels were found to be largely

unoccupied and many household and businesses rely on TV cable channels.

Cognitive Tasks: The cognitive process starts with the sensing of the frequency band and culminates with the

transmission of data in the suitable band. Basically there are three cognitive tasks:

1) Radio Scene Analysis, which is knowing about the frequency spectrum. Here

spectrum sensing is done to identify which channels are occupied by license holders.

To quantify the amount of interference and noise present, the amount of power

present at the receiver is converted to equivalent temperature, called as the

interference temperature. It serves as a ‘cap’ on the amount of RF energy that can be

introduced in the particular band of interest. So any transmission in that band is

considered to be harmful if it will increase the interference temperature beyond the

prescribed limit. And those bands can be used in which the transmission does not

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increase the set noise floor. Based on this sensing then we classify the spectrum in

a) Black Spaces, which are occupied by high power local interferers.

b) Grey Spaces, which are occupied by low power local interferers.

c) White Spaces, which are free of RF interferers.

These white spaces, for sure and grey spaces, to a lesser extent form a portion of

unutilised spectrum what is termed as spectrum hole, which can be utilised by the

unserviced operators.

2) Channel Identification, this involves estimation of channel. Here channel

modelling is done to account for multipath fading and other losses. This is first done

by sending a known sequence, called the pilot sequence before the actual

transmission of data.

3) Transmit Power Control, this is done to decide on what power the SU needs to

operate so that there is no interference to PU.

Tasks 1) and 2) are performed at the receiver while task 3) is done at the transmitter. The

modulation scheme used is the orthogonal frequency division multiplexing (OFDM).

Cognitive radio‘s design is paradigm shift from commonly done transmitter centric

approach, in which transmitter power is so regulated so as to maintain the prescribed SNR

at a fixed distance from the transmitter, to the innovative receiver centric approach, where

by transmission is done so as to not cross the prescribed interference at the receiver.

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Basic Cognitive Cycle focussing on the three cognitive tasks described above (Adapted from [3]).

The collision avoidance by a SU when operating along with PU is done as

1) Overlay Transmission: SU takes care that its transmission is in unused spectral

regions. So SU and PU are operating simultaneously in time domain but differ in

operation in frequency domain.

2) Underlay Transmission: SU is operating along with PU and is also spectrally

coincident with PU but SU takes care to induce only minimum tolerable interference.

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Fig. showing underlay and overlay (adapted from [8]).

The Optimal Sensing Problem: Quite a good number of channels are present in the cognitive radio network, but due to

hardware and energy constraints it is not possible for the secondary user to sense all the

available channels simultaneously. But as different channels have different channel gains,

different conditions of primary user activities and other time varying qualities the system

throughput, in our case number of bits transmitted, will vary with channel. Hence it is of

utmost important to the secondary or the cognitive radio user that he senses and selects

the appropriate channel for his use so that he can maximize his rewards, i.e. his throughput.

Not only sensing the channel which maximises the SUs throughput is important but doing

this sensing work in optimal time is also equivalently important. The system is divided in

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time slots wherein, each time slot consists of sensing time and transmission time.

So if sensing time is very less we would be scanning the spectrum for very less duration, this

means that we will have a higher probability of making errors while sensing. These sensing

errors can impact throughput as an idle channel with better channel qualities may go

undetected and a channel which was being used by the PU may be identified as an idle

channel, transmission on which may then result in zero throughput. On the other hand if

sensing time is large, the probability of errors is reduced but it will eat up the transmission

time hence throughput will be lowered. So the cognitive user also needs to keep in mind the

sensing time and must be able to strike a balance between throughput he wants to achieve

and the quantum of errors he can tolerate.

Hence the optimal sensing problem (OSP) is composure of both the optimal channel to be

sensed and that of optimal time.

Solution to the OSP: The discussion and analysis of the solution as presented in [6] is being dealt further.

Assumptions: 1) Secondary User can sense only one channel at a time.

2) System is time slotted.

3) State of a channel remains same in a particular time slot.

4) State transitions happen only at the beginning of a particular time slot.

5) System follows markov property.

sensing timetransmission

timetime slot

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6) The cognitive users operate only for fixed durations of time depending on their use

and donot operate continuously 24*7.

7) The transitions between the state are assumed to be markovic.

Solution: First a system model is created. This system is assumed to follow markov property. A

stochastic process has the Markov property if the conditional probability distribution of

future states of the process, given the present state and the past states, depend only upon

the present state [7]. A particular channel can have two states depending on the primary

user activity. Either the channel can be occupied due to primary user activity or it can be

idle. These two states can be represented as r0 or r1 respectively for a busy channel or for an

idle channel.

Fig. showing a markov model for primary transitions. The transition probabilities are

α and β.

Besides this due to the fluctuating channel conditions the secondary user also observes

channel in various states with respect to the signal to noise ratio (SNR) values. The channel

can then be divided into some ‘m’ number of states, with states being decided based on

SNR values. The SNR, denoted by u,at the receiver can be divided into m non-overlapping

intervals as u0 < u1 < u2 < …. < um-1. The channel is said to be in state k if uk < u < uk+1 . These

channel states follow markov transitions in which the next state in addition to being

dependent only on its current state is also arrived from its adjacent states alone.

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Fig. showing markov transitions for 3 states.

Note:

The division of channel states is done based on SNR also in addition to that of primary user’s

activity because when we have more number of channel states we have more knowledge

about the channel conditions, which then helps us in taking the optimal decision. For

example in case of two idle channels, the channel with better channel condition, i.e. one

with higher SNR value can be selected. Also sometimes it will be better to transmit over a

busy channel by underlay transmission, while taking care of the collision tolerance bound of

the primary user and achieve a higher throughput rather transmitting on an idle channel

with very poor channel condition because our final aim is to maximize SU’s throughput

while not crossing the tolerance level of PU’s.

The two states due to PU activity and m states due to channel fading together form a two

dimensional markov chain. Here we consider the SNR being divided in three states hence we

get a two dimensional markov chain with six states.

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Fig. showing 2 dimensional markov channel with 6 states.

The transitions due to primary activity and that due to channel conditions are independent

of each other. Hence the state transition probability matrix, Q can be formed as

Now what is done is that the OSP is now converted to a decision making problem, more

specifically into a partially observable markov decision process (POMDP).

An outline of POMDP:

POMDPs provide a rich framework to model uncertainty in a planning problem. They allow

action effects and state observations to be modeled probabilistically. POMDP is a more

general case of markov decision process (MDP). Markov Decision Processes provide a

mathematical framework for modelling decision making problems. In each time the process

is in some state s, the decision maker chooses an action a, from the set of actions avaliable

in that state so that the process goes to some new state s’, and giving the decision maker a

corresponding reward R. In MDP the current state is known by the agent but in POMDP the

agent doesn’t exactly know the underlying state, hence it maintains a probability

distribution, called the belief vector over the set of possible states based on a set of

observation and observation probabilities.

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Formally a POMDP is specified by the set <S,A,P,K,O,R>. S is set of possible states the system

can go into. In our case if the SNR at the receiver is divided in three, we have 6 states for

each channel. The states being r00, r0

1, r10, r1

1, r20, r2

1. A is the set of possible actions that can

be taken while the system is in state s. For us the action space consists of the channels to be

selected. P is the set which gives how much is the probability of channel going from one

state to another. K is the set of possible observations. O is the probability of observing

those observations and finally R is the set of rewards the decision maker gets, which here is

the number of packets transmitted by the SU in a particular time slot. Since our cognitive

user will operate for a fixed duration of time so we get a finite horizon partially observable

markov decision process.

Soln Contd.

Now what is done is that based on past or previous observations, we form a POMDP.

Solution for which gives the optimal channel to be sensed and the optimal sensing time

(OST) for a particular time epoch. Then the SU does the actual or real time sensing for our

guessed channel for the OST. The observation results then are used to update the belief

vector which then helps us in predicting the correct channel for next time epoch. Thus our

optimal decision sequence a1, a2 ….. at. forms the policy that maximises the aggregate

reward in the long run.

The one step transition of belief vector is

T(wj|a) = 𝑤𝑖𝑎

𝑖 𝑄𝑖𝑗𝑎 … (2)

where, a is the selected channel Q ij is the state transition probability as defined earlier and

wia is the probability of staying in state i of channel a.

Considering that the observation resultsmay not be perfectly correct for a secondary user in

state j. We assume that it indeed observes state j with probability 1-pf and gets a false alarm

i.e. probability of false detection is pf. Then,

Oajk =

1 − 𝑝𝑓, 𝑘 = 𝑗, 𝑗,𝑘 ⊑ 𝐾 − 𝑟′

𝑝𝑓, 𝑘 = 𝑟′ , 𝑗 ∈ 𝐾 − 𝑟′

0, 𝑘 ≠ 𝑗, 𝑗,𝑘 ⊑ 𝐾 − 𝑟′

…(3)

Here Oajk is the probability of observing some state k when taking action a in state j. K is the

set of possible observation states. Considering channel to be in some state rij, if j=1 i.e. the

channel is idle then the SU can determine ri through obervation after transmitting but if j=0

i.e. the channel is occupied by PU then ri = r’ where r’ = rso where s can be any either 0 or 1

or 2 (considering our 3 state modelling). Hence our observation set K is as K = r’, r01, r1

1,

r21.

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Further the false alarm is expressed in terms of channel bandwidth, W and sensing time ts

as

pf = Q(Q-1(1-pm)(1+µp) + µp 𝑡𝑠 ∗ 𝑊) ….. (4)

also here pm is the mis-detection probability i.e. the amount of collision which can be

tolerated by the PU and µp is the SNR of primary transmission.

The instant reward then can be expressed as a function of pf as

Rj = (1 – ts/tslot) * Bj * (1-pf) …. (5)

where Bj = log2(1+µs) µs , is the SNR of secondary transmission. tslot is the time for

one decision epoch. Here (1 – ts/tslot) * Bj denotes the effective throughput and (1 –

ts/tslot) * (1-pf) is the channel efficiency. From this equation (5) the optimal sensing time is

found out by maximizing the equation. The OTS so found from the above equation gives us

the maximum possible reward.

Then the optimal channel a is found from

𝑛𝑎∗ , 𝑡𝑠𝑎

∗ = 𝑎𝑟𝑔max𝑎 ( 𝑇(𝑤𝑗𝑗∈𝑛𝑎 𝑎 𝑅𝑗 + 𝑂𝑗𝑘

𝑎𝑘 𝑉𝑡−1

∗ )

….. (6)

The optimal joint selection na*,tsa

* specifying the index of selected channel and OST lead to

the highest expected throughput of SU. Now the SU initiates channel sensing with above

parameters and obtains observation results which are then deployed to update the belief

vector as,

Ω′𝑛 =

𝐼 Ω𝑛 , 𝑛 = 𝑛𝑎∗ ,𝑘 ∈ 𝐾 − 𝑟′

Ω𝑛𝑄′𝑛 , 𝑛 = 𝑛𝑎

∗ ,𝑘 = 𝑟′ Ω𝑛𝑄

𝑛 , 𝑛 ≠ 𝑛𝑎∗

…. (7)

Indication function, I(Ωn) returns a vector with all elements equal to zero except j-th

element Ij = 1, if observation, k matches the j-th channel state. Q’n is the modified

transition matrix of channel n given the observation that primary user is present, which can

be obtained by setting α and β to 0 in the state transition probability matrix.

Results and Interpretation:

The simulations were carried out for 3 channels and for a channel bandwidth of 4kHz and a

collision tolerance bound by the PU to be around 0.19% . The 3 state model is considered

with the average SNR at each state was taken to be 0db,5db and 10db. The belief vector is

assumed to be of gaussian distribution over every channel. If the constant sensing time

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(CST) was considered then sensing time was taken as 3ms. The state transition probabilities

zj = [z01 , z10 , z12 , z21] are respectively for each channel are taken as

z1=[0.05,0.15,0.05,0.25] , z2 = [0.15,0.05,0.05,0.15] and z3 = [0.25,0.05,0.15,0.05].

Fig. 1r)

The throughput of the SU depends on which state the channel is in. Hence when during the

simulation the SU is asked to enter its observation result, the throughput is based on its

observation result. If the SU observes better channel state his throughput is high but if he

observes channel in bad state he finds his throughput also lowered, which is as expected.

Fig. 2r)

0 20 40 60 80 1000

0.5

1

1.5

2

2.5

time in ms.

thro

ugh

pu

t o

f S

Uin

bit

s/s

lot

secondary user throughput

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The upper figure of fig. 2r shows probability of which channel being selected. We see that

channel 3 has the best channel condition among them as probability of going to a better

state is higher in channel 3 i.e. zij has a higher value when j>i as compared to when j<i . On

similar lines channel 1 has the worst condition among the 3 channels. Consequently we can

see from the results that the decision process in most cases selects the channel with better

channel condition and channel with worst condition is hardly selected.

The lower figure tells that the throughput concentrates on the channel with better

channel condition i.e. channel 3. The fourth bar depicts total throughput and not the

channel number.

1 2 30

0.2

0.4

0.6

0.8p

rob

abilit

y o

f se

nsed

cha

nne

l

channel number

1 2 3 40

5

10

15

20

channel number

thro

ugh

pu

t o

f S

U

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Fig. 3r)

We see that the channel efficiency of the proposed OST scheme is more than the CST

scheme. This because in OST the time was selected so as to maximize the reward i.e. the

throughput which may not be the case in CST always.

Ideas for further extention: 1) The work in [6] excels from other previous work in [9] because earlier the author had

only taken the primary activity into consideration but had not taken into account the

effect of channel fading. When the latter effect was taken in consideration, what it

did was to increase the number of observation states hence more knowledge about

the channel conditions can be known. This then helps the SU to make better choice

about the channel. So what can be done is that we can think of some way to increase

the number of observation states further by introducing some other parameter,

which then will also help us to observe the channel in a more better way.

2) Our objective is to maximize the throughput which is dependent on which state the

channel is. Hence what we need to do is to minimize the probability of the channel

being in bad state so that the more the chances of channel being in better state the

better the throughput can be. Hence instead of taking markov transitions among the

states, if we assume the transitions to be random then we have more chance of

state being in a better state.

0 5 10 15 20 25 30 35 40 450

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

time slots (unit 10 ms)

cha

nn

el

eff

icie

ncy

data1

data2CST

OST

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Acknowledgements:

First of all the author wishes to thank Allah, the most merciful. The author is then grateful to

Prof. S.N.Merchant who provided the opportunity to work in Signal Processing and Artificial

Neural Networking Lab (SPANN). He then expresses his sincere gratitude to Mr. Aaqib

Ashfaq Patel for being a constant support and guiding the author throughout his tenure. The

author also takes this opportunity to be thankful of his colleagues Mr. M.A.Faheem Siddique

and Mr. Syed Faizul Hai who along with the author worked and helped him in some or the

other way. Lastly the author is also debtful of other lab inmates of whom the author learned

a lot and some of whom who helped the author in doing the requisite lab arrangements.

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References: [1] http://forum.sunrom.com/index.php?topic=8.0

[2] Federal Communications Commission, “Spectrum Policy Task Force,”Rep. ET Docket no.

02-135, Nov 2002.

*3+ S. Haykin, “Cognitive Radio: Brain-Empowered Wireless Communications,” in IEEE Journal

on Selected Areas in Communications, vol. 23, no. 2, Feb 2005.

[4] C.R.Stevenson, Zhongding Lei, Gerald Chouinard, Wendong Hu, Stephen J. Shellhammer,

Winston Caldwell, “IEEE 802.22: The first cognitive radio wireless regional area network

standard,” Magazine IEEE 2009.

[5] http://www.csgnetwork.com/tvfreqtable.html

[6] Shimin Gong , Ping Wang, Wei Liu, Wei Yuan, “Maximize secondary user throughput via

optimal sensing in multi-channel cognitive radio networks”.

[7] http://en.wikipedia.org/wiki/Markov_property#Introduction

[8] V.D. Chakravarthy, Z. Wu, A. Shaw , M.A. Temple , R. Kannan and F. Garber,” A General

Overlay/Underlay Analytic Expression Representing Cognitive Radio Waveform”.

[9] Q. Zhao, L. Tong, A. Swami, and Y. Chen, “Decentralized cognitive mac for opportunistic

spectrum access in ad hoc networks: A pomdp framework,” Selected Areas in

Communications, IEEE Journal on, vol. 25, no. 3, pp. 589 –600, april 2007.