MIMO-OFDM based Cognitive Radio Networks Capacity analysis with

Water Filling Techniques

Remika Ngangbam

R. Anandan Chitralekha Ngangbam Department of Electronics and Department of Electronics and Department of Electronics

Communication Engineering, Communication Engineering and Communication Dhanalakshmi Srinivasan Dhanalakshmi Srinivasan Engineering, National College of Engineering and College of Engineering and Institute of Technology,

Technology, Anna University, Technology, Anna University, Imphal – 795001, Chennai-600025, India Chennai-600025, India Manipur, India

Email:ngangbamremika7@ Email:anandankd@gmail.com Email:ng.chitra@gmail.com

gmail.com

Abstract: In this paper proposed water filling algorithm is

discussed which has been used for allocating the

power to the MIMO channels in cognitive radio

network so as to enhance the capacity of the network.

Here we present a theoretical framework for allocating

the power considering a 4x4 MIMO system and the

system is assumed to be MIMO-OFDM based cognitive

network and the channel to be flat as under this the convolution integral becomes a simple multiplication

operator. In this paper we study the comparison of

various systems with and without the proposed water

filling algorithm for the available power budget. It can

be observed from the graphs that the efficiency of the

system is enhanced with the proposed water filling

algorithm and also it is observed that the outage

probability shows constant value as compared to the

outage observed in the systems without the water

filling algorithm. It is further seen that there is

enhancement in the capacity of a MIMO system.

Keywords: Cognitive Radio, MIMO-OFDM, Water

Filling, outage probability, system capacity

1. Introduction

The MIMO system has multiple transmit and

receive antennas and Orthogonal Frequency-Division Multiplexing (OFDM) is used as it is sought as one of

the solution for increasing the capacity and data rate of

a system in an environment where the communication

take place in a frequency-selective fading

environments and there can be probably more chances

for data corruption. It has been found that Multiple-

Input and Multiple-Output (MIMO) can be effectively used to increase the capacity of the system by a factor

of the minimum number of transmitter and receiver

antennas attached in the MIMO system as compared to

a Single-Input Single-Output (SISO) system that has

flat fading or frequency selective fading environment

or narrowband channels, OFDM can also increase

diversity gain and minimize the inter-symbol

interference on a time-varying multi-path fading

channel. When we know the parameters of the channel

both at the transmitter end and at the receiver end, we

can further increase the capacity of MIMO OFDM

systems by assigning power at the transmitter

according to the water filling algorithm to the

channels.

A cognitive radio is a transceiver which

automatically detects available channels in wireless

spectrum and accordingly changes its transmission or reception parameters so more wireless communications

may run concurrently in a given spectrum band at a

place. Therefore, regulatory bodies in the world have

been considering to allow unlicensed users in licensed

bands if they would not cause any interference to

licensed users. Cellular networks bands are overloaded

in most parts of the world, but other frequency bands

are insufficiently utilized. Therefore, regulatory bodies

in the world have been considering to allow unlicensed

users in licensed bands if they would not cause any

interference to licensed users. These initiatives have

focused cognitive-radio research on dynamic spectrum

access.

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2. Related work

A lot of work has been already done on the resour-

-ces allocation in non-cognitive and cognitive relay

systems. In [5], the authors proposed an algorithm to

select the best transmit way between the network

nodes. The algorithm can select direct, dual or

diversity transmission based on the available spectrum

as well as the maximum allowable transmission

powers. In [4] the authors studied a proposed algorithm

which has a much lower computational complexity and

the performance is close to optimal scheme but outage

probability has no change. In [6] optimal resource

allocation is done in cognitive networks with

interference constraints with the available power

budgets. In [19] it is seen that the proposed algorithm has a much lower computational complexity and the

performance is close to optimal scheme but no

information of outage probability.

To the best of our knowledge, no one has

analysed the capacity and outage probability of

cognitive radio networks together except the resources

allocation. The main contributions of the paper are the

capacity and outage probability analysis of the

secondary users with the help of water filling algorithm

by using some mixed integer programming problem

taking into account that the different relays are

applying DF-protocol.

3. System Model

A one-cell wireless system, in which the PU and

SU transceivers coexist in the same geographical

location is considered. The scenario is investigated for

downlink path and for a CR user. PUs‟ base station

transmits signals to N PUs, each of which occupies a

determined frequency band in the available spectrum.

Suppose that the CR base station and the CR user have

NT and NR antennas, respectively. The SU MIMO

channel for ith sub-carrier is denoted by an N × M

matrix Hi where its element hi, n, m denotes the channel gain for the channel between the mth transmit

and the nth receive antenna. The channel gain between

the SU transmitter and the lth PU receiver for the ith

sub-carrier is denoted by a 1 × M matrix, where gi, l, m

denote the channel gain for the channel between the

SU‟s mth transmit antenna and the lth PU receiver

antenna.

Since we assumed that the transmitter has the

perfect CSI, each sub-carrier channel can be

decomposed into parallel independent sub-channels by

singular value decomposition (SVD).

Hi=UiɅiVi* (1)

Where Ui ϵ CNR×NR and Vi ϵ CNR×NR

are unitary

matrices and Ʌi ϵ CNR×NT is a rectangular matrix

wose diagonal elements are non-negative real numbers.

The diagonal elements 𝛌1≥𝛌2≥.........𝛌 nmin are the

ordered singular values of the matrix Hi, where

nmin=min(NR,NT).

4. Proposed Water Filling algorithm

Water filling is a metaphor for the solution of

several optimization problems related to channel

capacity. Water filling refers to a technique whereby

the power for the spatial channels are adjusted based

on the channels gain. The channel with high gain and

signal to noise ratio is given more power. More power

maximizes the sum of data rates in all sub channels.

The data rate in each sub channel is related to the

power allocation by Shannon‟s Gaussian capacity

formula C = B log (1 + SNR). However, because of the

capacity is a logarithmic function of power, the data

rate is usually insensitive to the exact power allocation.

This motivates the search for simpler power allocation

schemes that can perform close to the optimal. The total amount of water filled (power allocated) is

proportional to the Signal to noise ratio of the channel.

The Capacity of a MIMO system is algebraic sum

of the capacities of all channels and is given by the

formula below.

(2)

we have to maximize the total number of bits to be

transported.

Figure1: Proposed water filling algorithm

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Algorithm steps:

1. Take the inverse of the channel gains. Water

filling has non uniform step structure due to

the inverse of the channel gain.

2. Initially take the sum of the total power Pt

and the inverse of the channel gain. It gives

the complete area in the water filling and

inverse power gain.

3. Decide the initial water level by the formula given below by taking the average power

allocated.

4. The power values of each sub channel are

calculated by subtracting the inverse channel gain of

each channel. In case the power allocated value

become negative stop iteration.

(3)

Where Pt is the power budget of the MIMO

system which is allocated among the different channels

and H is the channel matrix of the systems.

5. MIMO-OFDM Capacity And Outage

Probability

Consider a MIMO OFDM system with Nr

receivers and Nt transmit antennas. The system is

represented as

Y = hx + n (4)

Where „ x ‟is the (Ntx1) transmit vector, „y‟ is the

(Nrx1) receive vector, „h’ is the (NtxNr) channel matrix

and „ n ‟ is the (Nrx1)additive white Gaussian noise

(AWGN) vector at a given instant in time. Generally

the channel matrix is denoted by ℎ𝑖𝑗 and this

represents the complex gain of the channel between the

jth transmitter and the ith receiver. The channel capacity is associated to an outage

probability. Capacity treated as random variable

depends on the channel instantaneous reasons and

remains constants. If the channel capacity falls below

the outage capacity there is no possibility that the

transmitted block of information can be decoded with

no errors, in which error coding scheme employed. The

outage probability is

(5) Where Q=E[HH

+] is covariance, R is information rate

to be transmitted. It is conjectured that Pout is

minimized by using a uniform power allocation over a

subset of the transmit antennas.

6. Simulation Results

The channel mean capacity vs SNR curve of

different systems is shown in figure 2. It is shown that the mean capacity of the MIMO system with proposed

water filling has higher capacity than those without

water filling algorithm at the available power budget.

And also when a graph is plotted with outage

probability Vs SNR it is observed that the MIMO

system with proposed algorithm has constant outage

probability than other systems.

Figure 2: Plot of Mean Capacity Vs SNR in dB

Figure 3: Plot of outage probability Vs SNR in dB

7. Conclusion

In this paper, we investigated the power allocation

scheme for CR networks, employing the MIMO–

OFDM structure. It has been shown analytically that

the conventional power loading algorithm cannot be

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used in CR networks. Then, we proposed a new

algorithm that maximise the transmission capacity of

CR users; meanwhile the interference introduced to the

PUs remained below the specific threshold.

Furthermore, it described the Mean capacity allocation

in a wireless cellular network based on the water filling

power allocation in order to enhance the capacity of a

MIMO systems with different channel assumptions.

Here each transmitter decide the distribution of power to the several independent fading channels. Results

indicates that the water-filling scheme has better

capacity than without water filling with the available

power budgets. The variation in outage probability is

also discussed. In future we can try to to increase the

sensing of spectrum in CR network and make avail

more CR application with less expenditure systems.

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