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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:[email protected] Email:[email protected]
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.
Remika Ngangbam et al , International Journal of Computer Science & Communication Networks,Vol 3(3),160-163
160
ISSN:2249-5789
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
Remika Ngangbam et al , International Journal of Computer Science & Communication Networks,Vol 3(3),160-163
161
ISSN:2249-5789
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
Remika Ngangbam et al , International Journal of Computer Science & Communication Networks,Vol 3(3),160-163
162
ISSN:2249-5789
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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