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\title{Enhancing Transmission Capacity of a Cognitive Radio Network by Joint Spatial-Temporal Sensing with Cooperative Communication Strategy}
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\begin{document}

             \author[1]{Muntasir  Ahmed}

             \author[2]{Md. Anwar  Hossain}

             \author[3]{A F M Zainul  Abadin}

             \affil[1]{  Pabna Science and Technology University, Pabna-6600, Bangladesh}

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\date{\small \em Received: 14 December 2012 Accepted: 1 January 2013 Published: 15 January 2013}

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\begin{abstract}
        


In static cognitive radio network a secondary transmitter communicates directly with a secondary receiver only when the spectrum is not occupied by any primary user. The secondary user has to stop its transmission when no spectrum holes exist. To improve the transmission capacity, in this paper we approach to combine cognitive radio network with cooperative communication strategy employing spatial sensing as well as temporal sensing. In our proposed scheme when primary user is active, a secondary user transmits to another secondary user via a relay channel. By enabling the use of both the direct and relay channels, the transmission performance of the secondary system can be improved significantly. Our information-theoretic analysis as well as numerical results show that the proposed scheme significantly reduces the average symbol error probability compared to schemes based on pure temporal or spatial sensing.

\end{abstract}


\keywords{cognitive radio network; cooperative communication; joint spatial-temporal sensing; spectrum sensing; spectrum sharing.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
he radio spectrum is among the most heavily regulated and expensive natural resources around the world. In Europe, the 3G spectrum auction yielded 35 billion dollars in England and 46 billion in Germany. The question is whether spectrum is really this scarce. Although almost all spectrums suitable for wireless communications has been allocated, preliminary studies and general observations indicate that much of the radio spectrum is not in use for a significant amount of time, and at a large number of locations.\par
According to the statistics of the Federal Communications Commission (FCC), temporal and geographical variations in the utilization of the assigned spectrum range from 15\% to 85\% \hyperref[b0]{[1]}.\par
The limited available radio spectrum and the inefficiency in spectrum usage necessitate a new communication paradigm to exploit the existing spectrum dynamically. The FCC has realized that overcrowding of unlicensed bands is only going to worsen and is considering opening up licensed bands for opportunistic use by secondary radios/users. One of the most efficient paradigms is the cognitive radio network (CRN), first introduced by J. Mitola \hyperref[b1]{[2]}, which is built upon software-defined radio (SDR) technology. S. Haykin defines a cognitive radio (CR) as "an intelligent wireless communication system that is aware of its environment and uses the methodology of understanding-by-building to learn from the environment and adapt to statistical variations in the input stimuli" \hyperref[b2]{[3,}\hyperref[b3]{4]} with the overarching aim of providing reliable communication whenever and wherever needed while efficiently using the resources available to it.\par
A CRN is built on the following principle: a network of secondary users (SU) (users without license) continuously senses the use of a spectrum band by primary users (PU) and opportunistically utilizes the band when PUs are absent. Any SU in a CRN performs two main functions: (1) sensing spectrum usage to identify absence or presence of a PU, and (2) T transmitting at appropriate power if the PU is absent. Thus, the design principle for CRN regards the CR users as visitors in the spectrum they occupy (Fig. \hyperref[fig_0]{1}). The successful operation of these principles relies on the CRN users' ability to be aware of their surroundings, which is accomplished through spectrum sensing solutions.\par
Spectrum sensing (the optimization of sensing parameters in a single spectrum band, spectrum selection and scheduling, and an adaptive and cooperative sensing method) enables CR users to adapt to the radio environment by determining currently unused spectrum portions, so-called spectrum holes or spectrum white spaces, without causing interference to the primary network. Generally, spectrum sensing techniques can be classified into four groups: (1) primary transmitter detection (matched filter detection, energy detection, and feature detection), (2) cooperative detection, (3) primary receiver detection, and (4) interference temperature management \hyperref[b0]{[1]}. The SUs periodically sense the spectrum in order to identify and use the spectrum holes. When a SU senses that the PU is accessing the spectrum or determines that the PU is going to access the spectrum, it then vacates the spectrum and moves to the another spectrum or lowers its transmitting power. If there is another SU instead of the PU, then the first SU shares the spectrum with the new SU. Spectrum holes exist both in time and in space. A spectrum hole in time may arise when a PU of the spectrum is idle, i.e., not transmitting. In this case, temporal spectrum hole is the duration for which the primary user-transmitter (PU t ) is in the idle state (Fig. \hyperref[fig_1]{2} (a)). A spectrum hole in space with respect to a given frequency channel may occur if a given SU is sufficiently far from a PU that is actively transmitting (Fig. \hyperref[fig_1]{2 (b)}). In this case, the SU may transmit up to a certain level, which we called the maximum interference-free transmit power (MIFTP), without causing harmful interference to PUs who are receiving the transmissions. This results a useful spectrum sharing.\par
However, in the typical scenarios of static CRN where SU observe the activity of the PU in a fixed spectrum band and access the entire spectrum band if a spectrum opportunity is detected (based on IEEE 802.11 and IEEE 802.15.3 technologies), a SU transmitter communicates directly with SU receiver only when the PU is idle. A SU has to stop its transmission when no spectrum holes exist (Fig. \hyperref[fig_1]{2}  The SU transmitter communicates directly with the SU receiver, due to the existence of a (a) temporal spectrum hole or a (b) spatial spectrum hole with respect to PU t . 
\section[{Typical CRN transmission limitation due to lack of spectral holes in shown in (c)}]{Typical CRN transmission limitation due to lack of spectral holes in shown in (c)}\par
To improve the transmission capacity of CRN, here we approach to combine CRN with cooperative communication strategy employing joint spatialtemporal sensing to maximize the transmission capacity of SUs in a CRN. In these scenarios, when PU transmitter is active, SU transmits to another SU receiver via a relay channel. By enabling the use of both the direct and relay channels, the transmission performance of the secondary system (CRN) can be improved significantly. Our proposed approach is depicted in Fig. \hyperref[fig_3]{3}. 
\section[{SU-Transmitter}]{SU-Transmitter}\par
Actively Transmitting 
\section[{SU-Receiver}]{SU-Receiver}\par
Actively Receiving 
\section[{PU-Transceiver}]{PU-Transceiver}\par
Active 
\section[{NO Communication}]{NO Communication} 
\section[{SU-Transmitter}]{SU-Transmitter}\par
Actively Transmitting 
\section[{SU-Receiver}]{SU-Receiver}\par
Actively Receiving 
\section[{PU-Transceiver}]{PU-Transceiver}\par
Active or Idle  Cooperative communications is a new paradigm that draws from the ideas of using the broadcast nature of the wireless channel to make communicating nodes help each other, of implementing the communication process in a distribution fashion and of gaining the same advantages as those found in MIMO systems \hyperref[b4]{[5]}. The end result is a set of new tools that improve communication capacity, speed, and performance; reduce battery consumption and extend network lifetime; increase the throughput and stability region for multiple access schemes; expand the transmission coverage area; and provide cooperation tradeoff beyond source-channel coding for multimedia communications. This idea is true for wide varieties of wireless networks such as mobile ad hoc networks, sensor networks, or cellular networks. In this paper, we consider the decode-and-forward (DF) cooperative strategy focusing on the case of a single-hop relay channel. 
\section[{Direct}]{Direct} 
\section[{II.}]{II.} 
\section[{System model a) Transmission frames and PU t behavior}]{System model a) Transmission frames and PU t behavior}\par
Time on the wireless channel is divided into frames consisting of s N symbols. We shall assume perfect symbol level timing synchronization between the nodes of the secondary system. The primary usertransmitter (PU t ) alternates between active and idle states on a per-frame basis according to the active-idle Markov model of Fig. \hyperref[fig_6]{4}.\par
The active and idle durations can be modeled by geometric random variables with parameters q and p , respectively \hyperref[b5]{[6]}. We focus on scenarios in which p q > ; i.e., on average, PU t is more often in the active state than the idle state (which is more practical to assume). Let us suppose that kp q = , where k is an integer with 1 > k . Hence, if PU t is idle for one time frame on average, it will be active for K time frames, on average.\par
A similar approach can be used when q p > . 
\section[{b) Cooperative transmission protocol}]{b) Cooperative transmission protocol}\par
Suppose a secondary user-transmitter (SU t ) desires to transmit s N symbols; i.e., it requires one full frame in which PU t is idle. The cooperative protocol works as follows (Fig. \hyperref[fig_3]{3}): When PU t is active, SU t sends information to secondary user-receiver SU r via the relay nodes SU relay . When PU t is idle, SU t sends information directly to SU r . In order to achieve this, the secondary nodes (SU t , SU relay and SU r ) perform joint spatialtemporal sensing \hyperref[b6]{[7]}. In particular, all secondary users estimate their MIFTPs based on signal strength measurements, which they exchange with one another. They also decide whether the PU t is active or idle, by transmitting their local decisions to a fusion center, which then makes the final decision. We shall assume that there exists a communications path from SUt to SUr through SUrelay. This path would be established by a routing protocol. A repetition code \hyperref[b7]{[8]} is used to repeat the transmission of the signal over K 0 and 1 K frames, whereK K K = + 1 0 .\par
At each relay, the transmitted signal is amplified and forwarded to the next relay node until it reaches the destination. When PUt is idle, SUt can communicate s N symbols over one time frame directly to SUr. Due to broadcast wireless channel, SUrelay also received a copy of signal from SUt but ignores it. When SUr receives a signal from the relay path, it stores the received signal and waits until it receives the same signal directly from SUt and vice versa. The received signals at SUr are then combined using MRC. Finally, maximum likelihood (ML) detection is used to detect the signals. 
\section[{c) Cooperative Relaying}]{c) Cooperative Relaying}\par
The received signal of a simple wireless channel model with flat fading and no shadowing is given by \hyperref[b8]{[9]} ( )n hs P n s ? h d r d ? y + = + = ? (1)\par
Where 2 ? is the free space signal-power attenuation factor between the source and a reference distance r d , d is the distance between the source and destination, ? is the propagation exponent, ( )2 0 h ,? h\textasciitilde C? is a complex Gaussian random variable with variance 2 h ? , ( ) 0 0,N n\textasciitilde C?\par
, and s is the transmitted signal. In Eq. (  {\ref 1}),( ) ? ? ? d r d P 2 =\par
denotes the equivalent transmitted power after taking into account the effect of path loss. We also define   {\ref (} )( ) 0 0 2 0 ? ? ? d r d P = , (\textbf{)}1n s P g K i i n s P i g i g y 0 0 1 0 * 1 + ? = = + = ,\textbf{(2)}\par
Where? = = 0 1 2 \textasciitilde K i i g g and ? = = 0 1 * \textasciitilde K i i i n g n\par
, s is the transmitted symbol, 1 2 = s and i g is the channel gain between SU t and SU relay during time frame . The received signal at SU r due to relay SU relay is( ) ( ) R n s g A h P P K j j n n s P g A j h P j h R y + = ? = + + = 1 0 1 1 0 1 * , (3) Where ? = = 1 1 2 K j j h h , ? = + = ? ? ? ? ? ? 1 1 * 1 2 K j j n j h n P A j h R n\par
, j h is the channel gain between SU relay and SU r during time frame j . Here, A is the amplification factor which is chosen to maintain average constant power output at SU relay , ( )g N g P A 0 2 0 1 2 + = . The noise variance of R y is 0 0 2 1 2 2 N h N h g P A R + = ? where ? = = 1 1 2 \textasciitilde K j j h h . The direct transmission (SU t ? SU r ) channel model is T n s t P f T y + = , (\textbf{4})\par
Where f is the channel gain between SU t and SU r . ( ) ( ) r t R P P h g A N t P f w ? ? ? ? + = + = 2 1 0 2 0 2 ,\textbf{(5)}\par
Where ( )0 2 N t P f t = ? and\textbf{( ) ( ) (}\par
)1 1 0 1 0 2 1 0 2 \textasciitilde + + = = ? ? ? ? ? ? R P P h g A r ,\textbf{(6) with (}\par
)0 0 0 N P g = ? and\par
( )0 1 1 N P h = ?\par
. We assume that f , i g , j h are known at receiving end. The symbol error probability (SEP) conditioned on the instantaneous SNR is given by ( ) [10] where k is a constant that depends on the type of modulation andw k Q e P ? =( ) ( ) ? ? ? = x t e x Q dt 2 / 2 2 1 ?\par
is the standard Q -function.\par
III. 
\section[{Performance analysis}]{Performance analysis}\par
In this section, we derive a lower bound on the average SEP. We show that the SEP lower bound is minimized when1 0 K K =\par
for K even and \hyperref[formula_13]{6}), we can upper-bound r ? as follows:1 1 0 + = K K for K odd. From Eq. (( ) ( ) ( ) h g N P P r 0 2 1 0 2 1 0 1 0 1 0 = ? + ? ? ? ? ? ? ? ? ,\textbf{(7)}\par
Taking expectations on both sides, we have [ ] (\par
) [ ]h g E N P P r E 0 2 1 0 ? ? ,\textbf{(8)}\par
Note that ) , \textasciitilde  CN( j , h i g 1 0 then g 2 and h 2 are independent 2 ? -distributed random variables with 0 2K and 1 2K degrees of freedom, respectively. Applying Jensen's inequality,[ ] [ ] [ ] [ ] 1 0 2 2 2 1 \textasciitilde K K h E g E h g E h g E = = ? ,\textbf{(9)}\par
From Eq. ( \hyperref[formula_21]{8}) and Eq. ( \hyperref[formula_22]{9}), we have[ ] ( ) 1 0 0 2 1 0 K K N P P r E ? ? ,\textbf{(10)}\par
Assuming M-PSK modulation, the average SEP can be expressed as follows \hyperref[b10]{[11]}:( ) ( ) ( )d? 1 0 1 ? ? ? ? ? ? ? ? ? ? = r M M M t M SEP ,\textbf{(11)}\par
Where 1 0 K K e r E e r e E r M ? ? ? ?? ? ? ? ? ? = ? = ? ,\textbf{(12)}\par
Where( ) 0 0 2 1 0 ? ? N P P ? ? .\par
The lower bound for the SEP is then obtained by substituting the right hand side of Eq. ( \hyperref[formula_25]{12}) into Eq. ( \hyperref[formula_24]{11}). If K is even, i.e., m K 2 = wherem is an integer, m K K K K 2 1 0 1 0 2 = + ?\par
, with equality holding whenm K K = = 1 0\par
. In this case, Eq. ( \hyperref[formula_25]{12}) implies that the choice of1 0 K K =\par
maximizes the performance of our proposed scheme. If K is odd, i.e., 1 2 + = m K , information-theoretic results in \hyperref[b11]{[12]} suggest the choice1 0 K K >\par
, in order to maximize the SNR at the first hop.\par
Letn K K + = 1 0\par
, where 1 ? n is an integer. We have-n m K 1 2 1 2 + = , m m -n m m K K 4 2 4 2 1 4 2 4 1 0 4 + ? + + =\textbf{(13)}\par
The equality in (13) holds for1 1 0 + = K K\par
, which also suggests that choosing1 1 0 + = K K minimizes ( ) ? ? ? r M\par
and hence the SEP. Our analysis is confirmed by the simulation results presented in Section 4.\par
IV. 
\section[{Numerical results}]{Numerical results}\par
In this section, we present the simulated result of our proposed scheme in CRN. In the performance curves, the 95\% confidence intervals are omitted for clarity. BPSK modulation is used and ( )1 , 0 , , CN j h i g f\par
The frame length is 100 symbols. MRC and detection are used at the receiver.\par
In the first phase, we have assumed that the three channels have equal average SNRs, i.e. the distances between source, relay and destination are assumed to be equal. So it is logical to think the same MIFTPs for this case. , the transmission strategy follows the scheme described in Section 2, which we call (strategy 1). The traditional cooperative communication scheme, which we call strategy 2, transmits m times on the path SU t ? SU relay ? SU r over m branches. Fig. \hyperref[fig_5]{5} shows the SEP performance of our scheme with one relay and  In practice, the situation in the CRN becomes so much complex that it leads us to think different distances among the SU t , SU relay and SU r (instead of assuming equal distances among them having the same average SNRs) which results different fading characteristics of these three channels. Hence these three channels will have different average SNRs. The simulated result of this condition is presented in Fig. \hyperref[fig_9]{7} when the MIFTPs and the average SNRs ( ) . This also confirms the results in \hyperref[b11]{[12]} in which the maximum transmission capacity is achieved when the relay is situated slightly near the source terminal or in the middle between the source and the destination.  
\section[{Conclusion}]{Conclusion}\par
We proposed a scheme works with the cooperative communication strategy in cognitive radio networks so that the secondary users can get all time transmission connectivity by using both spatial spectrum white space sensing and temporal spectrum white space sensing. This results maximum possible spectrum utilization. The proposed scheme improves the transmission capacity of static cognitive radio network to a great extent.\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_2}E}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-5.png}
\caption{\label{fig_3}Figure 3 :E}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-6.png}
\caption{\label{fig_4}E}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5}\includegraphics[]{image-7.png}
\caption{\label{fig_5}Figure 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4}\includegraphics[]{image-8.png}
\caption{\label{fig_6}4 K}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6}\includegraphics[]{image-9.png}
\caption{\label{fig_7}Figure 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-10.png}
\caption{\label{fig_8}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7}\includegraphics[]{image-11.png}
\caption{\label{fig_9}Figure 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.04651741293532338\textwidth}P{0.42077114427860696\textwidth}P{0.025373134328358207\textwidth}P{0.0021144278606965174\textwidth}P{0.22412935323383085\textwidth}P{0.12475124378109452\textwidth}P{0.006343283582089552\textwidth}}
\tabcellsep \multicolumn{4}{l}{Enhancing Transmission Capacity of a Cognitive Radio Network by Joint Spatial-Temporal Sensing with}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep Cooperative Communication Strategy\\
\tabcellsep \multicolumn{4}{l}{active and t ? denotes the maximum transmit power of}\\
\tabcellsep SU t . When\tabcellsep ? << 0\tabcellsep ?\tabcellsep t\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep 0 K time frames [8]\\
013\tabcellsep as\tabcellsep \tabcellsep \\
2\tabcellsep \tabcellsep \tabcellsep \\
Year\tabcellsep \tabcellsep \tabcellsep \\
22\tabcellsep \tabcellsep \tabcellsep \\
D D D D ) E\tabcellsep \tabcellsep \tabcellsep \\
(\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep q\\
\tabcellsep 1-q\tabcellsep \multicolumn{3}{l}{active}\tabcellsep idle\tabcellsep 1-p\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep p\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep ( d powers from SU process ) t t d r t P ? ? ? 2 =\tabcellsep 1 d as the equivalent transmitted 2 1 ? ? ? r d P = and\\
\tabcellsep \multicolumn{4}{l}{© 2013 Global Journals Inc. (US)}\end{longtable} \par
  {\small\itshape [Note: t to SU relay , from SU relay to SU r , and from SU t to SU r , respectively. Here, 0 d , 1 d and t d denote the distances between the node pairs (SU t , SU relay ), (SU relay , SU r ), and (SU t , SU r ), respectively. Also 0 ? and 1 ? denote the MIFTPs of SU t and SU relay , respectively when PU t is Figure 4 : 2-state Markov chain model for PU t active/idle]} 
\caption{\label{tab_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.7741071428571428\textwidth}P{0.07589285714285714\textwidth}}
\multicolumn{2}{l}{R y and T y . The noise variables R n and T n have}\\
different powers because\tabcellsep R n includes a noise\\
\multicolumn{2}{l}{contribution at the relay. For this reason, noise}\\
\multicolumn{2}{l}{normalization is necessary for MRC of T y and R y as in}\\
{}[10]. The resulting SNR is\tabcellsep \end{longtable} \par
 
\caption{\label{tab_1}}\end{figure}
 			\footnote{© 2013 Global Journals Inc. (US)} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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\end{document}