CN103441806B - Pure discontinuous Markov process spectrum sensing method for cognitive radio - Google Patents

Abstract

The invention provides a pure discontinuous Markov process spectrum sensing method for a cognitive radio and belongs to the technical field of cognitive radios. In the prior art, an initial probability transfer matrix may not reflect the true change situation of a frequency band state, possibly loses frequency band state information within two disperse moments, and can not finish the task of tracking the state of a main user. A Q matrix of the birth and death process is utilized in the method for deriving the probability transfer matrix of the pure discontinuous Markov process of the busy and free state, and the probability transfer matrix can correspond to transfer probabilities of a frequency band in a free and free state, a free and busy state, a busy and free state and a busy and busy state respectively. The probability transfer matrix in the former step is utilized for deriving the probabilities of the frequency band in a free state or a busy state at any moments, and therefore the state of the frequency band is sensed. A mean value, a covariance and a variance of the frequency band state gamma (t) is calculated, and therefore the accumulative residence time, of the main user, on a time domain within a time period (0, t) can be obtained. Results of the former three steps are utilized for obtaining the distribution situation of the main user on the time domain, and therefore the state of the main user is tracked.

Description

The pure discontinuous Markov process frequency spectrum sensing method of cognitive radio

Technical field

The present invention relates to a kind of pure discontinuous Markov process frequency spectrum sensing method of cognitive radio, the method utilizes pure discontinuous markov (Markov) process apperception frequency range state, complete the tracking of primary user's state, realize the frequency spectrum perception of cognitive radio, belong to cognitive radio technology field.

Background technology

Along with the develop rapidly of wireless communication technology, people are also increasing to the needs of wireless communication resources, and the shortage of frequency spectrum resource becomes wireless communication technology and applies the key issue faced., a large amount of testing result shows, frequency spectrum resource not lacks, but most of frequency spectrum resource utilizes unreasonable, and some unauthorized frequency ranges take crowded, and meanwhile, some are authorized frequency range to be but in idle state but limit other people and use.The portion report display that FCC (FCC) provides, the utilance of having distributed frequency spectrum is only 15 ~ 85%.30 ~ 3000MHz frequency spectrum the utility efficiency carried out in the U.S. finds, the utilance of U.S.'s each department frequency spectrum resource is on average only 5.2%, the highest New York of utilance only 13.1%.In this case, the frequency spectrum distributing technique that can improve frequency spectrum resource utilization rate obtains to be applied more and more widely.And the prerequisite of spectrum allocation may is frequency spectrum perception.

In existing cognitive radio frequency spectrum cognition technology, have a kind of method HMM (hidden Markov model) being introduced cognitive radio frequency spectrum perception, i.e. the HMM frequency spectrum sensing method of cognitive radio, the method can accurately perception frequency range state.Described frequency range state refer to frequency range at any time occupy state, being busy condition when being occupied by primary user, not occupied then for idle condition by primary user.HMM is introduced the variation model that primary user occupies/do not occupy by the method, as shown in Figure 1, and a discrete time (1,2,3 ...) system in given state space S from a state change at random to another state.Here Y _nthe true frequency range state i in n moment, i.e. hidden state.X _nthe perception state b produced by certain perception mechanism, i.e. observer state, true frequency range probability transfer matrix A=[a _ij] be 2 × 2 matrixes, wherein i=0,1, j=0,1,0 to represent frequency range busy, and 1 represents the frequency range free time.Initial probability distribution p ₀=Pr (y _i=0), p ₁=Pr (y _i=1), observing matrix B is equally also 2 × 2 matrixes, and its probability meaning can be understood as hidden state i=0,1 ... N from all possible transmitting symbol b=0,1 ... the emission probability of random selecting in M, its distribution function is:

Pr(X _n＝b|Y _n＝i)＝e _i(b)

b＝0,1,2,…M,and

i＝0,1,2,…N

Described emission probability refers to that true frequency range state i launches a symbol arbitrarily from transmitting assemble of symbol b, and its distribution function is:

System mode: i, i=0 12 N

Emission state: 012 M

Emission probability: e _i(0) e _i(1) e _i(2) e _i(M)

Process X ₁, X ₂... observable.Under frequency range state aware background, the span of b and i between zero and one, that is, M=N=1.As previously mentioned, under frequency range state aware background, unavoidably perceptual error can be produced.When true frequency range state i is busy, perception state b is idle, described emission probability is PMD (error probability), represents with δ; When true frequency range state i for idle and perception state b is busy time, described emission probability is PFA (false alarm probability), represents with ε; When true frequency range state i for idle and perception state b also be the free time time, described emission probability is PD (detection probability), represents with 1-ε.Thus, a kind of observation probability matrix B is proposed _{2 × 2}, as shown in the table:

Mathematically, PFA and PMD is expressed as:

Pr(X _n＝0|Y _n＝0)＝e ₀(0)or(1-δ),

Pr(X _n＝1|Y _n＝0)＝e ₀(1)orδ,

Pr(X _n＝0|Y _n＝1)＝e ₁(0)orε,

Pr(X _n＝1|Y _n＝1)＝e ₁(1)or(1-ε),

Observation probability matrix B _{2 × 2}the HMM frequency spectrum perception process of cognitive radio can be simplified.

Adopt Monto-Carlo emulation mode checking observation probability matrix B _{2 × 2}.Getting probability transfer matrix is:

$P=\left(\begin{array}{cc}0.3& 0.7\\ 0.2& 0.8\end{array}\right),$

For ensureing the stationarity of Markov chain, getting initial distribution is:

(p ₀,p ₁)×P＝(p ₀,p ₁)

p ₀+p ₁＝1

Its accuracy is verified when two kinds different.

Situation one: δ=0.05, (1-ε)=0.95,0.9,0.85,0.8.

Situation two: ε=0.05, (1-δ)=0.95,0.9,0.85,0.8.

In simulation process, initial probability distribution and probability transfer matrix will remain unchanged.Process comprises four parts.

Step one: utilize initial distribution and probability transfer matrix to produce the Markov chain that a length is L=100, namely hidden state path y ₁, y ₂... y ₁₀₀.

Step 2: in each case a namely under different ε and δ, more precisely, is under the condition of different observing matrixes, utilizes the hidden state path produced in a first step to produce observation data x ₁, x ₂... x ₁₀₀.

Step 3: utilize Viterbi coding/decoding method to the observation data x in step 2 ₁, x ₂... x ₁₀₀decode, produce the hidden state path of perception

Step 4: calculate perception accuracy, namely detection probability (PA), computational methods are:

$\mathrm{PA}=\frac{\#\{1\≤i\≤100:y_i^{*}=y_i\}}{100}\×100$

Repeat step one and arrive step 4 10000 times.(δ=0.05 in situation one, ε=0.05,0.1,0.15,0.20), perception accuracy reduces along with the increase of ε, change comparatively obviously (Pd=95.0168 ~ 83.3593), as shown in Fig. 2 ~ Fig. 5, Std (standard deviation) is about 2 ~ 3, and amplitude of variation is little.(ε=0.05, δ=0.05,0.1,0.15 in situation two, 0.20), perception accuracy reduces along with the increase of ε equally, but amplitude of variation little (Pd=94.9850 ~ 91.6642), as shown in figs. 6-9, Std, about 2.5, changes less.

Pure discontinuous markov (Markov) process is also a prior art relevant with the present invention.Its definition is as described below with some fundamental propertys.

If random process the state space of X (t), t>=0} is S={0,1,2 ... if. right and i ₁, i ₂... i _n+1∈ S has:

P(X(t _n+1)＝i _n+1|X(t ₁)＝i ₁,X(t _n)＝i _n)

＝P(X(t _n+1)＝i _n+1|X(t _n)＝i _n)

Then { X (t), t >=0} is pure discontinuous Markov process to title, also claims continuous time Markov chain.As can be seen from definition, so-called pure discontinuous Markov process refers to the Markov chain of Time Continuous, state discrete.In other words, this is a kind of popularizing form of all discrete Markov chain of time, state.

Pure discontinuous Markov process has itself transition probability, namely:

p(s,i；s+t,j)＝P(X(s+t)＝j|X(s)＝i)

Above formula represents that system is in state i in the s moment, transfers to the transition probability of state j after elapsed time t.

If with τ _ijourney of recording a demerit, before transferring to another one state, in the time that state i stops, then has all s, t>=0:

P(τ _i>s+t|τ _i>s)＝P(τ _i>t)

As can be seen from above formula, τ _ihave without memory, therefore, τ _iobeys index distribution, and, when process leaves state i, then with Probability p _ijget the hang of j, and have

HMM is introduced cognitive radio frequency spectrum perception by prior art, utilizes a kind of observing matrix to make this perception simple and clear.But, there is its deficiency in this method.First, the probability transfer matrix of HMM is supposed out, not necessarily tally with the actual situation, and frequency range free time-free time, idle-busy, busy-idle, busy-busy transition probability calculate by probability transfer matrix, probability transfer matrix but not necessarily reflects the real change situation of frequency range state.Secondly, the time of HMM is discrete, has so just likely lost the frequency range state information in two discrete instants.Finally, this method can complete the frequency range state aware in statistical significance, but, fail the task that primary user's state is followed the tracks of, more do not find the rule that primary user distributes.In order to overcome the above-mentioned deficiency of prior art, we have invented a kind of pure discontinuous Markov process frequency spectrum sensing method of cognitive radio.

The pure discontinuous Markov process frequency spectrum sensing method of the cognitive radio of the present invention is characterized in that:

Step one: utilize the Q matrix of birth and death process to derive the probability transfer matrix of busy, the pure discontinuous Markov process of idle condition, respectively corresponding frequency band state free time-free time, idle-busy, busy-free time, busy-busy transition probability;

Step 2: utilize the probability transfer matrix in step one, deriving frequency range is idle or busy probability at any time, the state of perception frequency range thus;

Step 3: calculate frequency range state γ (t) average, covariance, variance, obtain thus primary user in time-domain (0, accumulated dwelling time t) in time period;

Step 4: utilize step one to obtain the distribution situation of primary user in time-domain to the result of step 3, follows the tracks of primary user's state thus.

Its technique effect of the present invention is, accurately can calculate and authorize in frequency range at any one, frequency range by the state transitions of current time to the state transition probability p of subsequent time state ₀₀, p ₀₁, p ₁₀, p ₁₁correspond respectively to frequency range busy-busy, busy-free time, idle-busy, free time-probability of free time.Utilize Fokker-Planck equation, the present invention accurately can calculate frequency range and be in busy Probability p at any time ₀the Probability p of (t) or free time ₁t (), has carried out the task of frequency range state being carried out to perception thus, under the background of continuous time, the present invention does not lose the information of frequency range state in two discrete instants.The present invention can accurately calculate primary user (0, t) occupy the cumulative time of frequency range in time period, and time dependent fluctuation situation of this cumulative time can be obtained on this basis.The present invention comparatively accurately can also calculate the distribution situation of primary user in time-domain, can complete the task of following the tracks of primary user's state thus.

Summary of the invention

Accompanying drawing explanation

Fig. 1 is the overall expression figure of HMM frequency spectrum sensing method of existing cognitive radio.Fig. 2 ~ Fig. 5 is the histogram frequency distribution diagram of the HMM frequency spectrum sensing method frequency range state aware accuracy of existing cognitive radio, and PMD δ=0.05, PFA ε are respectively numerical value pointed in each width histogram.Fig. 6 ~ Fig. 9 is the histogram frequency distribution diagram of the HMM frequency spectrum sensing method frequency range state aware accuracy of existing cognitive radio, and PFA ε=0.05, PMD δ are respectively numerical value pointed in each width histogram.Figure 10 is the method system model of the present invention, and this figure is simultaneously as Figure of abstract.Figure 11 is the pure discontinuous Markov process simulation curve of busy, idle two state.Figure 12 is busy, idle two state pure discontinuous Markov process state-transition matrix simulation curve.Figure 13 is the relation curve that initial distribution and primary user occupy the frequency range cumulative time.Figure 14 is state transitions number of times, distribution time, distribution probability relation three-dimensional graph.

Embodiment

As shown in Figure 10, a CR system comprises N number of mandate frequency range that independently can be used for perception to the system model that the method for the present invention adopts, and is referred to as f ₁, f ₂... f _n, each frequency range is divided into several part by vertical line, and each part represents the frequency range of current time.Black oblique line represents current time frequency range and is occupied by primary user, and perception user can not use, and it is idle that white cells then represents current time frequency range, and perception user can get involved.

Represent the state of any time frequency range with γ (t), γ (t) is controlled by pure discontinuous Markov process here, represent t l frequency range idle, perception user can signal transmission.On the contrary, represent t l frequency range busy, perception user can not signal transmission.

This class process is in the time of staying obeys index distribution of each state, and thus, supposing that primary user obeys parameter in the time that each state of each frequency range stops is the exponential distribution of λ, and the time obedience parameter that frequency range is in idle condition is the exponential distribution of μ.If represent that frequency range is idle with " 1 ", represent that frequency range is busy with " 0 ", statement was above equivalent to this process before transferring to state 1, at the index variable of to be parameter be the time that state 0 stops λ, and the index variable of to be parameter be the time that it rests on state 1 before the state of getting back to 0 μ.

In fig. 11, getting simulation time is 10ms, λ ^-1=1ms, μ ^-1=4.2ms, that is, E [λ]=1, E [μ]=4.2.Its probability meaning is primary user is 1ms in the average time that frequency range stops, and the average time of frequency range free time is 4.2ms.In fig. 11, frequency range state has change altogether 9 times, wherein has 5 " 0 " and 4 " 1 ", and that is, in 10ms, the number of times that primary user gets involved frequency range is 5 times, and the number of times of frequency range free time is 4 times.In fig. 11, the bound-time of state is respectively 1ms, 1.8ms, 2.0ms, 3.3ms, 4.3ms, 6.1ms, 7.9ms, 9.4ms, 10ms.In addition, at λ ^-1=1, μ ^-1under=4.2 conditions, can find out, the Stationary Distribution of this pure discontinuous Markov chain is π ₀=μ/(λ+μ)=0.1870, π ₁=λ/(λ+μ)=0.8130.

The Q matrix of this class process is:

$Q=\left(\begin{array}{cc}-\mathrm{\λ}& \mathrm{\λ}\\ \mathrm{\μ}& -\mathrm{\μ}\end{array}\right)$

The state-transition matrix obtaining the pure discontinuous Markov process of two states by means of Fokker-Planck equation is:

$\begin{array}{c}P\left(t\right)=\left(\begin{array}{cc}{P}_{00}\left(t\right)& P_{01}\left(t\right)\\ P_{10}& P_{11}\left(t\right)\end{array}\right)\\ =\left(\begin{array}{cc}{\mathrm{\μ}}_0+{\mathrm{\λ}}_0{e}^{-(\mathrm{\λ}+\mathrm{\μ})t}& {\mathrm{\λ}}_0-{\mathrm{\λ}}_0{e}^{-(\mathrm{\λ}+\mathrm{\μ})t}\\ {\mathrm{\μ}}_0-{\mathrm{\μ}}_0{e}^{-(\mathrm{\λ}+\mathrm{\μ})t}& {\mathrm{\λ}}_0+{\mathrm{\μ}}_0{e}^{-(\mathrm{\λ}+\mathrm{\μ})t}\end{array}\right)\end{array}$

λ ₀, μ ₀be respectively Stationary Distribution, wherein λ ₀=λ/(λ+μ), μ ₀=μ/(λ+μ).

In fig. 12, the state-transition matrix of the pure discontinuous Markov process of two states is given.Clearly, frequency range state is transferred to busy and idle probability and is down to/rises to Stationary Distribution π by busy respectively from 1 and 0 index ₀=0.1870 and π ₁=0.8130.And frequency range state is transferred to busy and idle probability by the free time and is risen to/be down to Stationary Distribution 0.1870 and 0.8130 respectively from 0 and 1 index.Suppose that initial value is P ₀=I, I are unit matrix, as can be seen from Figure 12, when emulate transfer time be greater than 3ms time, various transition probability will tend to be steady.When emulate transfer time be greater than 7ms time, regardless of initial condition, finally transfer to busy probability (p ₀₀, p ₁₀) will 0.1870 be constantly equal to, and transfer to idle probability (p ₀₁, p ₁₁) will 0.8130 be constantly equal to.

Suppose primary user at initial time with Probability p ₀occupy frequency range.

Can obtain frequency range from above formula is idle or busy probability at any time, namely

p ₀(t)＝p ₀P ₀₀(t)+(1-p ₀)P ₁₀(t)

＝μ ₀+(p ₀-μ ₀)e ^-(λ+μ)t,t≥0

p ₁(t)＝p ₀P ₀₁(t)+(1-p ₀)P ₁₁(t)

＝λ ₀+(1-p ₀-λ ₀)e ^-(λ+μ)t,t≥0

After obtaining state-transition matrix, next problem be primary user (0, the accumulative or mean residence time t).If make S _i(t) be:

$S_1\left(t\right)={\∫}_0^t\mathrm{\γ}\left(s\right)\mathrm{ds}$

$S_0\left(t\right)={\∫}_0^t(1-\mathrm{\γ}\left(s\right))\mathrm{ds}$

Then S _it () represents until t process dwell is in cumulative time of state i.Wherein, S ₀(t) represent primary user (0, occupy the cumulative time of frequency range t), and S ₁(t) then represent (0, the t) cumulative time of frequency range free time.S can be found out ₀(t)+S ₁(t)=t.

In fig. 13, give primary user (0, t) in frequency range occupy cumulative time curve S ₀t (), as a comparison, gives the idle cumulative time curve S of frequency range ₁(t).Clearly, these two times be added together will equal T.When initial distribution increases, frequency range occupies/the idle cumulative time will increase gradually/reduce, as shown in figure 13, but, fluctuation range not quite, S ₁t () changes to 7.5ms from 8.3ms, S ₀t () changes to 2.5ms from 1.7ms.

In order to calculate S _it (), first should determine the average of γ (t), variance and covariance function.

In fact,

E[γ(t)]＝P{γ(t)＝1}＝λ ₀-(p ₀-μ ₀)e ^-(λ+μ)t

E[γ(s)γ(t)]＝P{γ(t)＝γ(s)＝1}＝[λ ₀-(p ₀-μ ₀)e ^-(λ+μ)s]×[λ ₀+μ ₀e ^{-(λ+μ)(t-s)}]

And then obtain:

Cov[γ(s)γ(t)]＝E[γ(s)γ(t)]-E[γ(s)]E[γ(t)]

＝e ^{-(λ+μ)(t-s)}{μ ₀+(μ ₀-p ₀)e ^-(λ+μ)s}×{λ ₀+(p ₀-μ ₀)e ^-(λ+μ)s}

Further, S can be obtained _it the average of () and variance are:

$\begin{array}{c}E\left[S_0\left(t\right)\right]=E\left[{\∫}_0^t(1-\mathrm{\γ}\left(s\right))\mathrm{ds}\right]={\∫}_0^t[{\mathrm{\μ}}_0+(p_0-{\mathrm{\μ}}_0)e^{-(\mathrm{\λ}+\mathrm{\μ})s}]\mathrm{ds}\\ ={\mathrm{\μ}}_{0}t+(p_0-{\mathrm{\μ}}_0)\frac{1}{\mathrm{\λ}+\mathrm{\μ}}[1-e^{-(\mathrm{\λ}+\mathrm{\μ})t}]\end{array}$

$\begin{array}{c}E\left[S_1\left(t\right)\right]=E\left[{\∫}_0^t\mathrm{\γ}\left(s\right)\mathrm{ds}\right]={\∫}_0^t[{\mathrm{\λ}}_0+(p_0-{\mathrm{\μ}}_0)e^{-(\mathrm{\λ}+\mathrm{\μ})s}]\mathrm{ds}\\ ={\mathrm{\λ}}_{0}t+(p_0-{\mathrm{\μ}}_0)\frac{1}{\mathrm{\λ}+\mathrm{\μ}}[1-e^{-(\mathrm{\λ}+\mathrm{\μ})t}]\end{array}$

$\mathrm{Var}\left[\frac{S_0\left(t\right)}{t}\right]=\mathrm{Var}\left[\frac{S_1\left(t\right)}{t}\right]=\frac{1}{t^2}{\∫}_0^t{\∫}_0^t\mathrm{Cov}\left[\mathrm{\γ}\left(u\right)\mathrm{\γ}\left(v\right)\right]\mathrm{dudv}$

As t → ∞, S ₀(t)/t, S ₁t the variance of ()/t is

$\mathrm{tVar}\left[\frac{S_0\left(t\right)}{t}\right]=\mathrm{tVar}\left[\frac{S_1\left(t\right)}{t}\right]=\frac{1}{t^2}{\∫}_0^t{\∫}_0^t\mathrm{Cov}\left[\mathrm{\γ}\left(u\right)\mathrm{\γ}\left(v\right)\right]\mathrm{dudv}\stackrel{t\→\∞}{=}\frac{2\mathrm{\λ\μ}}{{(\mathrm{\λ}+\mathrm{\μ})}^3}$

So far, obtain (0, t), primary user occupies cumulative time and the average time of frequency range, also just corresponding cumulative time and average time obtaining the frequency range free time.Give its average level and variance function, average reflects the average time that primary user occupies frequency range, and variance then reflects its time dependent fluctuation situation.

Next problem is the distribution situation of primary user in time-domain, for this reason, must find S ₀the distribution function P{S of (t) ₀(t)≤s}, that is:

$\begin{array}{c}P\{S_0\left(t\right)\≤s\}=P\{N\left(t\right)=n\}\×P\{S_0\left(t\right)\≤s|N\left(t\right)=n\}\\ =P\{N\left(t\right)=n\}\×\left\{\mathrm{number\; of}{\mathrm{state}}^{\′}{0}^{\′}\right\}\×\left\{\mathrm{the\; total\; time\; spent\; in}{\mathrm{statr}}^{\′}{0}^{\′}\right\}\\ =\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{e}^{-(\mathrm{\λ}+\mathrm{\μ})t}\frac{{\left((\mathrm{\λ}+\mathrm{\μ})t\right)}^n}{n!}\underset{k=1}{\overset{n}{\mathrm{\Σ}}}\left(\begin{array}{c}n\\ k-1\end{array}\right){\left({\mathrm{\μ}}_0\right)}^{k-1}{\left({\mathrm{\λ}}_0\right)}^{n-k+1}\×\underset{i-k}{\overset{n}{\mathrm{\Σ}}}\left(\begin{array}{c}n\\ i\end{array}\right){\left(\begin{array}{c}s\\ t\end{array}\right)}^i{(1-\frac{s}{t})}^{n-i}\end{array}$

Here suppose that primary user occupies frequency range at initial time.N represent (0, t) frequency range state transitions number of times in time period.

Following table gives primary user the probability occupying frequency range distribution time, supposes (0, t), the change upper limit of state is 10 times, certainly, there is error here here.As shown in the table, when state transitions frequency n increases gradually, the probability that primary user occupies same time will reduce gradually, and this has also implied within the limited time, and pure discontinuous Markov process state variation is infinite is repeatedly impossible.Equally also can find out, under identical state transitions number of times, along with the increase gradually of distribution time, the distribution probability of primary user's Occupation time is also increasing gradually.Certainly, there is upper and lower bound in distribution probability.Due to supposition primary user occupy frequency range at initial time, as n=0, namely primary user (0, the probability always taking frequency range t) is the upper limit, and primary user has occupied frequency range when n=0, so as s=0, P{S ₀t ()≤s} is impossible event, be lower limit, and probability is zero, as shown in figure 14.

Claims (1)

1. a pure discontinuous Markov process frequency spectrum sensing method for cognitive radio, is characterized in that:

Step one: utilize the Q matrix of birth and death process to derive the probability transfer matrix of busy, the pure discontinuous Markov process of idle condition, respectively corresponding frequency band state free time-free time, idle-busy, busy-free time, busy-busy transition probability;

Step 2: utilize the probability transfer matrix in step one, deriving frequency range is idle or busy probability at any time, the state of perception frequency range thus;

Step 3: calculate frequency range state γ (t) average, covariance, variance, obtain thus primary user in time-domain (0, accumulated dwelling time t) in time period;

Step 4: utilize step one to obtain the distribution situation of primary user in time-domain to the result of step 3, follows the tracks of primary user's state thus.