CN102790995A - Information channel gain estimation method based on cognitive radio - Google Patents

Abstract

The invention discloses an information channel gain estimation method based on cognitive radio. By the adoption of the method, a cognitive user actively serves as a relay of a main user to transfer a main user signal after being received and amplified as a detection signal to a main user receiving end, a closed-loop power control of the main user is triggered via increasing a signal to noise ratio of the main user receiving end, finally, according to an observed change of the signal to noise ratio of the main user signal, the cognitive user can estimate the information channel gain of two crossed information channels, and can also estimate the information channel gain of a main user information channel, thus the average information channel content among cognitive users is enabled to be remarkably increased by the information, and meanwhile since the main user signal after being amplified is utilized by the cognitive user as the detection signal in the method, the disturbance on the main user from the cognitive user during a detection process is avoided on an average meaning according to the method.

Description

Channel gain method of estimation based on cognitive radio

Technical field

The invention belongs to the cognitive radio technology field, be specifically related to a kind of in cognitive radio networks in order to realize the coexistence of main user and cognitive user, improve the channel gain method of estimation of cognitive user ergodic capacity.

Background technology

Cognitive radio (CR, Cognitive Radio) is a kind of at the rare effective technology of following wireless communication field solution frequency spectrum resource.If cognitive user (CU; Cognitive User) can be to main user (PU; Primary User) cause disturb or cognitive user to main user's interference in the receivable scope of main user; This technology allows cognitive user to insert certain section frequency spectrum of having distributed to main user, realizes frequency spectrum share, thereby improves the availability of frequency spectrum.Cognitive user can insert target band through dual mode, and a kind of is that the opportunistic frequency spectrum inserts (OSA, Opportunistic Spectrum Access), and another kind is frequency spectrum share (SS, Spectrum Sharing).Under opportunistic frequency spectrum access way, cognitive user detects main user's operating state, if main user is in idle condition, cognitive user can insert target band; In case it is in running order to detect main user, cognitive user will discharge target band.Therefore in the opportunistic frequency spectrum inserted, in fact cognitive user had utilized main user on target band, to use the space, and cognitive user and main user can not be that identical frequency band is used in time or different location like this; But in the frequency spectrum share mode, if the interference that cognitive user causes main user is lower than the receivable interference threshold of main user, cognitive user still can be used target band in same place with main user simultaneously so.Therefore the frequency spectrum share mode can be utilized more spectrum opportunities with respect to the opportunistic access way.

In the frequency spectrum share mode, channel condition information (CSI, Channel State Information) is the key that realizes cognitive user and main user coexistence.According to the channel condition information that cognitive user obtains, cognitive user can coexist with main user under different restrictive conditions, thereby reaches different channel capacities.Fig. 1 is a typical cognitive user and main user's symbiotic system model, and this model has been considered two cognitive user and two main users, wherein, and PU ₁And PU ₂Represent two main users, CU ₁And CU ₂Represent two cognitive user, h _PpRepresent two main user PU ₁And PU ₂Between channel, h _CcRepresent two cognitive user CU ₁And CU ₂Between channel, h _CpExpression cognitive user CU ₁To main user PU ₂Between channel, h _PcRepresent main user PU ₁To cognitive user CU ₂Between channel.

From information-theoretical angle, knowing under the situation of all channel condition informations that the transmitting power of cognitive user only is subject to the interference (IC, Interference Control) to main user, at this moment cognitive user can reach maximum channel capacity.But the estimation of channel condition information is very challenging in cognitive radio system, because in actual cognitive radio system, main user is unwilling even can not carry out information exchange with cognitive user.In Fig. 1, although cognitive user can directly obtain cognitive channel h _CcChannel condition information, but obtain other channel condition information be very the difficulty.If obtain cross-channel h _PcChannel condition information, cognitive user need obtain main user's training sequence so; If obtain another one cross-channel h _CpChannel condition information, so main user need obtain the training sequence of cognitive user, and in real system, these conditions obviously are impossible satisfy, and for main subscriber channel h _Pp, owing to have only main user to estimate to it, therefore if obtain h _PpChannel condition information, this system need set up the based on feedback link between a main user and the cognitive user, main user is with h _PpChannel condition information feed back to cognitive user through based on feedback link, if there is not based on feedback link, cognitive user possibly obtain h hardly _PpChannel condition information.It is thus clear that in cognitive radio system, to two cross-channel h _Pc, h _Cp, and main subscriber channel h _PpBe estimated for realize main user and cognitive user the coexistence bottleneck, wherein to main subscriber channel h _PpObtaining of state information is the most difficult.

To the problems referred to above, some documents are studied the estimation of three channel condition informations of model shown in Figure 2, wherein, and main user PU ₁And PU ₂Have a transmit receive antenna respectively and be operated in tdd mode, CU ₁One transmit antennas and a reception antenna are arranged.Existing research method is based on the principle of active perception study; In the method, main user job is in that (under the effect of closed power control, main user's transmitting terminal is according to the signal to noise ratio (SNR of receiving terminal feedback under the condition of closed power control; Signal Noise Ratio) change information is adjusted transmitting power automatically; Guarantee that receiving terminal can receive the desired signal of constant signal to noise ratio, thereby guarantee the constant data rate transmission, so this technology is widely used in the current cognitive radio system); Cognitive user is through initiatively sending interfere information to main user's receiving terminal; Reduce the signal to noise ratio of main user's receiving terminal, thereby trigger main user's closed power control, the adjustment of the main user emission power that last cognitive user basis observes is to two cross-channel h _PcOr h _CpChannel gain estimate, obtain the gain of two cross-channel after, the transmit power limited of cognitive user when carrying out transfer of data is in the maximum interference power (ITC that main user allowed; Interference Temperture Control); But concrete list of references: R.Zhang, on active learning and supervised transmission of spectrum sharing based cognitive radios by exploiting hidden primary radio feedback, IEEE Trans.Commun.vol.58; No.10; Pp.2960-2970, Oct.2010 and I.Bajaj, and Y.Gong; Cross-channel estimation using supervised probing and sensing in cognitive radio networks; In Proc.IEEE Int.Conmun.Conf. (ICC), Jun.2011, pp.1-5.The problem of the existence of this method is: in detection process, cognitive user can temporarily reduce main user's communications performance to the interference signal that main user sends; In addition, this detection method can only estimate cross-channel h _PcAnd h _CpChannel gain, promptly

With

Can not estimate main subscriber channel h _PpChannel gain, promptly

Summary of the invention

The objective of the invention is to send the problem that interference signal can reduce main telex network performance and can not estimate main subscriber channel gain to main user, proposed a kind of channel gain method of estimation based on active probe in order to solve cognitive user in the existing channel gain estimation method.

Technical scheme of the present invention is: a kind of channel gain method of estimation based on cognitive radio specifically comprises the steps:

Step 1: first time slot, cognitive user are measured the main subscriber signal signal to noise ratio γ that the first main user sends _C1, cognitive user is with amplitude gain G simultaneously ₂The main subscriber signal that amplification receives from the first main user, and transmit with amplitude gain G to the second main user ₂Main subscriber signal after the amplification;

Step 2: second time slot, cognitive user are measured the main subscriber signal signal to noise ratio γ that the second main user sends _C2, cognitive user is with amplitude gain G simultaneously ₁The main subscriber signal that amplification receives from the second main user, and transmit with amplitude gain G to the first main user ₁Main subscriber signal after the amplification;

Step 3: the 3rd time slot, cognitive user are measured the main subscriber signal signal to noise ratio γ ' that the first main user sends _C1, cognitive user is with amplitude gain G ' simultaneously ₂The main subscriber signal that amplification receives from the first main user, and transmit with amplitude gain G ' to the second main user ₂Main subscriber signal after the amplification;

Step 4: the 4th time slot, cognitive user are measured the main subscriber signal signal to noise ratio γ ' that the second main user sends _C2

Step 5: the 5th time slot, cognitive user are measured the main subscriber signal signal to noise ratio γ that the first main user sends " _C1

Step 6: cognitive users were calculated, and the first primary user channel gain

cognitive user and the second main user channel gain

The first and second main primary user user channel increased

${\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2=\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}}{{\mathrm{\&gamma;}}_{c1}{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&sigma;}}_c^2}{(1+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2\mathrm{\&Delta;})}^2{\mathrm{\&sigma;}}_2^2-\frac{{\mathrm{\&sigma;}}_2^2}{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2},$

${\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2=\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}2}^{\&prime;}}{{\mathrm{\&gamma;}}_{c2}{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_1^2{\mathrm{\&sigma;}}_c^2}{(1+{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_1\mathrm{\&Delta;})}^2{\mathrm{\&sigma;}}_1^2-\frac{{\mathrm{\&sigma;}}_1^2}{{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_1^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2},$

${\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2=\frac{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2}{{\mathrm{\&Delta;}}^2},$

Wherein, $\mathrm{\&Delta;}=\frac{({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;\&prime;}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;})\&PlusMinus;\sqrt{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;\&prime;}{(G_2-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;})}^2+{\mathrm{\&gamma;}}_{r1}({\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;}-{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;\&prime;})({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2)}}{G_2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}({\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;}-{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;\&prime;})}.$

Beneficial effect of the present invention: the present invention has obtained main subscriber channel gain

in the system of cognitive user and main user coexistence when obtaining two cross-channel gains

and

, this information makes the ergodic capacity between the cognitive user that more significantly raising arranged.In the method for the invention; Cognitive user is initiatively served as main user's relaying; Main subscriber signal after receiving, amplifying is transmitted to main user's receiving terminal as detectable signal; Recently trigger main user's closed power through the noise that improves main user's receiving terminal and control, last cognitive user changes the channel gain that can not only estimate two cross-channel according to the signal to noise ratio of the main subscriber signal that observes, and can also estimate the channel gain of main subscriber channel.Therefore method of the present invention has also avoided in the detection process cognitive user to main user's interference on average meaning.

Description of drawings

Fig. 1 is existing a kind of cognitive user and main user's symbiotic system model sketch map.

Fig. 2 is the system model sketch map that the inventive method adopts.

Fig. 3 is the time slot schematic flow sheet of the inventive method.

Fig. 4 is cognitive user estimated performance sketch map to main subscriber channel gain under the different capacity restrictive condition.

Fig. 5 be unknown main subscriber channel gain

with known should the value situation under channel capacity probability density function (CDF) curve between the cognitive user contrast sketch map.

Embodiment

To combine accompanying drawing below, provide specific embodiment of the present invention.

Describe content of the present invention for ease, at first employed term among the present invention defined:

Definition 1: time division multiplexing (TDD, Time Division Duplex): communicating pair communicates on the different time sheet in same frequency.

Definition 2: time slot (Slot) a: timeslice of time division multiplexing.

Definition 3: signal to noise ratio: the ratio of signal power and noise power (user is used as all interference beyond the desired signal as noise processed).

Definition 4: closed power control (CLPC, Closed Loop Power Contro1): the power of transmitting terminal is according to the variation adjustment of receiving terminal signal to noise ratio, thus the quality of reception of assurance receiving terminal.

The model that adopts in the face of the present invention is down introduced:

As shown in Figure 2, considered two main user PU in the model that the present invention adopts ₁, PU ₂With a cognitive user CU ₁, in order to express easily, main subscriber channel h _Pp, two cross-channel h _PcAnd h _CpUse h respectively ₀, h ₁And h ₂Expression, corresponding channel gain is expressed as

With

Definition signal is from main user PU simultaneously ₁To PU ₂Direction be the fl transmission direction, be the reverse transfer direction on the contrary.

In the model, two main users use the f frequency range at main subscriber channel h ₀The mode that goes up with TDD intercoms mutually, and cognitive user also attempts to insert the f frequency range simultaneously, the interference that when communicating by letter main user is caused in order to be controlled at, and cognitive user need be according to main subscriber channel h ₀, cross-channel h ₁And h ₂Variation adjust transmitting power in real time.Use n in the model respectively ₁, n ₂And n _cExpression PU ₁, PU ₂And CU ₁The white Gaussian noise at place, obeying average respectively is 0, variance does

With Gaussian distribution, promptly

With

Introduce content of the present invention according to the time slot flow chart of Fig. 3 below; Wherein, laterally be time orientation, unit is a time slot; Vertically be respectively the operating state of direct link (Direct link) and repeated link (Relay link), 5 cycles that time slot is estimated as a channel gain.

First and third, five time slots: on the fl transmission direction, main user PU ₁With power p ₁(milliwatt is mw) to PU ₂Send signal

The sampling sequence number of k expression signal satisfies 1≤k≤K, and wherein, K representes maximum hits, p ₁Satisfy

${\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1=\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">T</figure-callout>}2}{\mathrm{\&sigma;}}_2^2}{{{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0}^2},---\left(1\right)$

Wherein, γ _T2Expression PU ₂Target signal to noise ratio.

Cognitive user CU ₁The main subscriber signal that receives is respectively with corresponding signal to noise ratio

$y_{c1}\left(k\right)=h_1\sqrt{p_1}{x}_{p_1}\left(k\right)+n_c\left(k\right),---\left(2\right)$

With

${\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}=\frac{p_1{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2}{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2},---\left(3\right)$

CU ₁When receiving main subscriber signal with amplitude gain G ₂Amplify this signal, the main subscriber signal after will amplifying then as detectable signal to PU ₂Transmit, detectable signal can be expressed as:

$x_{c1}\left(k\right)=G_2{y}_{c1}\left(k\right)=G_2(h_1\sqrt{p_1}{x}_{p_1}\left(k\right)+n_c\left(k\right)),---\left(4\right)$

Therefore, at first time slot, PU ₂Signal that the place receives and corresponding signal to noise ratio are:

With

${\mathrm{\&gamma;}}_2=\frac{p_1{({\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0+G_2{h}_1{h}_2)}^2}{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&sigma;}}_2^2},---\left(6\right)$

Under closed power control, at the second time slot PU ₂The change information of local signal to noise ratio is passed to PU through based on feedback link ₁, PU ₁The transmitting power that will adjust signal at the 3rd time slot does

${\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}=\frac{{\mathrm{\&gamma;}}_{T2}({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&sigma;}}_2^2)}{{({\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0+G_2{h}_1{h}_2)}^2},---\left(7\right)$

Therefore at the 3rd time slot CU ₁Can observe the signal to noise ratio of a main subscriber signal after the renewal:

${\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}=\frac{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}}{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2},---\left(8\right)$

At the 3rd time slot, if CU ₁With amplitude gain G ' ₂Amplify the main subscriber signal that receives and transmit the signal after amplifying, at the 5th time slot, CU ₁Can observe the signal to noise ratio of a main subscriber signal after the renewal once more:

${\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}=\frac{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}}{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2},---\left(9\right)$

Wherein, p " ₁For at the 5th time slot PU ₁Transmitting power, this power satisfies:

${\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}=\frac{{\mathrm{\&gamma;}}_{T2}({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&sigma;}}_2^2)}{{({\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{h}_1{h}_2)}^2},---\left(10\right)$

The second, four time slots: with the similar process of fl transmission direction, in the reverse transfer direction, if at the second time slot CU ₁With amplitude gain G ₁Amplify PU ₂The signal that sends is also transmitted the signal after amplifying, CU ₁Will observe the signal to noise ratio of main subscriber signal at second, four time slots respectively:

${\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}2}=\frac{{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_2}{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2},---\left(11\right)$

With

${\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}2}^{\&prime;}=\frac{{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_2^{\&prime;}}{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2},---\left(12\right)$

Wherein, p ₂, p ' ₂Be respectively PU ₂In the transmitting power of second time slot and the 4th time slot, satisfy respectively

${\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_2=\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">T</figure-callout>}1}{\mathrm{\&sigma;}}_1^2}{{{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0}^2},---\left(13\right)$

With

${\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_2^{\&prime;}=\frac{{\mathrm{\&gamma;}}_{T1}({\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&sigma;}}_1^2)}{{({\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0+G_1{h}_1{h}_2)}^2},---\left(14\right)$

Wherein, γ _T1Expression PU ₁The target signal to noise ratio at place.

Through above-mentioned active probe operation, CU ₁Just obtained to comprise channel gain

With

Information, provide CU below ₁Information through these acquisitions is right With

Estimation procedure.

Obtain through (3)/(8), (3)/(9)

${\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}=\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}}{{\mathrm{\&gamma;}}_{c1}}{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,---\left(15\right)$

With

${\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}=\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}}{{\mathrm{\&gamma;}}_{c1}}{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,---\left(16\right)$

Abbreviation (7) and (10) obtain:

${\mathrm{\&gamma;}}_{T2}({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&sigma;}}_2^2)={\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2+2G_2{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}{h}_0{h}_1{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2,---\left(17\right)$

With

${\mathrm{\&gamma;}}_{T2}({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&sigma;}}_2^2)={\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2+2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}{h}_0{h}_1{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2,---\left(18\right)$

Obtain through

:

${\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{\&gamma;}}_{T2}({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&sigma;}}_2^2)={\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}({\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2+2G_2{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}{h}_0{h}_1{h}_2),---\left(19\right)$

${\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{T2}({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&sigma;}}_2^2)={\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2({\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2+2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}{h}_0{h}_1{h}_2),---\left(20\right)$

Obtain through (19)-(20):

$({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2){\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">T</figure-callout>}2}{\mathrm{\&sigma;}}_2^2={\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2+$ $,\left(21\right)$

$2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{G}_2{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}{h}_0{h}_1{h}_2-2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}{h}_0{h}_1{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2$

Obtain through changing (21):

$({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2){\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">T</figure-callout>}2}{\mathrm{\&sigma;}}_2^2={\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2+\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2}{{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2}-\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;\&prime;}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2}{{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2}$ $,\left(22\right)$

$+\frac{2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{G}_2{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">p</figure-callout>}}_1^{\&prime;}{h}_0{h}_1{h}_2}{h_0}-\frac{2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">p</figure-callout>}}_0^{\&prime;\&prime;}{h}_0{h}_1{h}_2}{{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0}$

(22) are brought in (15) and (16) to be obtained:

$({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2){\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">T</figure-callout>}2}=\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}{p}_1{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2}{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}{\mathrm{\&sigma;}}_2^2}-\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}{p}_1{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2}{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}{\mathrm{\&sigma;}}_2^2}+\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}{p}_1{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2}{{\mathrm{\&gamma;}}_{c1}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2{\mathrm{\&sigma;}}_2^2}$ $,\left(23\right)$

$-\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}{p}_1{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2}{{\mathrm{\&gamma;}}_{c1}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2{\mathrm{\&sigma;}}_2^2}+\frac{2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}{p}_1{h}_0{h}_1{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2}{{\mathrm{\&gamma;}}_{c1}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0{\mathrm{\&sigma;}}_2^2}-\frac{2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}{p}_1{h}_0{h}_1{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2}{{\mathrm{\&gamma;}}_{c1}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0{\mathrm{\&sigma;}}_2^2}$

(23) are brought in (1) to be obtained:

${\mathrm{\&gamma;}}_{T2}({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2)=\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">T</figure-callout>}2}}{{\mathrm{\&gamma;}}_{c1}}-\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">T</figure-callout>}2}}{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}}+\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">T</figure-callout>}2}}{{\mathrm{\&gamma;}}_{c1}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2}$ $,\left(24\right)$

$-\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">T</figure-callout>}2}}{{\mathrm{\&gamma;}}_{c1}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2}+\frac{2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}{h}_1{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">T</figure-callout>}2}}{{\mathrm{\&gamma;}}_{c1}{h}_0}-\frac{2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}{h}_1{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">T</figure-callout>}2}}{{\mathrm{\&gamma;}}_{c1}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0}$

(24) both members is simultaneously divided by γ _T2Obtain:

${\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2=\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}}{{\mathrm{\&gamma;}}_{c1}}-\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}}{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}}+\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2}{{{\mathrm{\&gamma;}}_{c1}\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2}-\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;\&prime;2}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2}{{\mathrm{\&gamma;}}_{c1}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2}$ $,\left(25\right)$

$+\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}{h}_1{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2}{{\mathrm{\&gamma;}}_{c1}{h}_0}-\frac{2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}{h}_1{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2}{{\mathrm{\&gamma;}}_{c1}{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0}$

Abbreviation (25) obtains:

${\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2({\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}-{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;})\frac{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2}{{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2}+2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{G}_2({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;})\frac{h_1{h}_2}{{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0}+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}=0,---\left(26\right)$

Make

(26) to be write as:

${\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2({\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}-{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}){\mathrm{\&Delta;}}^2+2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{G}_2({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;})\mathrm{\&Delta;}+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}=0,---\left(27\right)$

Separating (27) obtains:

$\mathrm{\&Delta;}=\frac{({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;})\&PlusMinus;\sqrt{{({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;})}^2-({\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}-{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;})({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&gamma;}}_{c1}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}{\mathrm{\&gamma;}}_{c1})}}{G_2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}({\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}-{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;})},---\left(28\right)$

Abbreviation (28) obtains:

$\mathrm{\&Delta;}=\frac{({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;})\&PlusMinus;\sqrt{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;}{(G_2-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;})}^2+{\mathrm{\&gamma;}}_{c1}({\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}-{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;})({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2)}}{G_2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}({\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}-{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;\&prime;})},---\left(29\right)$

Therefore, CU ₁Can obtain:

h ₁h ₂=Δh ₀， （30）

The h here ₀, h ₁And h ₂Be appreciated that and be channel h ₀, h ₁And h ₂Channel coefficients.

(17) are brought in (30) can be obtained:

${\mathrm{\&gamma;}}_{T2}({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&sigma;}}_2^2)=\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}}{{\mathrm{\&gamma;}}_{c1}}{p}_1{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&Delta;}}^2\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}}{{\mathrm{\&gamma;}}_{c1}}{p}_1{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2+2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2\mathrm{\&Delta;}\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}}{{\mathrm{\&gamma;}}_{c1}}{p}_1{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2,---\left(31\right)$

Equality (31) two ends can be obtained divided by

simultaneously:

${\mathrm{\&gamma;}}_{T2}(\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2}{{\mathrm{\&sigma;}}_2^2}+1)=\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}}{{\mathrm{\&gamma;}}_{c1}}\frac{p_1{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2}{{\mathrm{\&sigma;}}_2^2}+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&Delta;}}^2\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}}{{\mathrm{\&gamma;}}_{c1}}\frac{p_1{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2}{{\mathrm{\&sigma;}}_2^2}+2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2\mathrm{\&Delta;}\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}}{{\mathrm{\&gamma;}}_{c1}}\frac{p_1{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2}{{\mathrm{\&sigma;}}_2^2},---\left(32\right)$

Bring equality (1) into (31), can obtain:

$\frac{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2}{{\mathrm{\&sigma;}}_2^2}+1=\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}}{{\mathrm{\&gamma;}}_{c1}}(1+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2+2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2\mathrm{\&Delta;}),---\left(33\right)$

Abbreviation (32) can obtain:

${\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2=\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}}{{\mathrm{\&gamma;}}_{c1}{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&sigma;}}_c^2}{(1+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2\mathrm{\&Delta;})}^2{\mathrm{\&sigma;}}_2^2-\frac{{\mathrm{\&sigma;}}_2^2}{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2},---\left(34\right)$

In like manner, after obtaining Δ, if consider reverse transfer, cognitive user can obtain so:

${\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2=\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}2}^{\&prime;}}{{\mathrm{\&gamma;}}_{c2}{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_1^2{\mathrm{\&sigma;}}_c^2}{(1+{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_1\mathrm{\&Delta;})}^2{\mathrm{\&sigma;}}_1^2-\frac{{\mathrm{\&sigma;}}_1^2}{{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_1^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2},---\left(35\right)$

Can obtain through (29), (30), (33) and (34):

${\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2=\frac{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2}{{\mathrm{\&Delta;}}^2},---\left(36\right)$

Through aforesaid operations, cognitive user has just obtained

and

Steps summarize with the inventive method is following at last:

Step 1: first time slot, CU ₁Measure PU ₁The main subscriber signal signal to noise ratio γ that sends _C1, while CU ₁With amplitude gain G ₂Amplification is from PU ₁The main subscriber signal that receives, and to PU ₂Forwarding is with amplitude gain G ₂Main subscriber signal after the amplification.

Step 2: second time slot, CU ₁Measure PU ₂The main subscriber signal signal to noise ratio r that sends _C2, while CU ₁With amplitude gain G ₁Amplification is from PU ₂The main subscriber signal that receives, and to PU ₁Forwarding is with amplitude gain G ₁Main subscriber signal after the amplification.

Step 3: the 3rd time slot, CU ₁Measure PU ₁The main subscriber signal signal to noise ratio γ ' that sends _C1, while CU ₁With amplitude gain G ' ₂Amplification is from PU ₁The main subscriber signal that receives, and to PU ₂Forwarding is with amplitude gain G ' ₂Main subscriber signal after the amplification.

Step 4: the 4th time slot, CU ₁Measure PU ₂The main subscriber signal signal to noise ratio γ ' that sends _C2

Step 5: the 5th time slot, CU ₁Measure PU ₁The main subscriber signal signal to noise ratio γ that sends " _C1

Step 6: calculate ${\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2=\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}1}^{\&prime;}}{{\mathrm{\&gamma;}}_{c1}{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&sigma;}}_c^2}{(1+{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2\mathrm{\&Delta;})}^2{\mathrm{\&sigma;}}_2^2-\frac{{\mathrm{\&sigma;}}_2^2}{{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2},$ ${\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2=\frac{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}2}^{\&prime;}}{{\mathrm{\&gamma;}}_{c2}{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_1^2{\mathrm{\&sigma;}}_c^2}{(1+{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_1\mathrm{\&Delta;})}^2{\mathrm{\&sigma;}}_1^2-\frac{{\mathrm{\&sigma;}}_1^2}{{\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_1^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">c</figure-callout>}}^2}$ With ${\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002018101700021.png,HDA00002018101700022.png"\; state="\{\{state\}\}">h</figure-callout>}}_0^2=\frac{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_1^2{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_2^2}{{\mathrm{\&Delta;}}^2},$ Wherein, $\mathrm{\&Delta;}=\frac{({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;\&prime;}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;})\&PlusMinus;\sqrt{{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;}{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;\&prime;}{(G_2-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;})}^2+{\mathrm{\&gamma;}}_{r1}({\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;}-{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;\&prime;})({\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;2}-{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^2)}}{G_2{\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">G</figure-callout>}}_2^{\&prime;}({\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;}-{\mathrm{\&gamma;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">r</figure-callout>}1}^{\&prime;\&prime;})}.$

Need to prove,, thereby can define amplitude gain G according to Power Limitation here because each node has Power Limitation ₁, G ₂, G ' ₂, the G of theoretic optimum ₁, G ₂, G ' ₂Be inaccessible in actual power limit, those skilled in the art can choose according to actual conditions.In addition, because CU ₁The sum of errors amplitude gain G of the main user's signal to noise ratio that observes ₂, G ' ₂Non-positive root or imaginary number root may appear in inappropriate choosing, (29), this time CU ₁Think and estimate failure, then estimate next time; On the contrary, CU ₁An arithmetic number root that obtains is regarded as once successfully estimating.In addition, if occur two arithmetic number roots, CU simultaneously ₁Will one of them root of random choose proceed the estimation of channel gain, emulation proves that the method for estimation of this suboptimum still can reach preferable performance.

Principle of the present invention: under the effect of closed power control, if the signal to noise ratio of receiving terminal reduces, transmitting terminal will increase transmitting power at next transmission time slot so; On the contrary, if the signal to noise ratio of receiving terminal increases, transmitting terminal will reduce transmitting power at next transmission time slot so.Cognitive user changes the change information that can obtain main user's transmitting terminal power through the signal to noise ratio of the main subscriber signal that receives.Be transmitted as example with forward direction, can know CU from (7) and (8) ₁The signal to noise ratio that receives has comprised h ₀, h ₁And h ₂Information, i.e. γ ' _C1=f (h ₀, h ₁, h ₂), therefore, CU ₁Utilize the main user's signal to noise ratio that is observed to channel gain

With Estimate it is feasible.

Can find out the necessary condition of estimating main subscriber channel gain the present invention from top step:

1. main user job is under tdd mode.

2. the main subscriber signal after cognitive user needs to amplify is transmitted to main user's receiving terminal as detectable signal.

Consider the system model among Fig. 2, wherein, cognitive user CU ₁Be positioned at two main user PU ₁And PU ₂Between, get PU ₁And PU ₂Distance be 0.25km, represent CU with d ₁To PU ₁Distance, represent CU with 0.25-d ₁To PU ₂Distance.Electromagnetic wave is propagated the influence that receives shadow fading and free space decline in wireless channel, wherein, shadow fading obedience average is 10 logarithm normal distribution, and free space decline model is:

P _L(dB)=128.1+37.6log ₁₀(l)l≥0.035km，（37）

Wherein, l representes the distance of electromagnetic wave propagation.

Consider main user PU in the instance ₁Target received signal to noise ratio γ _T1=15dB, main user PU ₂Target received signal to noise ratio γ _T2=5dB, main user PU ₁, PU ₂With cognitive user CU ₁The noise energy at place is respectively

With

Further consider main user PU ₁And PU ₂Max power constraint be respectively ${\mathrm{<figure-callout\; id="1"\; label="P\; Max"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">P</figure-callout>}}_{{\mathrm{Max}}_{}}=20\mathrm{DBm}$ With ${\mathrm{<figure-callout\; id="2"\; label="P\; Max"\; filenames="HDA00002018101700013.png"\; state="\{\{state\}\}">P</figure-callout>}}_{{\mathrm{Max}}_{}}=10\mathrm{DBm}.$

Fig. 4 has provided cognitive user CU ₁Be respectively in Power Limitation

With

Estimated performance contrast under two kinds of situation, wherein, left vertical is represented the evaluated error of channel gain, and right vertical representes to be estimated power, and ε representes average evaluated error relatively, is defined as

Expression

Estimated value;

Average success rate, N are estimated in expression _mExpression overall estimate number of times, N _fThe frequency of failure is estimated in expression;

Expression cognitive user CU ₁Max power constraint; D representes cognitive user CU ₁Apart from main user PU ₁Distance.

From figure, can clearly see; During as

; Because the variation of cognitive user position; Average evaluated error minimum relatively can be low to moderate 1.5%, and average success rate is up to 90%; During as

; Average evaluated error minimum relatively can be low to moderate 2%; Average success rate is higher than 85%, and visible, this method of estimation has shown estimated performance preferably; And cognitive user maximum constraints power is high more, and estimated performance is good more.

Below, in the system of cognitive user and main user coexistence, cross-channel gain that the main subscriber channel that utilizes the present invention to obtain gains and cross-channel gains with respect to only obtain can improve the ergodic capacity of cognitive user more significantly through the emulation proof.

As shown in Figure 1, consider that 4 users lay respectively at elongated four summits of square of 100m that are, main user PU ₁With cognitive user CU ₁Max power constraint all be 20dBm, main user PU ₁And PU ₂Average data rate be 4.65Mbps, the average interrupt rate is 4%, the maximum interruption rate that main user allows is 5%.

If cognitive user can only obtain cross-channel h _CpAnd h _PcChannel gain, cognitive user can only limit at interference temperature under (ITC) condition and work so.Fig. 5 provided unknown main subscriber channel gain

and known should the value situation under channel capacity probability density function (CDF) curve comparison diagram between the cognitive user; Wherein, C representes channel capacity; Unit is bits per second (bps), and Mbps representes MBPS.Can learn that from Fig. 5 in this case, the ergodic capacity of cognitive user only is 0.056Mbps; Yet; Under the same conditions, if cognitive user can reach 1.17Mbps through the ergodic capacity of the present invention's acquisition

and

cognitive user.It is thus clear that in the system of cognitive user and main user coexistence, the present invention can improve the ergodic capacity of cognitive user near 20dB.

Above instance is merely preferred example of the present invention, and use of the present invention is not limited to this instance, and is all within spirit of the present invention and principle, any modification of being made, is equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (1)

1. the channel gain method of estimation based on cognitive radio specifically comprises the steps:

Step 1: first time slot, cognitive user are measured the main subscriber signal signal to noise ratio γ that the first main user sends _C1, cognitive user is with amplitude gain G simultaneously ₂The main subscriber signal that amplification receives from the first main user, and transmit with amplitude gain G to the second main user ₂Main subscriber signal after the amplification;

Step 2: second time slot, cognitive user are measured the main subscriber signal signal to noise ratio γ that the second main user sends _C2, cognitive user is with amplitude gain G simultaneously ₁The main subscriber signal that amplification receives from the second main user, and transmit with amplitude gain G to the first main user ₁Main subscriber signal after the amplification;

Step 3: the 3rd time slot, cognitive user are measured the main subscriber signal signal to noise ratio γ ' that the first main user sends _C1, cognitive user is with amplitude gain G ' simultaneously ₂The main subscriber signal that amplification receives from the first main user, and transmit with amplitude gain G ' to the second main user ₂Main subscriber signal after the amplification;

Step 4: the 4th time slot, cognitive user are measured the main subscriber signal signal to noise ratio γ ' that the second main user sends _C2

Step 5: the 5th time slot, cognitive user are measured the main subscriber signal signal to noise ratio γ ' that the first main user sends _C1

Step 6: cognitive users were calculated, and the first primary user channel gain

cognitive user and the second main user channel gain

The first and second main primary user user channel increased

$h_2^2=\frac{{\mathrm{\&gamma;}}_{c1}^{\&prime;}}{{\mathrm{\&gamma;}}_{c1}{G}_2^2{\mathrm{\&sigma;}}_c^2}{(1+G_2\mathrm{\&Delta;})}^2{\mathrm{\&sigma;}}_2^2-\frac{{\mathrm{\&sigma;}}_2^2}{G_2^2{\mathrm{\&sigma;}}_c^2},$

$h_1^2=\frac{{\mathrm{\&gamma;}}_{c2}^{\&prime;}}{{\mathrm{\&gamma;}}_{c2}{G}_1^2{\mathrm{\&sigma;}}_c^2}{(1+G_1\mathrm{\&Delta;})}^2{\mathrm{\&sigma;}}_1^2-\frac{{\mathrm{\&sigma;}}_1^2}{G_1^2{\mathrm{\&sigma;}}_c^2},$

$h_0^2=\frac{h_1^2{h}_2^2}{{\mathrm{\&Delta;}}^2},$

Wherein, $\mathrm{\&Delta;}=\frac{(G_2{\mathrm{\&gamma;}}_{r1}^{\&prime;\&prime;}-G_2^{\&prime;}{\mathrm{\&gamma;}}_{r1}^{\&prime;})\&PlusMinus;\sqrt{{\mathrm{\&gamma;}}_{r1}^{\&prime;}{\mathrm{\&gamma;}}_{r1}^{\&prime;\&prime;}{(G_2-G_2^{\&prime;})}^2+{\mathrm{\&gamma;}}_{r1}({\mathrm{\&gamma;}}_{r1}^{\&prime;}-{\mathrm{\&gamma;}}_{r1}^{\&prime;\&prime;})(G_2^{\&prime;2}-G_2^2)}}{G_2{G}_2^{\&prime;}({\mathrm{\&gamma;}}_{r1}^{\&prime;}-{\mathrm{\&gamma;}}_{r1}^{\&prime;\&prime;})}.$

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