CN113099534A - Resource allocation method of environment backscattering communication system - Google Patents

Resource allocation method of environment backscattering communication system Download PDF

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CN113099534A
CN113099534A CN202110335751.9A CN202110335751A CN113099534A CN 113099534 A CN113099534 A CN 113099534A CN 202110335751 A CN202110335751 A CN 202110335751A CN 113099534 A CN113099534 A CN 113099534A
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backscattering
radio frequency
antenna
signal
backscatter
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CN113099534B (en
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张晓暄
李勇
程伟
宋静怡
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Northwestern Polytechnical University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/046—Wireless resource allocation based on the type of the allocated resource the resource being in the space domain, e.g. beams

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Abstract

The invention discloses a resource allocation method of an environment backscattering communication system, which comprises the following steps that firstly, a multi-antenna radio frequency signal source transmits a pilot signal; a single antenna receiver and a backscattering device receive pilot signals and estimate direct link channel vectors and forward channel vectors respectively; the multi-antenna radio frequency signal source transmits the pilot signal again, the backscattering equipment collects energy and performs backscattering, and the single-antenna receiver estimates a backscattering channel g of the backscattering equipment; then the single-antenna receiver feeds back the direct link channel vector, the forward channel vector and the backward channel g to a multi-antenna radio frequency signal source; the multi-antenna radio frequency signal source designs an optimal transmission beam forming precoding matrix by utilizing information fed back by the single-antenna receiver, and the optimal transmission beam forming precoding matrix is used for transmitting data signals; and completing the resource allocation. The invention provides additional multipath for the main transmission system through the backscattering equipment, thereby improving the main transmission rate.

Description

Resource allocation method of environment backscattering communication system
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a resource allocation method of a communication system.
Background
The internet of things and 5G are one of the main applications of future wireless networks. As the number of internet of things devices has increased exponentially, radio spectrum resources and energy requirements have increased. For future development of the internet of things, new spectrum resources need to be developed and energy-efficient communication technologies need to be used.
Backscatter communications is one solution to the energy savings of the internet of things. The backscattering device not only can modulate the information thereof through a carrier transmitter signal in the environment, but also can collect the energy of a radio frequency signal in the environment to assist the information modulation and the functional operation thereof. The backscattering equipment does not contain an active radio frequency assembly, and the communication power requirement in the Internet of things is reduced. Radio frequency identification is a typical type of backscatter communication. Ambient backscattering Communication (AmBC) is a Communication method recently proposed at present, and can utilize the existing radio frequency excitation source (cellular network, WiFi, TV) in the environment to transmit information. Therefore, a special radio frequency source is not needed to support the backscattering communication, and the communication of the Internet of things is more energy-saving.
The AmBC system model studies the achievable rate range of main transmission and Backscatter Device (BD) transmission. The AmBC system mainly researches that the signal period of BD transmission is the same as that of main transmission at present, the complexity in the aspect of algorithm design is high, and the BD is an active device.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a resource allocation method of an environment backscattering communication system, which comprises the steps of firstly, transmitting a pilot signal by a multi-antenna radio frequency signal source; a single antenna receiver and a backscattering device receive pilot signals and estimate direct link channel vectors and forward channel vectors respectively; the multi-antenna radio frequency signal source transmits the pilot signal again, the backscattering equipment collects energy and performs backscattering, and the single-antenna receiver estimates a backscattering channel g of the backscattering equipment; then the single-antenna receiver feeds back the direct link channel vector, the forward channel vector and the backward channel g to a multi-antenna radio frequency signal source; the multi-antenna radio frequency signal source designs an optimal transmission beam forming precoding matrix by utilizing information fed back by the single-antenna receiver, and the optimal transmission beam forming precoding matrix is used for transmitting data signals; and completing the resource allocation. The invention provides additional multipath for the main transmission system through the backscattering equipment, thereby improving the main transmission rate.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a resource allocation method of an environment backscattering communication system comprises a multi-antenna radio frequency signal source, backscattering equipment and a single-antenna receiver; the method comprises the following steps:
step 1: a multi-antenna radio frequency signal source transmits a pilot signal;
step 2: single antenna receiver receives pilot signal and estimates direct link channel vector h1＝[h1,1,...,hM,1]T∈CM×1，h1,1,...,hM,1Representing direct link channel coefficients from each antenna of the multi-antenna radio frequency source to the single-antenna receiver, wherein M represents the total number of antennas of the multi-antenna radio frequency source, and C represents a complex field; the backscatter device receives the pilot signal, collects a portion of the energy and estimates a forward channel vector h2＝[h1,2,...,hM,2]T∈CM×1，h1,2,...,hM,2Representing the forward channel coefficient from each antenna of the multi-antenna radio frequency source to the backscattering device, and feeding the forward channel vector back to the single-antenna receiver by the backscattering device;
and step 3: the multi-antenna radio frequency signal source transmits the pilot signal again, the backscattering equipment collects energy and performs backscattering, and the single-antenna receiver estimates a backscattering channel g of the backscattering equipment;
and 4, step 4: single antenna receiver will direct link channel vector h1Forward channel vector h2Feeding back the backward channel g to the multi-antenna radio frequency signal source;
and 5: the multi-antenna radio frequency signal source designs an optimal transmission beam forming precoding matrix by using the information fed back by the single-antenna receiver in the step 4, and the optimal transmission beam forming precoding matrix is used for transmitting data signals;
step 6: the backscattering equipment receives the data signals and performs radio frequency energy collection and backscattering;
and 7: the single-antenna receiver detects data signals from a multi-antenna radio frequency signal source from received signals, carries out serial interference elimination and then detects backscattering signals;
and 8: the single antenna receiver decodes the backscatter signal to obtain information for the backscatter device.
Preferably, the method for designing an optimal transmit beamforming precoding matrix in step 5 includes the following steps:
step 5-1: constructing a receiving model of the single-antenna receiver;
in N main signal periods TsIn the above embodiment, the signal y (n) received by the single antenna receiver is:
Figure BDA0002997521290000021
in the formula: p is transmitting power, H represents the conjugate transpose of the matrix, w is the signal beam forming vector sent by the multi-antenna radio frequency signal source, and s (n) is the period T sent by the multi-antenna radio frequency signal sourcesα is a following reflection coefficient, g is a back channel coefficient of the backscatter device, c is a signal transmitted by the backscatter device, and z (n) is white gaussian noise;
the second signal term in the formula (1)
Figure BDA0002997521290000022
Viewed as the main signal s (n) through the channel
Figure BDA0002997521290000023
The single antenna receiver treats the backscatter device signal as a multipath component decoded primary signal s (n), the equivalent channels used to decode s (n) are:
Figure BDA0002997521290000031
decoding s (N) by non-coherent detection, if N > 1, the rate that non-coherent can achieve is approximately the rate that coherent can achieve, as shown in equation (2):
Figure BDA00029975212900000319
wherein ：
Figure BDA0002997521290000032
to the rate achievable with non-coherent detection for a given c,
Figure BDA0002997521290000033
is obeyed to a non-central chi-squared χ by giving the SNR of c-decode s (n)2Distribution with degree of freedom of 2, sigma2Is the variance;
thus, the host signal averages the host rate
Figure BDA0002997521290000034
Comprises the following steps:
Figure BDA0002997521290000035
wherein ,
Figure BDA0002997521290000036
represents the statistical expectation for a given c;
the primary signal probability density function is:
Figure BDA0002997521290000037
wherein ,
Figure BDA0002997521290000038
lambda is a non-centrality parameter,
Figure BDA00029975212900000320
parameter of gaussian variance
Figure BDA0002997521290000039
I0(.) isFirst order modified Bessel function:
Figure BDA00029975212900000310
wherein m is a Bessel parameter, and gamma (eta) is a gamma function;
the non-centrality parameter λ is the SNR of the direct link, and the gaussian variance related parameter 2 Σ is the SNR of the backscatter link; thus making
Figure BDA00029975212900000311
By the formula (4), the average main rate in the formula (3)
Figure BDA00029975212900000312
The expansion is as follows:
Figure BDA00029975212900000313
when the SNR is
Figure BDA00029975212900000314
When approaching to infinity, the average principal rate
Figure BDA00029975212900000315
Can be obtained in the following closed form:
Figure BDA00029975212900000316
wherein e is a natural index,
Figure BDA00029975212900000317
performing exponential integration;
after decoding s (n), the single antenna receiver applies a direct interference cancellation technique to cancel direct link interference; assuming that the main signal component is completely removed, the intermediate signal is obtained as:
Figure BDA00029975212900000318
wherein s ═ s (1), s (2), …, s (N)]TIs the main signal vector, z is the additive gaussian noise vector;
because E [ | s (n) & gtdoes not see light2]The SNR for decoding a backscatter device symbol c by maximal ratio combining MRC is approximately 1:
Figure BDA0002997521290000041
since only one backscatter device symbol is transmitted in N consecutive periods of the main signal, the main signal s (N) is considered to be a spreading code of length N of the backscatter device symbol; thus, for decoding backscatter device symbols
Figure BDA0002997521290000042
At the cost of a reduced symbol rate (1/N) by a factor of N; the backscatter devices can achieve rates of:
Figure BDA0002997521290000043
in an environmental backscatter communication system, backscatter requires collecting radio frequency signals in an environment for energy collection, and energy collected by a backscatter device is:
E＝η(1-α)p||s(n)||2
wherein eta ∈ [0,1] represents energy collection efficiency;
since the squared envelope of s (n) follows an exponential distribution, its probability density function is f (x) e-x,x>0; the energy collected by the backscatter device is therefore as follows:
Figure BDA0002997521290000044
step 5-2: obtaining a resource allocation mode of a radio frequency signal source by solving the problems of weighting and rate maximization and transmission power minimization;
step 5-2-1: weighted sum rate maximization problem WSRM;
the weighted sum of the main rate and the backscatter rate is maximized by optimizing the transmit beamforming vector w.
P1:
Figure BDA0002997521290000045
s.t.||w||2＝1 (12b)
E≥Emin (12c)
Step 5-2-2: transmission power minimization problem TPM;
the transmit power of the rf signal source is minimized for a given primary rate and backscatter rate requirement by jointly optimizing the transmit beamforming vector w and the transmit power p.
P2：
Figure BDA0002997521290000051
Figure BDA0002997521290000052
Figure BDA0002997521290000053
||w||2＝1 (13d)
E≥Emin (13e)
wherein ,
Figure BDA0002997521290000054
and
Figure BDA0002997521290000055
velocity requirements of the main system and the backscatter device, respectively, EminRepresenting minimum energyA demand;
step 5-3: for the WSRM problem, an equivalence problem with a semi-positive PSD matrix variable is adopted, and the expected operation is realized by a Monte Carlo method;
let W be pwwH，
Figure BDA0002997521290000056
Then P1 reconverts to the equivalent of the following:
P1-PSD:
Figure BDA0002997521290000057
s.t.Tr(W)＝p (14b)
Rank(W)＝1 (14c)
E≥Emin (14d)
for the TPM problem, P2 translates into the equivalent problem:
P2-PSD:
Figure BDA0002997521290000058
Figure BDA0002997521290000059
Figure BDA00029975212900000510
Rank(W)＝1 (15d)
E≥Emin (15e)
step 5-4: calculating to obtain the optimal solution W of the optimization problem P1-PSD by a convex optimization method*Solving the WSRM problem;
step 5-4-1: knowing the transmitted power p, minimum energy requirement EminChannel correlation coefficient h1,h2G; setting an integer D;
step 5-4-2: to W*Carrying out singular valuede-SVD, i.e. W*＝UΣUH，U＝[u1,...,uM]；
Step 5-4-3: if Rank (W)*)＝1，w*＝u1；
Step 5-4-4: otherwise D1.. D, a random vector is generated
Figure BDA0002997521290000061
θiObeying a uniform distribution of U (0,2 π);
step 5-4-5: optimal solution
Figure BDA0002997521290000062
Step 5-5: calculating P2-PSD optimal solution W by convex optimization method*And solving the TPM problem.
Step 5-5-1: minimum energy requirement EminChannel correlation coefficient h1,h2G, setting a larger integer D;
step 5-5-2: to W*Singular Value Decomposition (SVD), i.e. W*＝UΣUH，U＝[u1,...,uM]；
Step 5-5-3: let p be Tr (Σ);
step 5-5-4: if Rank (W)*)＝1，p*＝p，w*＝u1；
Step 5-5-5: otherwise, D is 1
Figure BDA0002997521290000063
θiObeying a uniform distribution of U (0,2 π);
step 5-5-6: p is a radical of*＝p，w*＝wd。
Preferably, the pilot signal is any signal that is known.
The invention has the following beneficial effects:
compared with the traditional multiple-input single-output MISO system, the invention is mainly based on the symbiotic radio concept, and provides additional multipath for the main transmission system through the backscattering equipment, thereby improving the main transmission rate.
Drawings
Fig. 1 is a model schematic diagram of an ambient backscatter communications system of the present invention.
Fig. 2 shows the co-generation of radio transmission frame structures within a fading block by the method of the present invention.
Fig. 3 shows the main transmission rates of the method of the present invention under different snr conditions.
FIG. 4 shows the method of the present invention
Figure BDA0002997521290000064
Transmission rate under constraint
Figure BDA0002997521290000065
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
The invention aims to provide a resource allocation scheme in future communication of the Internet of things, which is used for overcoming the limitation of huge energy consumption in the current communication of the Internet of things and enabling the communication of the Internet of things with high capacity and low power consumption to be possible.
The environmental backscatter communication system mainly comprises a multi-antenna radio frequency signal source, a single backscatter device and a single antenna receiver, wherein the multi-antenna radio frequency signal source is used for receiving and transmitting signals, and mainly comprises two modes of channel estimation and backscatter communication, and a schematic diagram of a model is shown in figure 1.
In the channel estimation mode, a radio frequency signal source transmits a downlink pilot signal, a backscattering device is used for estimating a forward channel between the receiver and the radio frequency signal source, a direct link channel between the receiver and the radio frequency signal source is estimated, the backscattering device performs backscattering by using a fixed reflection coefficient, and the receiver estimates a backward channel between the receiver and the backscattering device.
In a backscatter communication mode, a radio frequency signal source sends a downlink data signal and a backscatter device sends the signal to a receiver by changing a load impedance. The receiver first demodulates the rf source signal and then performs serial interference cancellation to detect the signal from the backscatter device.
A resource allocation method of an environment backscattering communication system comprises a multi-antenna radio frequency signal source, backscattering equipment and a single-antenna receiver; the method comprises the following steps:
step 1: a multi-antenna radio frequency signal source transmits a pilot signal;
step 2: single antenna receiver receives pilot signal and estimates direct link channel vector h1＝[h1,1,...,hM,1]T∈CM×1，h1,1,...,hM,1Representing direct link channel coefficients from each antenna of a radio frequency signal source to a receiver, M representing the number of antennas of the radio frequency signal source, and C representing a complex field; the backscatter device receives the pilot signal, collects a portion of the energy and estimates a forward channel vector h2＝[h1,2,...,hM,2]T∈CM×1，h1,2,...,hM,2The forward channel coefficient of no antenna of the radio frequency signal source to the backscattering equipment is represented, and the backscattering equipment feeds back a forward channel vector to the single-antenna receiver; the backscattering equipment switches the load impedance to a matching state, no signal is backscattered, and the channel estimation mode comprises any existing method;
and step 3: the multi-antenna radio frequency signal source transmits the pilot signal again, the backscattering equipment collects energy and performs backscattering, and the single-antenna receiver estimates a backscattering channel g of the backscattering equipment; the power reflection coefficient of the backscatter device is configured to be a constant known to the receiver;
and 4, step 4: single antenna receiver will direct link channel vector h1Forward channel vector h2Feeding back the backward channel g to the multi-antenna radio frequency signal source;
and 5: the multi-antenna radio frequency signal source designs an optimal transmission beam forming precoding matrix by using the information fed back by the single-antenna receiver in the step 4, and the optimal transmission beam forming precoding matrix is used for transmitting data signals;
step 6: the backscattering equipment receives the data signals and performs radio frequency energy collection and backscattering;
and 7: the single-antenna receiver detects data signals from a multi-antenna radio frequency signal source from received signals, carries out serial interference elimination and then detects backscattering signals;
and 8: the single antenna receiver decodes the backscatter signal to obtain information for the backscatter device.
Co-existing radio is based on the main signal period TsWith period T of the backscattered signalcThe relationship between, i.e. Tc＝NTsWherein N is an integer and N > 1, as shown in FIG. 2;
preferably, the method for designing an optimal transmit beamforming precoding matrix in step 5 includes the following steps:
step 5-1: constructing a receiving model of the single-antenna receiver;
in N main signal periods TsIn the above embodiment, the signal y (n) received by the single antenna receiver is:
Figure BDA0002997521290000081
in the formula: p is transmitting power, H represents matrix transposition, w is signal beam forming vector sent by the multi-antenna radio frequency signal source, and s (n) is the period T sent by the multi-antenna radio frequency signal sourcesAlpha is a following reflection coefficient, g is a backward channel of the backscattering equipment, c is a signal sent by the backscattering equipment, and z (n) is Gaussian white noise;
the second signal term in the formula (1)
Figure BDA0002997521290000082
Viewed as the main signal s (n) passing through a slowly varying channel
Figure BDA0002997521290000083
The single antenna receiver treats the backscatter device signal as a multipath component decoded primary signal s (n), the equivalent channels used to decode s (n) are:
Figure BDA0002997521290000084
since the single antenna receiver has no a priori knowledge of the backscatter device signal c, so that the partially coherent channel parameters (CSI) are unknown, it is necessary to decode s (N) by non-coherent detection, and if N > 1, the rate at which non-coherent can be achieved is approximately the rate at which coherent can be achieved, as shown in equation (2):
Figure BDA0002997521290000085
wherein ,
Figure BDA0002997521290000086
to achieve a demodulation rate for non-coherent demodulation for a given c,
Figure BDA0002997521290000087
is obeyed to a non-central chi-squared χ by giving the SNR of c-decode s (n)2Distribution with degree of freedom of 2 and variance of σ2(ii) a This approximation can be explained by channel training, where the PT sends a limited number of training symbols to estimate the channel, and the training error is ignored in each backscatter device symbol period because N is large.
Thus, the host signal averages the host rate
Figure BDA0002997521290000091
Comprises the following steps:
Figure BDA0002997521290000092
wherein ,
Figure BDA0002997521290000093
represents the statistical expectation for a given c;
the primary signal probability density function is:
Figure BDA0002997521290000094
wherein ,
Figure BDA0002997521290000095
lambda is a non-centrality parameter,
Figure BDA0002997521290000096
parameter of gaussian variance
Figure BDA0002997521290000097
I0(.) is a first order modified Bessel function:
Figure BDA0002997521290000098
wherein m is a Bessel parameter, and gamma (eta) is a gamma function;
the non-centrality parameter λ is the SNR of the direct link, and the gaussian variance related parameter 2 Σ is the SNR of the backscatter link; thus making
Figure BDA0002997521290000099
By the formula (4), the average main rate in the formula (3)
Figure BDA00029975212900000910
The expansion is as follows:
Figure BDA00029975212900000911
when the SNR is
Figure BDA00029975212900000912
When approaching to infinity, the average principal rate
Figure BDA00029975212900000913
Can be obtained in the following closed form:
Figure BDA00029975212900000914
wherein e is a natural index,
Figure BDA00029975212900000915
performing exponential integration;
after decoding s (n), the single antenna receiver applies a direct interference cancellation technique to cancel direct link interference; assuming that the main signal component is completely removed, the intermediate signal is obtained as:
Figure BDA00029975212900000916
wherein s ═ s (1), s (2), …, s (N)]TIs the main signal vector, z is the additive gaussian noise vector;
because E [ | s (n) & gtdoes not see light2]The SNR for decoding a backscatter device symbol c by maximal ratio combining MRC is approximately 1:
Figure BDA00029975212900000917
since only one backscatter device symbol is transmitted in N consecutive periods of the main signal, the main signal s (N) is considered to be a spreading code of length N of the backscatter device symbol; thus, for decoding backscatter device symbols
Figure BDA00029975212900000918
At the cost of a reduced symbol rate (1/N) by a factor of N; the backscatter devices can achieve rates of:
Figure BDA0002997521290000101
in an environmental backscatter communication system, backscatter requires collecting radio frequency signals in an environment for energy collection, and energy collected by a backscatter device is:
E＝η(1-α)p||s(n)||2
wherein eta ∈ [0,1] represents energy collection efficiency;
since the squared envelope of s (n) follows an exponential distribution, its probability density function is f (x) e-x,x>0; the energy collected by the backscatter device is therefore as follows:
Figure BDA0002997521290000102
step 5-2: obtaining a resource allocation mode of a radio frequency signal source by solving the problems of weighting and rate maximization and transmission power minimization;
step 5-2-1: weighted sum rate maximization problem WSRM;
the weighted sum of the main rate and the backscatter rate is maximized by optimizing the transmit beamforming vector w.
P1:
Figure BDA0002997521290000103
s.t.||w||2＝1 (12b)
E≥Emin (12c)
Since the objective function (12a) is non-convex with respect to w and also has the desired operation, it is difficult to obtain the optimal solution of P1.
Step 5-2-2: transmission power minimization problem TPM;
the transmit power of the rf signal source is minimized for a given primary rate and backscatter rate requirement by jointly optimizing the transmit beamforming vector w and the transmit power p.
P2：
Figure BDA0002997521290000104
Figure BDA0002997521290000111
Figure BDA0002997521290000112
||w||2＝1 (13d)
E≥Emin (13e)
wherein ,
Figure BDA0002997521290000113
and
Figure BDA0002997521290000114
velocity requirements of the main system and the backscatter device, respectively, EminRepresents a minimum energy requirement;
equation (13b) cannot be translated into the SNR constraint in problem P2 because it is difficult to obtain a closed form expression for the primary rate from the SNR perspective. In addition, because constraints (13b) and (13c) are non-convex with respect to w, P2 is also difficult to solve in its current form.
Step 5-3: for the WSRM problem, an equivalence problem with a semi-positive PSD matrix variable is adopted, and the expected operation is realized by a Monte Carlo method;
let W be pwwH，
Figure BDA0002997521290000115
Then P1 reconverts to the equivalent of the following:
P1-PSD:
Figure BDA0002997521290000116
s.t.Tr(W)＝p (14b)
Rank(W)＝1 (14c)
E≥Emin (14d)
since the desired operation of the logarithm preserves the concavity in (14a), the objective function in (P1-PSD) is a concave function. Therefore, (P1-PSD) is a convex optimization problem that can be effectively solved by optimization.
For the TPM problem, P2 translates into the equivalent problem:
P2-PSD:
Figure BDA0002997521290000117
Figure BDA0002997521290000118
Figure BDA0002997521290000119
Rank(W)＝1 (15d)
E≥Emin (15e)
in the simulation, the desired operation in (15b) is realized by the monte carlo method. After solving the optimal solution for P2-PSD, a substantially approximate beamforming solution w is obtained*And a transmission power P of (P2)*。
Step 5-4: calculating to obtain the optimal solution W of the optimization problem P1-PSD by a convex optimization method*Solving the WSRM problem;
step 5-4-1: knowing the transmitted power p, minimum energy requirement EminChannel correlation coefficient h1,h2G; setting an integer D;
step 5-4-2: to W*Performing singular value decomposition SVD, i.e. W*＝UΣUH，U＝[u1,...,uM]；
Step 5-4-3: if Rank (W)*)＝1，w*＝u1；
Step 5-4-4: otherwise D1.. D, a random vector is generated
Figure BDA0002997521290000121
θiObeying a uniform distribution of U (0,2 π);
step 5-4-5: optimal solution
Figure BDA0002997521290000122
Step 5-5: calculating P2-PSD optimal solution W by convex optimization method*And solving the TPM problem.
Step 5-5-1: minimum energy requirement EminChannel correlation coefficient h1,h2G, setting a larger integer D;
step 5-5-2: to W*Singular Value Decomposition (SVD), i.e. W*＝UΣUH，U＝[u1,...,uM]；
Step 5-5-3: let p be Tr (Σ);
step 5-5-4: if Rank (W)*)＝1，p*＝p，w*＝u1；
Step 5-5-5: otherwise, D is 1
Figure BDA0002997521290000123
θiObeying a uniform distribution of U (0,2 π);
step 5-5-6: p is a radical of*＝p，w*＝wd。
FIG. 3 illustrates that in ambient backscatter communications, the backscatter path can increase the primary rate
Figure BDA0002997521290000124
As the signal-to-noise ratio increases, the backscatter rate increases simultaneously with the main rate. FIG. 4 illustrates the backscattering rate requirement
Figure BDA0002997521290000125
For main rate
Figure BDA0002997521290000126
The effect of (c) is that as the backscatter rate increases, the curves begin to remain constant and then gradually rise to eventually coincide with each other.

Claims (3)

1. A resource allocation method of an environment backscattering communication system is characterized in that the environment backscattering communication system comprises a multi-antenna radio frequency signal source, backscattering equipment and a single-antenna receiver; the method comprises the following steps:
step 1: a multi-antenna radio frequency signal source transmits a pilot signal;
step 2: single antenna receiver receives pilot signal and estimates direct link channel vector h1＝[h1,1,...,hM,1]T∈CM ×1，h1,1,...,hM,1Representing direct link channel coefficients from each antenna of the multi-antenna radio frequency source to the single-antenna receiver, wherein M represents the total number of antennas of the multi-antenna radio frequency source, and C represents a complex field; the backscatter device receives the pilot signal, collects a portion of the energy and estimates a forward channel vector h2＝[h1,2,...,hM,2]T∈CM×1，h1,2,...,hM,2Representing the forward channel coefficient from each antenna of the multi-antenna radio frequency source to the backscattering device, and feeding the forward channel vector back to the single-antenna receiver by the backscattering device;
and step 3: the multi-antenna radio frequency signal source transmits the pilot signal again, the backscattering equipment collects energy and performs backscattering, and the single-antenna receiver estimates a backscattering channel g of the backscattering equipment;
and 4, step 4: single antenna receiver will direct link channel vector h1Forward channel vector h2Feeding back the backward channel g to the multi-antenna radio frequency signal source;
and 5: the multi-antenna radio frequency signal source designs an optimal transmission beam forming precoding matrix by using the information fed back by the single-antenna receiver in the step 4, and the optimal transmission beam forming precoding matrix is used for transmitting data signals;
step 6: the backscattering equipment receives the data signals and performs radio frequency energy collection and backscattering;
and 7: the single-antenna receiver detects data signals from a multi-antenna radio frequency signal source from received signals, carries out serial interference elimination and then detects backscattering signals;
and 8: the single antenna receiver decodes the backscatter signal to obtain information for the backscatter device.
2. The method of claim 1, wherein the method for designing the optimal transmit beamforming precoding matrix in step 5 comprises the following steps:
step 5-1: constructing a receiving model of the single-antenna receiver;
in N main signal periods TsIn the above embodiment, the signal y (n) received by the single antenna receiver is:
Figure FDA0002997521280000011
in the formula: p is transmitting power, H represents the conjugate transpose of the matrix, w is the signal beam forming vector sent by the multi-antenna radio frequency signal source, and s (n) is the period T sent by the multi-antenna radio frequency signal sourcesα is a following reflection coefficient, g is a back channel coefficient of the backscatter device, c is a signal transmitted by the backscatter device, and z (n) is white gaussian noise;
the second signal term in the formula (1)
Figure FDA0002997521280000021
Viewed as the main signal s (n) through the channel
Figure FDA0002997521280000022
The single antenna receiver treats the backscatter device signal as a multipath component decoded primary signal s (n), the equivalent channels used to decode s (n) are:
Figure FDA0002997521280000023
decoding s (N) by non-coherent detection, if N > 1, the rate that non-coherent can achieve is approximately the rate that coherent can achieve, as shown in equation (2):
Figure FDA0002997521280000024
wherein ：
Figure FDA0002997521280000025
to the rate achievable with non-coherent detection for a given c,
Figure FDA0002997521280000026
is obeyed to a non-central chi-squared χ by giving the SNR of c-decode s (n)2Distribution with degree of freedom of 2, sigma2Is the variance;
thus, the host signal averages the host rate
Figure FDA0002997521280000027
Comprises the following steps:
Figure FDA0002997521280000028
wherein ,
Figure FDA0002997521280000029
represents the statistical expectation for a given c;
the primary signal probability density function is:
Figure FDA00029975212800000210
wherein ,
Figure FDA00029975212800000211
lambda is a non-centrality parameter,
Figure FDA00029975212800000212
parameter of gaussian variance
Figure FDA00029975212800000213
I0(.) is a first order modified Bessel function:
Figure FDA00029975212800000214
wherein m is a Bessel parameter, and gamma (eta) is a gamma function;
the non-centrality parameter λ is the SNR of the direct link, and the gaussian variance related parameter 2 Σ is the SNR of the backscatter link; thus making
Figure FDA00029975212800000215
By the formula (4), the average main rate in the formula (3)
Figure FDA00029975212800000216
The expansion is as follows:
Figure FDA00029975212800000217
when the SNR is
Figure FDA00029975212800000218
When approaching to infinity, the average principal rate
Figure FDA00029975212800000219
Can be obtained in the following closed form:
Figure FDA00029975212800000220
wherein e is a natural index,
Figure FDA00029975212800000221
performing exponential integration;
after decoding s (n), the single antenna receiver applies a direct interference cancellation technique to cancel direct link interference; assuming that the main signal component is completely removed, the intermediate signal is obtained as:
Figure FDA0002997521280000031
wherein s ═ s (1), s (2), …, s (N)]TIs the main signal vector, z is the additive gaussian noise vector;
because E [ | s (n) & gtdoes not see light2]The SNR for decoding a backscatter device symbol c by maximal ratio combining MRC is approximately 1:
Figure FDA0002997521280000032
since only one backscatter device symbol is transmitted in N consecutive periods of the main signal, the main signal s (N) is considered to be a spreading code of length N of the backscatter device symbol; thus, for decoding backscatter device symbols
Figure FDA0002997521280000033
At the cost of a reduced symbol rate (1/N) by a factor of N; the backscatter devices can achieve rates of:
Figure FDA0002997521280000034
in an environmental backscatter communication system, backscatter requires collecting radio frequency signals in an environment for energy collection, and energy collected by a backscatter device is:
E＝η(1-α)p||s(n)||2
wherein eta ∈ [0,1] represents energy collection efficiency;
since the squared envelope of s (n) follows an exponential distribution, its probability density function is f (x) e-x,x>0; the energy collected by the backscatter device is therefore as follows:
Figure FDA0002997521280000035
step 5-2: obtaining a resource allocation mode of a radio frequency signal source by solving the problems of weighting and rate maximization and transmission power minimization;
step 5-2-1: weighted sum rate maximization problem WSRM;
maximizing the weighted sum of the main rate and the backscattering rate by optimizing a transmit beamforming vector w;
P1:
Figure FDA0002997521280000036
s.t.||w||2＝1 (12b)
E≥Emin (12c)
step 5-2-2: transmission power minimization problem TPM;
minimizing the transmit power of the radio frequency signal source for a given primary rate and backscatter rate requirement by jointly optimizing a transmit beamforming vector w and the transmit power p;
P2：
Figure FDA0002997521280000041
Figure FDA0002997521280000042
Figure FDA0002997521280000043
||w||2＝1 (13d)
E≥Emin (13e)
wherein ,
Figure FDA0002997521280000049
and
Figure FDA00029975212800000410
velocity requirements of the main system and the backscatter device, respectively, EminRepresents a minimum energy requirement;
step 5-3: for the WSRM problem, an equivalence problem with a semi-positive PSD matrix variable is adopted, and the expected operation is realized by a Monte Carlo method;
let W be pwwH，
Figure FDA0002997521280000044
Then P1 reconverts to the equivalent of the following:
P1-PSD:
Figure FDA0002997521280000045
s.t.Tr(W)＝p (14b)
Rank(W)＝1 (14c)
E≥Emin (14d)
for the TPM problem, P2 translates into the equivalent problem:
P2-PSD:
Figure FDA0002997521280000046
Figure FDA0002997521280000047
Figure FDA0002997521280000048
Rank(W)＝1 (15d)
E≥Emin (15e)
step 5-4: calculating to obtain the optimal solution W of the optimization problem P1-PSD by a convex optimization method*Solving the WSRM problem;
step 5-4-1: knowing the transmitted power p, minimum energy requirement EminChannel correlation coefficient h1,h2G; setting an integer D;
step 5-4-2: to W*Performing singular value decomposition SVD, i.e. W*＝UΣUH，U＝[u1,...,uM]；
Step 5-4-3: if Rank (W)*)＝1，w*＝u1；
Step 5-4-4: otherwise D1.. D, a random vector is generated
Figure FDA0002997521280000051
θiObeying a uniform distribution of U (0,2 π);
step 5-4-5: optimal solution
Figure FDA0002997521280000052
Step 5-5: calculating P2-PSD optimal solution W by convex optimization method*Solving the TPM problem;
step 5-5-1: minimum energy requirement EminChannel correlation coefficient h1,h2G, setting a larger integer D;
step 5-5-2: to W*Singular Value Decomposition (SVD), i.e. W*＝UΣUH，U＝[u1,...,uM]；
Step 5-5-3: let p be Tr (Σ);
step 5-5-4: if Rank (W)*)＝1，p*＝p，w*＝u1；
Step 5-5-5: otherwise, D is 1
Figure FDA0002997521280000053
θiObeying a uniform distribution of U (0,2 π);
step 5-5-6: p is a radical of*＝p，w*＝wd。
3. The method of claim 1, wherein the pilot signal is any known signal.
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