CN107592149A - A kind of full duplex filtering forward relay structure and its discrete frequency domain response design method - Google Patents
A kind of full duplex filtering forward relay structure and its discrete frequency domain response design method Download PDFInfo
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Abstract
The invention discloses a kind of relay structure of digital full duplex filtering forwarding (FF FD) system and its Optimization Design of discrete frequency domain response, including low-converter, front end cascade VVA, base-band digital wave filter, rear end cascade VGA, upconverter and amplification module；Based on FF FD systems, the relaying DFR optimization problems under digital baseband are built, meets transmit power limitation and finds optimal relaying discrete frequency domain response；When channel is frequency non-selective channel, optimal relaying DFR coefficients are directly obtained；When channel is frequency-selective channel, CSI is whether there is according to originator, is converted into the convex optimization problem of power distribution, effectively solve optimal relaying DFR coefficients；The relaying DFR coefficients of suboptimum are further obtained, thus reduce computation complexity.The present invention can strengthen the availability of FF FD systems, obtain the systematic function better than existing AF FD, while reduce system complexity and computation complexity, maximize the achievable rate of system.
Description
Technical Field
The invention belongs to the field of wireless communication, relates to a wireless relay communication technology, and particularly relates to a relay structure of a digital full-duplex filtering and forwarding system and an optimal design method of discrete frequency domain response of the relay structure.
Background
The relay communication technology can expand the communication range, enhance the link quality and improve the spectrum efficiency, so that the relay communication technology is widely researched and applied at present. Conventional relays typically operate in half-duplex mode, requiring two orthogonal time-frequency resources to transmit a single signal. Different from a half-duplex mode, a full-duplex technology can simultaneously transmit and receive data at the same frequency, and theoretically can realize doubling of frequency spectrum efficiency, so that the full-duplex technology is considered as a key technology of a future wireless network. In practice, a transmitting antenna of a full-duplex system causes interference to a receiving antenna, so that an effective transmission signal is submerged in a self-interference signal, and the system performance is seriously deteriorated, thereby greatly reducing the feasibility of the application of the full-duplex technology. In order to eliminate self-interference signals, many researchers in recent years have been working on effective self-interference cancellation schemes, typical techniques being antenna isolation, analog domain cancellation, and digital domain processing. Through the effective combination of various interference technologies, the suppression of self-interference signals can reach 80dB or even more than 100dB, and therefore the performance superior to that of the traditional half-duplex is obtained.
Although better interference cancellation schemes can achieve better system performance, they can also significantly increase system complexity and reduce system energy efficiency. In a common full-duplex application scenario, the self-interference signal is generally considered to be a harmful interference signal and needs to be eliminated. In a full-duplex relay scene, a self-interference signal is essentially a useful signal copy sent from a source end S to a destination end D at the previous moment, and by effectively utilizing the redundant signal, a complex interference elimination technology can be avoided, and the system performance of the full-duplex relay can be improved, so that the method has important research significance and application value. Currently, there is little research work on the utilization of self-interference signals, and only one article describes an ideal analog Full-Duplex filtering and forwarding (FF-FD) system: the received mixed signal is forwarded after being subjected to linear filtering processing at the relay, so that the self-interference signal is utilized. Although a pure analog system can eliminate the influence of quantization noise, the design of a filtering structure is too complex, the flexibility is low, and dynamic adjustment and optimization under a time-varying channel are difficult; meanwhile, the relay frequency domain response design scheme described in the article needs approximately continuous sampling points to obtain the optimal performance, and is difficult to be directly popularized to a digital domain, so that the calculation complexity is high, and the usability of the system is seriously reduced.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a digital full duplex filtering and forwarding (FF-FD) relay structure and a design method of relay Frequency Response (DFR). Digital FF-FD relay is a relay structure of full duplex filtering-forwarding (FF-FD) system suitable for digital domain processing. Under the condition that Channel State Information (CSI) is known at a relay, an optimal design method of relay Discrete Frequency Response (DFR) is further provided based on a maximum system reachable rate criterion. Under the condition of a frequency non-selection channel, the invention provides an expression of the optimal DFR of the relay; under the frequency selective channel, aiming at the condition that whether a sending end has CSI or not, the invention provides the optimization design and the low-complexity design of the relay DFR. By utilizing the novel digital FF-FD relay, the system design and processing complexity can be reduced, the system availability can be enhanced, and the system performance superior to that of the traditional full-duplex amplified forwarding (AF-FD) can be obtained.
The technical scheme provided by the invention is as follows:
a digital FF-FD relay architecture for a full duplex filtered forwarding (FF-FD) system, comprising: the digital signal processing circuit comprises a down converter, a Voltage Variable Attenuator (VVA) cascaded at the front end, a baseband digital filter, a Voltage Variable Amplifier (VGA) cascaded at the rear end, an up converter and an amplifying module. The front-end cascaded VVA is used for attenuating a received signal containing strong self-interference, so that a sampling signal can fall into a dynamic threshold sampled by an Analog-to-digital converter (ADC); according to the attenuation multiple of VVA, the VGA cascaded at the rear end amplifies the signal by the same multiple; the VVA/VGA cascade modules at the front end and the rear end can ensure that the equivalent frequency domain response of the relay is the same as that of the digital baseband filter on one hand, and can flexibly regulate and control the signal intensity and eliminate the influence of nonlinear quantization noise on the other hand. Since the relay can avoid nonlinear quantization noise, the whole digital FF-FD relay is equivalent to a linear filter. Considering that the equivalent amplification factor of the VVA/VGA cascade module at the front end and the rear end is 1, the design of the discrete frequency domain response of the digital filter of the linear filter is equivalent to the optimization in a digital baseband. Since linear quantization noise is introduced in the digital domain processing, the influence of the linear quantization noise needs to be considered when designing the relay DFR.
The invention also provides a design method of the digital FF-FD relay DFR, which is characterized in that based on the FF-FD system, the relay DFR optimization problem under the digital baseband is established, and the optimal relay discrete frequency domain response β is found under the condition of meeting the limitation of the sending powerE[i]. If the channel is a frequency non-selective channel, directly obtaining an optimal relay DFR coefficient; if the channel is a frequency selective channel, converting the original optimization problem into a convex optimization problem of power distribution according to the existence of CSI at the transmitting end, and effectively solving the coefficient of the optimal relay DFR; and further giving suboptimal relay DFR coefficients based on the DFR optimal result, thereby reducing the computational complexity.
Based on an FF-FD system, constructing an optimization problem of a relay DFR under a digital baseband, specifically, according to the relation of a system transmission link, based on a maximum system reachable rate criterion, firstly calculating linear quantization noise of sampling according to the parameters of the system; then calculating the transmission power spectral density of each sampling point at the relay R; calculating the power spectral density of the effective signal and the noise signal at the destination end D to obtain the reachable rate of each sampling point; root of herbaceous plantAccording to the maximum transmission power P at the source ends S and RSAnd PRThe optimization problem P.1 is established.
According to the fact that whether CSI exists at a sending end or not, the original optimization problem is converted into a convex optimization problem of power distribution, and the coefficient of the optimal relay DFR can be effectively solved; the method comprises the following steps: the maximum transmit power spectral density at sample point i, denoted P, for R and S, respectively, is givenR[i]And PS[i]Calculating the maximum achievable rate function at a single sampling point: marked as I (P) without CSIR[i]) (ii) a Is marked as I (P) under the condition of CSIS[i]，PR[i]) (ii) a Expanding the reachable rate function of a single sampling point to all sampling points, and converting the original optimization problem P.1 into a convex optimization problem of power distribution: the optimization problem without CSI is p.2; the optimization problem with CSI is P.3; establishing a Lagrange function, and solving by using a KKT condition to obtain an optimal power spectral density distribution scheme of all sampling points; and calculating the obtained DFR coefficient of the filter by using the obtained power spectral density.
By utilizing the characteristic that the self-interference signal is far larger than the effective sending signal, the optimal power spectral density distribution is carried out after the form of the DFR of the optimal filter is approximated, and the specific steps comprise: if the originating side has no CSI, the power at S and R is directly distributed evenly, i.e.Wherein W is the communication band bandwidth; if the originating end has CSI, orderUsing an objective functionAnd optimizing the power distribution of the sampling points of the transmitting end, wherein K is the subcarrier number of the OFDM system, and M is the up-sampling multiple. The process of solving the optimization problem P.4 is similar to p.2; the filter DFR coefficients obtained with the obtained power distribution scheme.
Aiming at the filter frequency domain response method for the full-duplex filtering forwarding FF-FD system, further:
setting the number of subcarriers of an OFDM system as K, selecting an ADC with N-bit, and taking the up-sampling multiple as M; the method comprises the following steps:
1) linear quantization noise n is calculated by formula 1qPower spectral density of (a):
nq(dB/Hz)＝10log10PR-10log10W-(6.02N+1.76+10log10m) (formula 1)
2) Aiming at a sampling point i, the frequency domain responses of channels from an S transmitting end to an R receiving end, from an R transmitting end to the R receiving end and from the R transmitting end to a D are respectively made to be HSR[i]、HRR[i]And HRD[i]And the transmit power spectral density at S is Si]Power spectral density of Gaussian thermal noise of n0The processing delay time at the relay is one symbol period; under digital baseband, the power spectral density P of the useful signal at D is obtained by the equations 2 and 3FF,S[i]Power spectral density P of sum noise signalFF,N[i]：
3) Order toBased on the criterion of maximizing the achievable rate of the system, the following optimization problem P.1 is established, and the objective function and the limiting conditions of P.1 are respectively given by an equation 4-1 and an equation 4-2:
wherein Si is the power spectral density of a sampling point i at S;
4) when the channel has no frequency selectivity, the optimization design of the relay DFR is as follows:
5) when the channel is frequency selective, if the sending end has no CSI, the optimization method of the relay DFR is as follows:
51) the originating power being distributed evenly over the frequency band, i.e.
52) Setting the maximum power spectral density of a sampling point i sent at R as PR[i]Then, the objective function and the constraint for the capacity optimization problem of the sampling point are expressed as equation 6-1 and equation 6-2, respectively:
the objective function of the optimization problem is a monotonically increasing function with respect to Ψ [ i ];
53) when in useWhen the target function is at the maximum, it is denoted as I (P)R[i])；
54) Further extending to all sampling points, the original relay DFR design is expressed as the following power distribution problem P.2, and the objective function and the limiting condition are respectively given by an equation 7-1 and an equation 7-2
The objective function represented by equation 7 is a strict concave function;
55) establishing a Lagrangian function as shown in equation 8:
p.2 optimalThe following Karush-Kuhn-Tucker (KKT) condition can be used for solving:
56) the DFR of the globally optimal relay is represented by equation 10:
therefore, when the sending end has no CSI, the optimized relay DFR is obtained;
6) when the channel has frequency selectivity and the sending end has CSI, the optimization method of the relay DFR comprises the following steps:
61) setting the transmission power spectral density of a sampling point i to be limited by P at S and R respectivelyS[i]And PR[i]Then the objective function and the constraint for the sampling point capacity optimization problem are respectively expressed by equation 11-1 and formula 11-2 give:
using monotonic increments of the objective function with respect to S [ i ] and Ψ [ i ], the optimal system velocity can be accurately approximated as:
62) further extending to all sampling points, the objective function and constraints of the original relay DFR design expressed as the following power distribution problem P.3, P.3 are given by equations 13-1 and 13-2, respectively:
(equation 13-1) represents an objective function that is strictly concave;
63) establishing a Lagrangian function as in equation 14:
p.3 optimalAndthe solution can be effectively solved by the following KKT condition:
64) the DFR of the globally optimal relay is represented by equation 16:
therefore, when the sending end has CSI, the optimized relay DFR is obtained;
7) under a frequency selective channel, a relay DFR suboptimal method with low computational complexity comprises the following steps:
71) the originating has no CSI, at this timeThe DFR of the relay is:
72) CSI is transmitted from the transmitting sideThe DFR of the relay is:
whereinIs the optimal solution of the optimization problem P.4, where the objective function and constraints of P.4 are given by equations 19-1 and 19-2, respectively: :
p.4 the specific solution process can be analogized to p.2.
In the process of constructing an optimization problem of relay discrete frequency domain response under a digital baseband, calculating linear quantization noise of sampling according to parameters of a system based on a maximum system reachable rate criterion according to the relation of system transmission links; then calculating the transmission power spectral density of each sampling point of R; calculating the power spectral density of the effective signal and the noise signal at the position D to obtain the reachable rate of each sampling point; according to the transmission power P at S and RSAnd PRThe optimization problem P.1 is established.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a novel digital FF-FD relay structure, provides a discrete frequency domain response method of a relay, can enhance the usability of an FF-FD system, obtains system performance superior to full-duplex amplified forwarding (AF-FD), simultaneously reduces the complexity of system design and processing, achieves the maximum reachable rate of the system, and simultaneously ensures the technical effect of low computational complexity. Compared with the prior art, the invention has the following advantages:
the digital full-duplex filtering and forwarding relay structure is innovatively provided, the self-interference information can be effectively utilized, the complex interference elimination technology is avoided, and the capacity performance superior to that of a full-duplex amplification and forwarding system is obtained.
And (II) based on the maximum system reachable rate criterion, the DFR of the relay is optimized under the condition that the originating terminal has CSI or not, and a suboptimal scheme for effectively reducing the computational complexity is further provided.
Drawings
Fig. 1 is a flow chart of a filter frequency domain response method for a full-duplex filtering forwarding system according to the present invention.
FIG. 2 is a simplified model of a prior art full-duplex filtering and forwarding system;
wherein h isSR(t)、hRR(t) and hRD(t) channel impulse responses from S to R, R to R, and R to D, respectively, βE(t) is the impulse response equivalent to relay R.
FIG. 3 is a structure of a digital full duplex relay provided by the present invention;
the digital-to-analog converter is mainly formed by sequentially cascading a down converter, a voltage variable attenuator, an analog-to-digital converter, a digital domain baseband filter, a digital-to-analog converter, a voltage variable amplifier, an up converter and an amplifying module.
Fig. 4 is a comparison of the achievable rates of the digital Full-Duplex Filter-and-Forward (FF-FD) system and the conventional Full-Duplex Amplify-and-Forward (AF-FD) system when different bit Analog-to-digital converters (ADCs) are used.
Fig. 5 is a comparison of the achievable rates of the digital FF-FD system of the present invention and the conventional AF-FD system at different sampling multiples.
Fig. 6 is a comparison of the achievable rates of the digital FF-FD system of the present invention and the conventional AF-FD system under different self-interference channel strengths.
Fig. 7 is a system achievable rate comparison between the relay discrete frequency domain optimization method proposed by the present invention and the low-complexity relay discrete frequency domain design method based on the digital FF-FD system.
Detailed Description
The invention will be further described by way of examples, without in any way limiting the scope of the invention, with reference to the accompanying drawings.
The invention provides a relay structure of a digital full-duplex filter forwarding system (FF-FD), and provides a Discrete Frequency Response (DFR) design method of a relay, which can enhance the usability of the FF-FD system and realize the effective utilization of self-interference information, thereby obtaining the system performance superior to the traditional full-duplex amplified forwarding system (AF-FD), simultaneously reducing the complexity of system design processing, maximizing the reachable rate of the system and simultaneously ensuring the technical effect of lower computational complexity. In the invention, under the condition that Channel State Information (CSI) is known at a relay, aiming at the condition that whether a sending end has CSI or not, DFR design of a filter is converted into an optimization problem of (joint) power distribution, and Karush-Kuhn-Tucker (KKT) conditions are utilized to effectively solve the problem. According to the form of the obtained optimal relay DFR, a simplified filter DFR design scheme is further provided, and the calculation complexity can be obviously reduced under the condition that the system capacity loss is small. Fig. 1 is a flowchart of a filter frequency domain response method for a full-duplex filtering and forwarding system according to the present invention.
Fig. 2 is a simplified full-duplex filtering forwarding system model: and S transmits information to a relay R, the R performs linear filtering processing on the received mixed signal and forwards the mixed signal to D through a transmitting antenna, and the S to D have no effective transmission link due to the influence of shadow or shielding. Maximum transmission power at S and R is PSAnd PRPower spectral density of white gaussian noise of n0The communication frequency bandwidth is W. h isSR、hRRAnd hRDFor a fading channel, the channel conditions remain unchanged within one transport block.
Fig. 3 is a structure of a digital full duplex relay provided by the present invention. To enhance the flexibility of the system and reduce the complexity of the practical application, in fig. 3, we present a relay structure suitable for digital baseband processing: we call digital FF-FD relay. The FF-FD relay is equivalent to a linear digital filter, and the core module of the structure is a Voltage Variable Attenuator (VVA) cascaded at the front end, a baseband filter in the digital domain, and a Voltage Variable Amplifier (VGA) cascaded at the back end. The front-end cascaded VVA is to attenuate the received signal that contains strong self-interference so that the sampled signal can fall within the dynamic threshold of the ADC sampling. And according to the attenuation multiple of VVA, the VGA cascaded at the rear end amplifies the signal by the same multiple. The VVA/VGA cascade modules at the front end and the rear end can ensure that the equivalent frequency domain response of the relay is the same as that of the digital baseband filter on one hand, and can flexibly regulate and control the signal intensity and eliminate the influence of nonlinear quantization noise on the other hand.
Considering that an Orthogonal frequency-division multiplexing (OFDM) technology is applied to our research scenario, the number of subcarriers of a system is kE[i]To maximize the achievable rate of the system. If an ADC with N-bit is selected, the up-sampling multiple is M, and the relay sending power is PRWhen the communication band is W, the power spectral density of the linear quantization noise is represented by formula 1:
nq(dB/Hz)＝10log10PR-10log10W-(6.02N+1.76+10log10m) (formula 1)
Aiming at a sampling point i, the channel frequency domain responses from the S to the R receiving end, from the R sending end to the R receiving end and from the R sending end to the D are respectively set to be HSR[i]、HRR[i]And HRD[i]If the processing delay time at the relay is one symbol period, the power spectral density P of the useful signal at D can be obtained under the digital basebandFF,S[i]Power spectral density P of sum noise signalFF,N[i]Respectively expressed as formula 2 and formula 3:
order toBased on the criterion of maximizing the system reachable rate, the following optimization problem P.1 is established:
where Si is the power spectral density of sample point i at S.
For this objective optimization problem, the following is an optimization method of the discrete frequency domain response DFR of the relay under different situations.
The optimization design method under the condition that the S end has no Channel State Information (CSI) under the frequency selective channel comprises the following steps:
if the S-terminal has no CSI, the power of the transmitting terminal is uniformly distributed on the frequency band, namelyIf the maximum power spectral density of the sampling point i transmitted at R is PR[i]Then the objective function and the constraint for the capacity optimization problem for that sample point are represented by equations 5-1 and 5-2, respectively:
since the objective function of the optimization problem is with respect to Ψ [ i ]]When the monotonically increasing function ofWhen the target function is at the maximum, it is denoted as I (P)R[i]) And further expanding to all sampling points, the original relay DFR design problem is converted into the following power distribution problem, and the objective function and the limiting condition of the power distribution problem are respectively represented by an equation 6-1 and an equation 6-2:
the objective function can be proven to be a strict concave function. The following lagrange function was established:
p.2 optimalThe following KKT condition can be used to effectively solve:
the DFR of the globally optimal relay is therefore:
● optimization design of CSI at the S terminal under the frequency selective channel:
if the S end has CSI, the limitation of the transmitting power spectral density of the sampling point i in S and R is respectively PS[i]And PR[i]Then for this point, the capacity optimization problem for this sampling point is:
using monotonic increments of the objective function with respect to S [ i ] and Ψ [ i ], the optimal system velocity can be accurately approximated as:
further extending to all sampling points, the corresponding relay DFR optimization problem turns into the joint power distribution problem P.3 as follows:
the objective function can be proven to be a strict concave function. The following lagrange function was established:
p.3 corresponding bestAndthe solution can be effectively solved by the KKT condition as follows:
the DFR of the optimal relay is therefore:
● relay DFR design scheme with low complexity under frequency selective channel:
observation ofThe self-interference channel strength is far greater than the transmission link strength, so that the self-interference channel strength can be obtained
I.e. the approximation of the coefficients of the optimal relay DFR and PR[i]Is irrelevant. To satisfy the power constraint, P can be simply setR[i]Is arranged asThus only requiring the originating Si]Consideration may be given.
1. The originating has no CSI, at this timeThe DFR of the relay is:
2. CSI is transmitted from the transmitting sideThe DFR of the relay is therefore:
whereinIs the optimal solution to the optimization problem P.4 as follows:
the specific solving process can be similar to p.2, and therefore, it is not described in detail.
● Relay DFR design under frequency non-selective channel:
under the frequency non-selective channel, if the originating terminal has CSI, the Jensen inequality is used to obtain:
the optimal relay DFR is therefore:
further, the equation can be verified to be also applicable to the optimal case under the condition of no CSI at the originating end, so that the equation is a design scheme of frequency non-selective channel relay DFR.
Fig. 4 and 5 show the comparison of system capacity of FF-FD and AF-FD at different bit ADCs and different sampling rates, respectively. It can be seen from the figure that as the number of bits of the ADC increases and the sampling rate increases, the capacity of both systems is improved, but the performance of FF-FD is significantly better than that of AF-FD, and especially when a high-bit ADC is used, the system quantization noise of FF-FD is small, so that the relay DFR designed by the optimization scheme can obtain the system performance close to the ideal analog FF-FD, but the hardware complexity and the computational complexity of the system are both significantly reduced.
Fig. 6 shows the system achievable rates of FF-FD and AF-FD under different self-interference channel strengths. As can be seen, the achievable rate of the FF-FD system is independent of the strength of the self-interference signal, while the achievable rate of the AF-FD system decreases significantly as the strength of the self-interference channel increases. The system performance similar to that of FF-FD can be obtained only when the interference cancellation strength of AF-FD is large, but the complexity of the interference cancellation scheme is also increased significantly.
Fig. 7 shows the comparison of the capacity of the optimized scheme and the simplified scheme FF-FD system under the conditions of CSI-S and CSI-no-S. As can be seen from the figure, the simplified scheme can achieve results close to the optimal scheme. Therefore, when the small system capacity loss can be accepted, the DFR of the relay can be designed by adopting a low-complexity scheme.
It is noted that the disclosed embodiments are intended to aid in further understanding of the invention, but those skilled in the art will appreciate that: various substitutions and modifications are possible without departing from the spirit and scope of the invention and appended claims. Therefore, the invention should not be limited to the embodiments disclosed, but the scope of the invention is defined by the appended claims.
Claims (8)
1. A digital full duplex filtering and forwarding relay structure, comprising: the device comprises a down converter, a voltage variable attenuator cascaded at the front end, a baseband digital filter, a voltage variable amplifier cascaded at the rear end, an up converter and an amplification module; the filter is formed by sequentially cascading the components and is used for a full-duplex filtering forwarding system; the voltage variable attenuator cascaded at the front end is used for attenuating a received signal containing strong self-interference, so that a sampling signal can fall into a sampling dynamic threshold of the analog-digital converter; the voltage variable amplifier cascaded at the rear end amplifies the signal by the same time according to the attenuation times of the voltage variable attenuator; the voltage variable attenuator cascaded at the front end and the voltage variable amplifier cascaded at the rear end enable the frequency domain response equivalent to the relay to be the same as the frequency domain response of the digital baseband filter, the signal intensity is flexibly regulated and controlled, and the influence of nonlinear quantization noise is eliminated.
2. An optimization design method for discrete frequency domain response of a digital full-duplex filtering forwarding relay is characterized in that based on a full-duplex filtering forwarding system, a relay discrete frequency domain response optimization problem under a digital baseband is established, and an optimal relay discrete frequency domain response is obtained under the condition that the limitation of transmission power is met; the digital full-duplex filtering forwarding relay is a relay structure formed by sequentially cascading a down converter, a voltage variable attenuator cascaded at the front end, a baseband digital filter, a voltage variable amplifier cascaded at the rear end, an up converter and an amplification module.
3. The method according to claim 2, wherein when the channel is a frequency non-selective channel, directly obtaining an optimal relay discrete frequency domain response coefficient; when the channel is a frequency selective channel, converting the relay discrete frequency domain response optimization problem into a convex optimization problem of power distribution according to the existence of channel state information at the transmitting end, and effectively solving the coefficient of optimal discrete frequency domain response; based on the analysis of the optimal result, a suboptimal relay discrete frequency domain response design method is further obtained, and the calculation complexity can be obviously reduced.
4. The optimal design method of discrete frequency domain response according to claim 2, wherein an optimization problem of the relay discrete frequency domain response under the digital baseband is constructed based on a full duplex filtering and forwarding system, and specifically, according to the relation of system transmission links, based on a criterion of maximizing the system reachable rate, the linear quantization noise of the sampling is first calculated according to the parameters of the system; then calculating the transmission power spectral density of each sampling point at the relay R; calculating the power spectral density of the effective signal and the noise signal at the destination end D to obtainThe achievable rate of each sampling point; according to the maximum transmission power P at the source S and the relay RSAnd PREstablishing an optimization problem P.1 under the limiting condition of the system; the method comprises the following steps:
1) linear quantization noise n is calculated by formula 1qPower spectral density of (a):
nq(dB/Hz)＝10log10PR-10log10W-(6.02N+1.76+10log10m) (formula 1)
2) Aiming at a sampling point i, the frequency domain responses of channels from an S transmitting end to an R receiving end, from an R transmitting end to the R receiving end and from the R transmitting end to a D are respectively made to be HSR[i]、HRR[i]And HRD[i]And the transmit power spectral density at S is Si]Power spectral density of Gaussian thermal noise of n0The processing delay time at the relay is one symbol period; under digital baseband, the power spectral density P of the useful signal at D is obtained by the equations 2 and 3FF,S[i]Power spectral density P of sum noise signalFF,N[i]：
3) When the channel has no frequency selectivity, the optimal design of the relay discrete frequency domain response is as follows:
4) when the channel has frequency selectivity, orderBased on the criterion of maximizing the achievable rate of the system, the following optimization problem P.1 is established, wherein the objective function and the limiting condition of P.1 are respectively expressed as formula 4-1 and formula 4-2:
P.1.
s.t.
where Si is the power spectral density of sample point i at S.
5. The optimal design method of discrete frequency domain response according to claim 4, wherein the optimal design of discrete frequency domain response under the channel selective channel, specifically according to whether the originating has channel state information, converts the optimization problem into a convex optimization problem of power distribution, and effectively solves the coefficient of optimal relay discrete frequency domain response; the method comprises the following steps:
11) let the maximum transmit power spectral density at sample point i at R and S be denoted P respectivelyR[i]And PS[i]Calculating the maximum achievable rate function at a single sampling point: is marked as I (P) under the condition of no channel state informationR[i]) (ii) a Is marked as I (P) under the condition of channel state informationS[i]，PR[i])；
12) Expanding the reachable rate function of a single sampling point to all sampling points, and converting the optimization problem P.1 into a convex optimization problem of power distribution: the optimization problem without channel state information is p.2, where the objective function and the constraint of p.2 are expressed as equation 6-1 and equation 6-2, respectively:
P.2.
s.t.
the optimization problem with channel state information is P.3, where the objective function and constraint of P.3 are expressed as equation 12-1 and 12-2, respectively:
P.3.
s.t.
the objective functions represented by equations 6-1 and 12-1 are strictly concave functions;
13) establishing a Lagrange function, and solving by using a KKT condition to obtain an optimal power spectral density distribution scheme of all sampling points; and calculating the obtained discrete frequency domain response coefficient of the filter by using the obtained power spectral density.
6. The method as claimed in claim 5, wherein in step 12), the lagrangian function is established as formula 7 for the optimization design of the discrete frequency domain response under the frequency selective channel, specifically aiming at the optimization problem p.2 without channel state information:
solving for P.2 optimality using the following Karush-Kuhn-Tucker (KKT) condition
The discrete frequency domain response of the globally optimal relay is represented by equation 10:
thus, when the transmitting end has no channel state information, the optimized relay discrete frequency domain response is obtained;
aiming at the optimization problem P.3 under the channel state information, a Lagrange function is established as shown in the formula 13:
efficient solution P.3 of optimality by KKT condition as followsAnd
the discrete frequency domain response of the globally optimal relay is represented by equation 15:
therefore, the optimized relay discrete frequency domain response is obtained when the transmitting end has the channel state information.
7. The method as claimed in claim 5, wherein the sub-optimal design of discrete frequency domain response under frequency selective channel is to perform sub-optimal power spectral density distribution after approximating the form of discrete frequency domain response of the optimal filter; the method comprises the following specific steps:
if the originating end has no channel state information, the power at S and R is directly distributed evenly, that isWherein W is the communication band bandwidth;
if the originating end has channel status information, orderUsing an objective functionOptimizing the power distribution of the sampling points of the transmitting end, wherein K is the number of sub-carriers of the OFDM system, and M is an up-sampling multiple; and obtaining the response coefficient of the discrete frequency domain of the filter by using the obtained power distribution scheme.
8. The method as claimed in claim 7, wherein for the sub-optimal design of the discrete frequency domain response under the frequency selective channel, if the originating end has no channel status information, the discrete frequency domain response of the relay is represented by formula 17:
if the originating side has channel status information, the discrete frequency domain response of the relay is expressed as formula 18:
wherein,is the optimal solution of the optimization problem P.4, where the objective function and the constraints of P.4 are expressed as equations 19-1 and 19-2, respectively:
P.4.
s.t.
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