CN104010371A - Power distribution and subcarrier pairing combination method in OFDM multi-relay network - Google Patents

Abstract

The invention discloses a power distribution and subcarrier pairing combination method in an OFDM multi-relay network. According to the method, in the relay network, one subcarrier pair can be distributed to a source node and multiple relay nodes so that space diversity can be provided for a system; then under the condition that the total power of the system is limited, a subcarrier pairing and power distribution combination algorithm is provided for maximizing the system capacity from end to end. Through defining an equivalent channel gains and using the new power distribution method based on a Cauchy-Schwartz inequality, an optimization problem model is simplified into a typical two-dimensional distribution problem which is solved through a Hungary algorithm. The resource distribution combination method is superior to a traditional resource distribution method with the space diversity or without the space diversity in system capacity performance.

Description

Power division and subcarrier pairing integrated processes in the many junction networks of a kind of OFDM

Technical field

The invention discloses power division and subcarrier pairing integrated processes in the many junction networks of a kind of OFDM, belong to the technical field of radio communication.

Background technology

Multiple-input and multiple-output (MIMO) technology can effectively be resisted the impact that in radio communication, multipath fading brings, but owing to being subject to the condition restriction such as equipment size, cost and hardware performance, is difficult to be applied in actual wireless communication terminal.Cooperative communication technology, by utilizing the mutual cooperation between single antenna mobile terminal, is shared antenna each other, forms a virtual MIMO system, thereby obtains space diversity.Following wireless communication system need to provide multimedia service and the data service of more two-forties, and the object of collaboration communication is exactly to make full use of node resource in network to help that the node of communication requirement carries out at a high speed, radio communication reliably.

Cooperative communication technology developed mainly contains the factor of two aspects: the gain that in network, the existence of idling-resource and collaboration communication can provide.

1. the existence of idling-resource in network

The mobile communication system of take illustrates existing of vacant resource in wireless network as example.In section, may only have part mobile terminal to have communication requirement in mobile communication system sometime, thus in network more mobile terminal in idle condition.But traditional mobile communication system is regarded all mobile terminals as the individuality of not communicating by letter mutually, thereby this part idle hardware resource is wasted; On the other hand, the mobile terminal in mobile communication system often has otherness, as has different computing abilities and different communication capacities etc.Can be mutually or the part integral body of intercommunication mutually if regard these mobile terminals as one, the existence of otherness can make different mobile terminals in network, bear different roles, thereby is conducive to the raising of whole communication system performance.Therefore the mobile terminal that, how to utilize idling-resource to help communication requirement carries out efficient communication and just becomes a problem that is worth further investigation.

2. collaboration communication gain

In radio communication, owing to being subject to the restriction of bandwidth, through-put power, add the multipath fading of wireless channel, be difficult to the transmission rate and the communication quality that reach desirable.In order to solve the bottleneck problem of wireless channel capacity, people have provided MIMO technology.This technology is by placing many antennas at transmitting terminal and receiving terminal, form a plurality of independently send out/collections of letters road, thereby reach the object of utilizing space diversity to improve wireless channel transmittability, but owing to being subject to the condition restriction such as equipment size, cost and hardware performance, wireless terminal not necessarily supports many antennas to install.And cooperative communication technology can utilize the broadcast characteristic of wireless channel, allow single antenna terminal equipment by certain rule, to share other users' antenna in multi-user environment, form virtual antenna array, make same information to arrive receiving terminal by different independent wireless channels.Research shows, collaboration communication can provide whole space diversity gain effects, and the space diversity gain that n node that participates in collaboration communication provides is equal to information source node and has n the space diversity gain that independently transmitting antenna provides.

The many junction networks of 3.OFDM

In OFDM relay system, a subcarrier pair is only assigned to a relaying conventionally, and source node conventionally keeps silent status in via node forwarding information.Along with improving constantly of terminal processing capacity, a subcarrier pair is distributed to a plurality of relayings becomes possibility.Source node and relaying together transmitted signal and a plurality of relaying can forward same subcarrier pair simultaneously and can bring space diversity for system, and greatly improve power system capacity, thereby need a kind of new OFDM junction network resource allocation methods to realize above-mentioned improvement.

Summary of the invention

Technical problem: the computation complexity that the present invention is directed to traditional many junction networks of OFDM resource allocation methods is high, the inadequate deficiency of the utilization of resources, provides power division and subcarrier pairing integrated processes in a kind of superior performance, many junction networks of OFDM that complexity is low.

Technical scheme: power division and subcarrier pairing integrated processes in the many junction networks of a kind of OFDM of the present invention, comprise the steps:

1) obtain instantaneous channel information: destination node obtains the instantaneous channel information of each channel by training sequence, comprising source node S to the channel of destination node D the instantaneous channel gain on i subcarrier s is to via node R _kthe instantaneous channel gain of channel on i subcarrier and via node R _kinstantaneous channel gain to the channel of destination node D on j subcarrier each via node obtains the instantaneous channel gain of forward and backward channel separately by training sequence and destination node is obtained the power N of additive white Gaussian noise in system ₀, and initialization dual variable μ;

2) calculate the equivalent channel gain of subcarrier pair SP (i, j) ${\mathrm{\γ}}_{(i,j)}=\frac{1}{N_0}[{\mathrm{\τ}}_{(i,j)}^{*}{\left|h_i^{s,d}\right|}^2+(1-{\mathrm{\τ}}_{(i,j)}^{*}){\left|h_j^{s,d}\right|}^2+{\mathrm{\τ}}_{(i,j)}^{*}(1-{\mathrm{\τ}}_{(i,j)}^{*})\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\frac{{\left|h_{(i,k)}^{s,r}\right|}^2{\left|h_{(j,k)}^{r,d}\right|}^2}{{\mathrm{\τ}}_{(i,j)}^{*}{\left|h_{(i,k)}^{s,r}\right|}^2+(1-{\mathrm{\τ}}_{(i,j)}^{*}){\left|h_{(j,k)}^{r,d}\right|}^2}],$ Wherein SP (i, j) is illustrated in the information that a time slot sends by i subcarrier and forwards on j subcarrier at second time slot, and K is via node number available in system, to make equivalent channel gain γ _{(i, j)}obtain peaked optimal solution, its value can be passed through above-mentioned γ _{(i, j)}expression formula interval (0,1] above use dichotomy to solve to obtain;

3) calculate subcarrier pairing decision factor x wherein ⁺=max (0, x), definition matrix L={ L _i,j, by Hungary Algorithm, obtain decision matrix t={t _{(i, j)}that each row of from L every a line are taken out is an element and maximum, t wherein _{(i, j)}=1 represents that i subcarrier and j subcarrier pair match, t _{(i, j)}=0 represents that i subcarrier j the subcarrier pair of getting along well matches;

4) upgrade μ, wherein μ calculates to arrive by dichotomy and makes gross power confined condition with equal sign, set up, wherein P is the maximum exportable power of system;

5) repeating step 3) and step 4) until the absolute value of the difference of the μ value of adjacent twice is less than ε or iterations is greater than 50 times, wherein ε is constant, optimizing decision matrix t is also determined simultaneously, i.e. subcarrier pairing process completes;

6) with dichotomy, upgrade μ so that gross power confined condition with equal sign, set up, calculate p wherein _{(i, j)}for the gross power of subcarrier pair SP (i, j) two time slots consumption, according to formula $P_i^{s1}={\mathrm{\τ}}_{(i,j)}{P}_{(i,j)},{\mathrm{\τ}}_{(i,j)}\∈\left(\mathrm{0,1}\right]$ And formula $P_{(i,j)}^{p2}=(1-{\mathrm{\τ}}_{(i,j)})P_{(i,j)}$ Calculate respectively and wherein be illustrated in the power of distributing to source node S on first time slot subcarrier pair SP (i, j), represent that second time slot allocation is to the gross power of subcarrier pair SP (i, j);

7) according to formula $l_{(i,j)}=\sqrt{\frac{1}{P_{(i,j)}^{p2}(\frac{{\left|h_j^{s,d}\right|}^2}{P_i^{s1}}+\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\frac{{\left|h_{(i,k)}^{s,r}{h}_{(j,k)}^{r,d}\right|}^2{\mathrm{\θ}}_{(i,j)}^k}{(1+{\mathrm{\θ}}_{(i,j)}^k{\left|h_{(j,k)}^{r,d}\right|}^2{P}_{(i,j)}^{p2}{)}^2})}},$ Formula $P_{(i,j,k)}^r=\frac{l_{(i,j)}^2{\left({\mathrm{\β}}_{(i,j)}^k\right)}^2}{1/P_{(i,j)}^{p2}+{\mathrm{\θ}}_{(i,j)}^k{\left|h_{(j,k)}^{r,d}\right|}^2}$ And formula $P_j^{s2}=l_{(i,j)}^2{\left({\mathrm{\β}}_{(i,j)}^{K+1}\right)}^2{P}_{(i,j)}^{p2}$ To meeting t _{(i, j)}all subcarrier pair SP (i, j) of=1 calculate l _{(i, j)}, and to obtain power allocation information, wherein be illustrated in second time slot and on subcarrier pair SP (i, j), distribute to the power of source node S, be illustrated in and on subcarrier pair SP (i, j), distribute to via node R _kpower, and ${\mathrm{\β}}_{(i,j)}^k=\left\{\begin{array}{c}\frac{\left|h_{(i,k)}^{s,r}{h}_{(j,k)}^{r,d}\right|\sqrt{{\mathrm{\θ}}_{(i,j)}^k}}{\sqrt{1/P_{(i,j)}^{p2}+{\mathrm{\θ}}_{(i,j)}^k{\left|h_{(j,k)}^{r,d}\right|}^2}},k\≤K\\ \sqrt{P_{(i,j)}^{p2}/P_i^{s1}}\left|h_j^{s,d}\right|,k=K+1\end{array}\right.,$ ${\mathrm{\θ}}_{(i,j)}^k=\left\{\begin{array}{c}1/(P_i^{s1}{\left|h_{(i,k)}^{s,r}\right|}^2+N_0),k\≤K\\ 0,k=K+1\end{array}\right.;$

8) destination node by subcarrier unpaired message and power allocation information by broadcast channel broadcasts to source node and each via node.

Beneficial effect: the present invention compared with prior art, has the following advantages:

1. power division aspect, the invention provides a kind of brand-new, power distribution method based on Cauchy's Schwarz inequality, and the method does not need to carry out iteration while carrying out power division on subcarrier pair, can obtain better power system capacity performance.

2. different with the many junction networks of traditional OFDM, at second time slot, we allow source node by another one carrier wave, to resend the information that it sends at first time slot at second time slot, can further improve like this volumetric properties of system.

3. in order to simplify system model to obtain the low federated resource distribution method of complexity, based on power distribution method provided by the invention, we are equivalent to an equivalent channel by a plurality of trunk channels on a subcarrier pair, and calculator equivalent channel gain.By definition equivalent channel gain, we are converted into complicated mixed integer nonlinear programming problem can pass through the typical two-dimentional assignment problem of Hungarian Method.

Accompanying drawing explanation

Fig. 1 is many junction networks of OFDM structural representation of the inventive method.

Fig. 2 is the overall flow logic diagram of the inventive method.

Embodiment

Below in conjunction with embodiment and Figure of description, the present invention is further illustrated:

One, many relay network systems of OFDM model

In the present invention, we consider so many junction networks of double bounce OFDM, and such junction network is by a source node S, a destination node D and the via node set { R being comprised of K relaying ₁, R ₂..., R _k. the transmission bandwidth that source node S is distributed in our supposition is divided into N subcarrier, and each channel takies identical bandwidth and experiences separate frequency selectivity Rayleigh fading.We suppose that each via node knows the instantaneous channel information of own forward and backward, and all channel prompting messages are all known in source node S and destination node D place.Communication pattern adopts semiduplex mode, and whole communication process is divided into two time slots.At first time slot, source node S is by information broadcasting destination node and all via nodes oneself wanting to send.At second time slot, the signal that all relayings are received first time slot amplifies and is transmitted to destination node.Different with the many junction networks of traditional OFDM, at second time slot, we allow source node by another one carrier wave, to resend the information that it sends at first time slot at second time slot, can further improve like this volumetric properties of system.If the information sending by i subcarrier at a time slot S forwards on j subcarrier at second time slot, we are denoted by SP (i, j).We can obtain being respectively in the upper signal to noise ratio obtaining of SP (i, j) at first time slot and second time slot so

${\mathrm{SNR}}_i^{p1}=\frac{{\left|h_i^{s,d}\right|}^2{P}_i^{s1}}{{\mathrm{\σ}}_{d\left(i\right)}^2},---\left(1\right)$

${\mathrm{SNR}}_{(i,j)}^{p2}=\frac{{(\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\frac{\left|h_{(i,k)}^{s,r}{h}_{(j,k)}^{r,d}\right|\sqrt{P_i^{s1}{P}_{(i,j,k)}^r}}{\sqrt{P_i^{s1}{\left|h_{(i,k)}^{s,r}\right|}^2+{\mathrm{\σ}}_{k\left(i\right)}^2}}+|h_j^{s,d}\left|\sqrt{P_j^{s2}}\right)}^2}{{\mathrm{\σ}}_{d\left(j\right)}^2+\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{\left(\frac{\left|h_{(j,k)}^{r,d}\right|\sqrt{P_{(i,j,k)}^r}}{\sqrt{P_i^{s1}{\left|h_{(i,k)}^{s,r}\right|}^2+{\mathrm{\σ}}_{k\left(i\right)}^2}}\right)}^2{\mathrm{\σ}}_{k\left(i\right)}^2},---\left(2\right)$

Wherein with be illustrated respectively in first time slot and second time slot distributed to the power of source node S on subcarrier pair SP (i, j). be illustrated in and on subcarrier pair SP (i, j), distribute to via node R _kpower. with be respectively S to the channel of D and S to R _kthe instantaneous channel information of channel on i subcarrier. for via node R _kinstantaneous channel information to the channel of destination node D on j subcarrier pair. with represent respectively via node R _kbe in the variance of i the zero-mean additive white Gaussian noise on subcarrier with destination node D.For formula of reduction (1) and formula (2) are to for further analysis, suppose at destination node D place, we adopt high specific merging mode to merge the signal of two time slots.So the capacity that we can obtain on subcarrier pair SP (i, j) is

$R_{(i,j)}=\frac{1}{2}\log (1+{\mathrm{SNR}}_{(i,j)})=\frac{1}{2}\log (1+{\mathrm{SNR}}_i^{p1}+{\mathrm{SNR}}_{(i,j)}^{p2}).---\left(3\right)$

We define the decision matrix t={t of a N * N dimension _{(i, j)}, t wherein _{(i, j)}=1 represents that i subcarrier and j subcarrier pair match, t _{(i, j)}=0 represents that i subcarrier j the subcarrier pair of getting along well matches.Due to each subcarrier can with and only can with the pairing of subcarrier, decision matrix t necessarily meets so

$t_{(i,j)}\∈\left\{\mathrm{0,1}\right\},\∀i,j,---\left(4\right)$

$\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{t}_{(i,j)}=1,\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{t}_{(i,j)}=1,\∀i,j.---\left(5\right)$

The gross power confined condition of system under peak power output P-condition can be expressed as so

$\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{P}_i^{s1}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{P}_j^{s2}+\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{t}_{(i,j)}{P}_{(i,j,k)}^r\≤P.---\left(6\right)$

So, the optimization problem model with the total end-to-end capacity of maximization system can be expressed as

$\underset{\left\{P_i^{s1}\right\},\left\{P_j^{s2}\right\},\left\{P_{(i,j,k)}^r\right\},\left\{t_{(i,j)}\right\}}{\max }\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{t}_{(i,j)}{R}_{(i,j)}---\left(7\right)$

s.t. (4),(5)and(6).

This optimization problem is a typical MIXED INTEGER Nonlinear Optimization Problem, and this problem is because the essence of its mixing has sizable algorithm complex conventionally.Next we will provide a kind of associating optimal case to come layering to solve the optimization problem proposing in formula (7)

Two, the power distribution method on subcarrier pair SP (i, j)

First, we are designated as subcarrier pair SP (i, j) respectively at second time slot with at the power of two time slot consumption and P _{(i, j)}.We can access

$P_{(i,j)}^{p2}=P_j^{s2}+\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{P}_{(i,j,k)}^r,P_j^{s2}\≥0,P_{(i,j,k)}^r\≥0---\left(8\right)$

$P_{(i,j)}=P_i^{s1}+P_{(i,j)}^{p2}---\left(9\right)$

Wherein can regard total energy that subcarrier pair SP (i, j) consumes at first time slot as.Here, suppose given with value, we propose with individual to maximize R _{(i, j)}power allocation scheme distribute with how to distribute with will in ensuing article, make elaboration.For given with value, in order to maximize R _{(i, j)}, according to formula (1) and formula (3), be definite value, maximize R _{(i, j)}optimization problem can be reduced to

$\underset{\{P_{(i,j,k)}^r,P_j^{s2}\}}{\max }{\mathrm{SNR}}_{(i,j)}^{p2}s.t.\left(8\right)---\left(10\right)$

In order to solve the optimization problem in formula (10), according to formula (8), first we are by formula (2) and formula (10) expression formula again equivalence be rewritten as

${\mathrm{SNR}}_{(i,j)}^{p2}=\frac{P_i^{s1}}{N_0}\·\frac{{(\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\frac{\left|h_{(i,k)}^{s,r}{h}_{(j,k)}^{r,d}\right|\sqrt{P_{(i,j,k)}^r}}{\sqrt{P_i^{s1}{\left|h_{(i,k)}^{s,r}\right|}^2+N_0}}+|h_j^{s,d}\left|\sqrt{\frac{P_j^{s2}}{P_i^{s1}}}\right)}^2}{\frac{P_j^{s2}+\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{P}_{(i,j,k)}^r}{P_{(i,j)}^{p2}}+\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\frac{{\left|h_{(j,k)}^{r,d}\right|}^2{P}_{(i,j,k)}^r}{P_i^{s1}{\left|h_{(i,k)}^{s,r}\right|}^2+N_0}}---\left(11\right)$

Then, we define following variable

${\mathrm{\θ}}_{(i,j)}^k=\left\{\begin{array}{c}1/(P_i^{s1}{\left|h_{(i,k)}^{s,r}\right|}^2+N_0),k=\mathrm{1,2},\·\·\·\·\·\·K\\ 0,k=K+1\end{array}\right.---\left(12\right)$

${\mathrm{\α}}_{(i,j)}^k=\left\{\begin{array}{c}\sqrt{1/P_{(i,j)}^{p2}+{\mathrm{\θ}}_{(i,j)}^k{\left|h_{(j,k)}^{r,d}\right|}^2}\sqrt{P_{(i,j,k)}^r},k=\mathrm{1,2},\·\·\·\·\·\·K\\ \sqrt{P_j^{s2}/P_{(i,j)}^{p2}},k=K+1\end{array}\right.---\left(13\right)$

${\mathrm{\β}}_{(i,j)}^k=\left\{\begin{array}{c}\frac{\left|h_{(i,k)}^{s,r}{h}_{(j,k)}^{r,d}\right|\sqrt{{\mathrm{\θ}}_{(i,j)}^k}}{\sqrt{1/P_{(i,j)}^{p2}+{\mathrm{\θ}}_{(i,j)}^k{\left|h_{(j,k)}^{r,d}\right|}^2}}k=\mathrm{1,2},\·\·\·\·\·\·K\\ \sqrt{P_{(i,j)}^{p2}/P_i^{s1}}\left|h_j^{s,d}\right|,k=K+1\end{array}\right.---\left(14\right)$

Subscript k=K+1 represents that this variable is associated with second time slot source node S.Following two vectors of application according to formula (11), the volume optimization problem proposing in formula (10) can be converted to by equivalence

$\underset{\left\{P_{(i,j,k)}^r{P}_j^{s2}\right\}}{\max }{\mathrm{SNR}}_{(i,j)}^{p2}=\frac{P_i^{s1}}{N_0}\frac{{({\mathrm{\β}}_{(i,j)},{\mathrm{\α}}_{(i,j)})}^2}{({\mathrm{\α}}_{(i,j)},{\mathrm{\α}}_{(i,j)})}s.t.\left(8\right),---\left(15\right)$

Wherein (x, y) represents the inner product of vector x and vectorial y.According to Cauchy-Schwarz inequality, we can obtain

$\frac{{({\mathrm{\β}}_{(i,j)},{\mathrm{\α}}_{(i,j)})}^2}{({\mathrm{\α}}_{(i,j)},{\mathrm{\α}}_{(i,j)})}\≤\frac{({\mathrm{\β}}_{(i,j)},{\mathrm{\β}}_{(i,j)})({\mathrm{\α}}_{(i,j)},{\mathrm{\α}}_{(i,j)})}{({\mathrm{\α}}_{(i,j)},{\mathrm{\α}}_{(i,j)})}=({\mathrm{\β}}_{(i,j)},{\mathrm{\β}}_{(i,j)})---\left(16\right)$

Inequality (16) is got equal sign and if only if vectorial α _{(i, j)}with vectorial β _{(i, j)}linear correlation,

${\mathrm{\α}}_{(i,j)}^k=l_{(i,j)}{\mathrm{\β}}_{(i,j)}^k.---\left(17\right)$

According to formula (8), formula (13) and formula (17), l _{(i, j)}can be expressed as

$l_{(i,j)}=\sqrt{\frac{1}{P_{(i,j)}^{p2}(\frac{{\left|h_j^{s,d}\right|}^2}{P_i^{s1}}+\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\frac{{\left|h_{(i,k)}^{s,r}{h}_{(j,k)}^{r,d}\right|}^2{\mathrm{\θ}}_{(i,j)}^k}{(1+{\mathrm{\θ}}_{(i,j)}^k{\left|h_{(j,k)}^{r,d}\right|}^2{P}_{(i,j)}^{p2}{)}^2})}}.---\left(18\right)$

Then, according to formula (13), second time slot distributed to source node S and via node R on subcarrier pair SP (i, j) _kpower can represent literary composition respectively

$P_{(i,j,k)}^r=\frac{{\left({\mathrm{\α}}_{(i,j)}^k\right)}^2}{1/P_{(i,j)}^{p2}+{\mathrm{\θ}}_{(i,j)}^k{\left|h_{(j,k)}^{r,d}\right|}^2}=\frac{l_{(i,j)}^2{\left({\mathrm{\β}}_{(i,j)}^k\right)}^2}{1/P_{(i,j)}^{p2}+{\mathrm{\θ}}_{(i,j)}^k{\left|h_{(j,k)}^{r,d}\right|}^2}---\left(19\right)$

$P_j^{s2}={\left({\mathrm{\α}}_{(i,j)}^{K+1}\right)}^2{P}_{(i,j)}^{p2}=l_{(i,j)}^2{\left({\mathrm{\β}}_{(i,j)}^{K+1}\right)}^2{P}_{(i,j)}^{p2}---\left(20\right)$

Three, power division and subcarrier pairing unified algorithm

Under gross power confined condition to maximize the unified algorithm of the power division of total end-to-end system capacity and subcarrier pairing.First illustrate for a given P _{(i, j)}in situation, how to distribute with

Formula (19) and formula (20) are brought in formula (11) expression formula in, can obtain

$\begin{array}{c}{\mathrm{SNR}}_{(i,j)}={\mathrm{SNR}}_i^{p1}+{\mathrm{SNR}}_{(i,j)}^{p2}\\ ={\left|h_i^{s,d}\right|}^2{P}_i^{s1}/N_0+{\left|h_i^{s,d}\right|}^2{P}_{(i,j)}^{p2}/N_0+\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\frac{P_i^{s1}{\left|h_{(i,k)}^{s,r}\right|}^2/N_0\·P_{(i,j)}^{p2}{\left|h_{(j,k)}^{r,d}\right|}^2/N_0}{P_i^{s1}{\left|h_{(i,k)}^{s,r}\right|}^2/N_0+P_{(i,j)}^{p2}{\left|h_{(j,k)}^{r,d}\right|}^2/N_0+1}---\left(21\right)\end{array}$

Under large state of signal-to-noise, we ignore SNR in formula (21) _{(i, j)}constant 1 in expression formula denominator.We define

$P_i^{s1}={\mathrm{\τ}}_{(i,j)}{P}_{(i,j)},{\mathrm{\τ}}_{(i,j)}\∈\left(0.1\right],---\left(22\right)$

τ wherein _{(i, j)}represent account for P _{(i, j)}ratio.τ _{(i, j)}=1 represents source node S not by relaying but by direct path with power P _{(i, j)}communicate on subcarrier pair SP (i, j) with destination node, this situation is normally enough good because of source node S and the channel of destination node D on i subcarrier, to such an extent as to does not need the help of via node.According to formula (9), can access

$P_{(i,j)}^{p2}=(1-{\mathrm{\τ}}_{(i,j)})P_{(i,j)}---\left(23\right)$

Then, formula (21) can approximate representation be

SNR _(i,j)≈γ _(i,j)P _(i,j) (24)

γ wherein _{(i, j)}can regard the equivalent channel gain on subcarrier pair SP (i, j) as, it has played and has simplified the effect of expression formula, and can be represented as

${\mathrm{\γ}}_{(i,j)}=\frac{1}{N_0}[{\mathrm{\τ}}_{(i,j)}{\left|h_i^{s,d}\right|}^2+(1-{\text{\τ}}_{(i,j)}){\left|h_j^{s,d}\right|}^2+{\mathrm{\τ}}_{(i,j)}(1-{\mathrm{\τ}}_{(i,j)})\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\frac{{\left|h_{(i,k)}^{s,r}\right|}^2{\left|h_{(j,k)}^{r,d}\right|}^2}{{\mathrm{\τ}}_{(i,j)}{\left|h_{(i,k)}^{s,r}\right|}^2+(1-{\mathrm{\τ}}_{(i,j)}){\left|h_{(j,k)}^{r,d}\right|}^2}]---\left(25\right)$

According to formula (25), γ _{(i, j)}about τ _{(i, j)}monotonic function, according to formula (24) and formula (25), its optimal value determined SNR _{(i, j)}and γ _{(i, j)}size.For a given P _{(i, j)}, according to formula (22) and formula (23), determined simultaneously with between best proportion, its value can be by dichotomy in interval on solve.

Then according to formula (3) and formula (24), can access

$R_{(i,j)}=\frac{1}{2}\log (1+{\mathrm{SNR}}_{(i,j)})\≈\frac{1}{2}\log (1+{\mathrm{\γ}}_{(i,j)}{P}_{(i,j)})---\left(26\right)$

Further, according to formula (8) and formula (9), the gross power confined condition in formula (6) can be rewritten as

$\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{t}_{(i,j)}{P}_{(i,j)}\≤P---\left(27\right)$

Thereby the optimization problem proposing in formula (7) can be expressed equivalently as

$\underset{\left\{P_{(i,j)}\right\},\left\{t_{(i,j)}\right\}}{\max }\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\frac{t_{(i,j)}}{2}\log (1+{\mathrm{\γ}}_{(i,j)}{P}_{(i,j)})---\left(28\right)$

s.t. (4),(5),and(27)

According to KKT condition, the power that we can obtain being assigned on SP (i, j) can be expressed as

$P_{(i,j)}={(\frac{1}{2\mathrm{\μ}}-\frac{1}{{\mathrm{\γ}}_{(i,j)}})}^{+}---\left(29\right)$

X wherein ⁺(0, x), μ is a given dual variable value to=max.Calculate subcarrier pairing decision factor definition matrix L={ L _i,j, by Hungary Algorithm, obtain decision matrix t={t _{(i, j)}.

The present invention proposes power division and subcarrier pairing unified algorithm and can be summarized as:

Step 1. is calculated optimal value with dichotomy make formula (25) obtain maximum, according to formula (25), calculate γ simultaneously _{(i, j)}, γ wherein _{(i, j}) be the channel gain of an equivalent direct channel of a plurality of trunk channels on subcarrier pair SP (i, j), according to this equivalence, to gain, we are converted into typical two-dimentional assignment problem by former optimization problem;

Step 2. is chosen the initial value of a suitable dual variable μ, loop initialization factor of n=0;

Step 3.n=n+1, and by Hungary Algorithm, take μ and obtain decision matrix t as calculation of parameter;

Step 4. is upgraded μ with t, and wherein μ calculates to arrive by dichotomy the gross power confined condition of formula (27) is set up with equal sign;

Step 5. repeating step 3 and step 4 are until the absolute value of the difference of the μ value of adjacent twice is less than ε or iterations n is greater than 50 times, and wherein ε is constant.Simulation result shows, we generally need the iteration of 4 to 6 times to obtain the dual variable μ of such convergence.Now corresponding optimum decision matrix t has also been determined;

Step 6. pair meets t _{(i, j)}all subcarrier pair SP (i, j) of=1 calculate and γ _{(i, j)}.With dichotomy, upgrade μ,

According to formula (29), P _{(i, j)}determined.According to formula (22) and formula (23), calculate respectively and

Step 7., according to Cauchy-Schwarz inequality, utilizes formula (18), formula (19) and formula (20) to meeting t _{(i, j)}all subcarrier pair SP (i, j) of=1 calculate l _{(i, j)}, and

Step 8. destination node by subcarrier unpaired message and power allocation information by broadcast channel broadcasts to source node and each via node.

Claims (1)

1. power division and a subcarrier pairing integrated processes in the many junction networks of OFDM, is characterized in that, the method comprises the following steps:

1) obtain instantaneous channel information: destination node obtains the instantaneous channel information of each channel by training sequence, comprising source node S to the channel of destination node D the instantaneous channel gain on i subcarrier s is to via node R _kthe instantaneous channel gain of channel on i subcarrier and via node R _kinstantaneous channel gain to the channel of destination node D on j subcarrier each via node obtains the instantaneous channel gain of forward and backward channel separately by training sequence and destination node is obtained the power N of additive white Gaussian noise in system ₀, and initialization dual variable μ;

2) calculate the equivalent channel gain of subcarrier pair SP (i, j) ${\mathrm{\γ}}_{(i,j)}=\frac{1}{N_0}[{\mathrm{\τ}}_{(i,j)}^{*}{\left|h_i^{s,d}\right|}^2+(1-{\mathrm{\τ}}_{(i,j)}^{*}){\left|h_j^{s,d}\right|}^2+{\mathrm{\τ}}_{(i,j)}^{*}(1-{\mathrm{\τ}}_{(i,j)}^{*})\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\frac{{\left|h_{(i,k)}^{s,r}\right|}^2{\left|h_{(j,k)}^{r,d}\right|}^2}{{\mathrm{\τ}}_{(i,j)}^{*}{\left|h_{(i,k)}^{s,r}\right|}^2+(1-{\mathrm{\τ}}_{(i,j)}^{*}){\left|h_{(j,k)}^{r,d}\right|}^2}],$ Wherein SP (i, j) is illustrated in the information that a time slot sends by i subcarrier and forwards on j subcarrier at second time slot, and K is via node number available in system, to make equivalent channel gain γ _{(i, j)}obtain peaked optimal solution, its value can be passed through above-mentioned γ _{(i, j)}expression formula interval (0,1] above use dichotomy to solve to obtain;

3) calculate subcarrier pairing decision factor x wherein ⁺=max (0, x), definition matrix L={ L _i,j, by Hungary Algorithm, obtain decision matrix t={t _{(i, j)}that each row of from L every a line are taken out is an element and maximum, t wherein _{(i, j)}=1 represents that i subcarrier and j subcarrier pair match, t _{(i, j)}=0 represents that i subcarrier j the subcarrier pair of getting along well matches;

4) upgrade μ, wherein μ calculates to arrive by dichotomy and makes gross power confined condition with equal sign, set up, wherein P is the maximum exportable power of system;

5) repeating step 3) and step 4) until the absolute value of the difference of the μ value of adjacent twice is less than ε or iterations is greater than 50 times, wherein ε is constant, optimizing decision matrix t is also determined simultaneously, i.e. subcarrier pairing process completes;

6) with dichotomy, upgrade μ so that gross power confined condition with equal sign, set up, calculate p wherein _{(i, j)}for the gross power of subcarrier pair SP (i, j) two time slots consumption, according to formula $P_i^{s1}={\mathrm{\τ}}_{(i,j)}{P}_{(i,j)},{\mathrm{\τ}}_{(i,j)}\∈\left(\mathrm{0,1}\right]$ And formula $P_{(i,j)}^{p2}=(1-{\mathrm{\τ}}_{(i,j)})P_{(i,j)}$ Calculate respectively and wherein Pis1 is illustrated in the power of distributing to source node S on first time slot subcarrier pair SP (i, j), represent that second time slot allocation is to the gross power of subcarrier pair SP (i, j);

7) according to formula $l_{(i,j)}=\sqrt{\frac{1}{P_{(i,j)}^{p2}(\frac{{\left|h_j^{s,d}\right|}^2}{P_i^{s1}}+\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\frac{{\left|h_{(i,k)}^{s,r}{h}_{(j,k)}^{r,d}\right|}^2{\mathrm{\θ}}_{(i,j)}^k}{(1+{\mathrm{\θ}}_{(i,j)}^k{\left|h_{(j,k)}^{r,d}\right|}^2{P}_{(i,j)}^{p2}{)}^2})}},$ Formula $P_{(i,j,k)}^r=\frac{l_{(i,j)}^2{\left({\mathrm{\β}}_{(i,j)}^k\right)}^2}{1/P_{(i,j)}^{p2}+{\mathrm{\θ}}_{(i,j)}^k{\left|h_{(j,k)}^{r,d}\right|}^2}$ And formula $P_j^{s2}=l_{(i,j)}^2{\left({\mathrm{\β}}_{(i,j)}^{K+1}\right)}^2{P}_{(i,j)}^{p2}$ To meeting t _{(i, j)}all subcarrier pair SP (i, j) of=1 calculate l _{(i, j)}, and to obtain power allocation information, wherein be illustrated in second time slot and on subcarrier pair SP (i, j), distribute to the power of source node S, be illustrated in and on subcarrier pair SP (i, j), distribute to via node R _kpower, and ${\mathrm{\β}}_{(i,j)}^k=\left\{\begin{array}{c}\frac{\left|h_{(i,k)}^{s,r}{h}_{(j,k)}^{r,d}\right|\sqrt{{\mathrm{\θ}}_{(i,j)}^k}}{\sqrt{1/P_{(i,j)}^{p2}+{\mathrm{\θ}}_{(i,j)}^k{\left|h_{(j,k)}^{r,d}\right|}^2}},k\≤K\\ \sqrt{P_{(i,j)}^{p2}/P_i^{s1}}\left|h_j^{s,d}\right|,k=K+1\end{array}\right.,$ ${\mathrm{\θ}}_{(i,j)}^k=\left\{\begin{array}{c}1/(P_i^{s1}{\left|h_{(i,k)}^{s,r}\right|}^2+N_0),k\≤K\\ 0,k=K+1\end{array}\right.;$

8) destination node by subcarrier unpaired message and power allocation information by broadcast channel broadcasts to source node and each via node.