CN101702703A - Vandermonde frequency-division multiplexing method based on multi-carrier modulation technology - Google Patents

Abstract

The invention discloses a vandermonde frequency-division multiplexing method based on a multi-carrier modulation technology, which is characterized by constructing a vandermonde pre-coder matrix based on a technical model of orthogonal frequency division multiplexing of cognitive wireless network; obtaining system multiplexing gain by using cyclic prefix redundancy and channel frequency selectivity of an orthogonal frequency division multiplexing symbol; eliminating interference of a cognitive user on communication of a main user to obtain an achievable transmission velocity of the cognitive user; and further obtaining full-multiplexing gain of the system by using a frequency domain water-filling power allocation method and different cyclic prefix length values based on the obtained achievable transmission velocity such that the cognitive user can obtain a maximum transmission velocity and share the frequency spectrum with the main user.

Description

Vandermonde frequency-division multiplexing method based on multi-carrier modulation technology

Technical field

The present invention relates to cognitive radio (the Cognitive Radio in the wireless communication system, CR) technology, particularly a kind of Vandermonde frequency-division multiplexing (Vandermonde Frequency Division Multiplexing based on multi-carrier modulation technology, VFDM) method belongs to the Information and Communication Engineering technical field.

Background technology

Current, the sustainable growth of various radio communication service demands causes wireless communication system that the demand of frequency spectrum resource is constantly increased, thereby makes radio spectrum resources become more and more rare.Yet spectrum measurement studies show that, authorizes the utilization rate of frequency spectrum but very low, causes authorizing the waste of frequency spectrum hole serious.Its reason is: do not match between static spectrum allocation may system and the dynamic spectrum utilization mode, cause wireless frequency spectrum planning nervous, and utilization ratio is low.In order to develop the wireless communication system of sharing frequency spectrum resource, from the utilization ratio of system-level angle raising frequency spectrum resource, (CognitiveRadio's cognitive radio CR) arises at the historic moment as an emerging technology.

Cognitive radio is also referred to as cognitive radio, it can not influence main user (Primary Users, PUs) under Tong Xin the prerequisite, utilize a large amount of idle frequency spectrums to satisfy time user (Secondary Users intelligently, SUs) be cognitive user (Cognitive Users, CUs) reliable communication, thus realize sharing frequency spectrum resource, improve the utilance of wireless frequency spectrum.Cognition wireless network can carry out optimum utilization to the frequency spectrum cavity-pocket that perceives, to improve the data throughput capabilities of cognitive user network to greatest extent according to the network architecture, Radio Resource, default etc.

Constantly idle main user, cognitive radio (CR) system allows cognitive user chance ground to insert main subscriber authorisation frequency range, and utilizes this frequency range to carry out transceive data, and cognitive user this moment (SUs) is " blind " for main user (PUs).Frequency spectrum perception is to realize the important step of cognitive radio, and it comprises that cognitive user is to available spectrum chance in the perception of main subscriber authorisation frequency range, spectrum analysis, the frequency range of perception mandate in real time etc.Usually, do not share mutual information between main user transmitter and the cognitive user transmitter.At present, the information theory model of cognitive radio channel capacity is still a pendent problem under Gauss's interference channel, many literature research the cognitive user achievable rate upper limit in the cognitive radio channel.For example, the interference channel problem that contains main user profile in the cognitive user transmitter.In these documents, the optimal transmission scheme is promptly eliminated the known disturbances to the cognitive user receiver in advance all based on " dirty paper code " strategy in main user profile transmission.Yet this optimal policy is very complicated in actual applications, is difficult to carry out practicability.

Summary of the invention

The present invention seeks to overcome the deficiencies in the prior art, propose a kind of transmission plan that more approaches the actual channel model, promptly based on Vandermonde frequency-division multiplexing (VFDM) method of multi-carrier modulation technology.Current, (Multi-carrierModulation, MCM) technology is considered to the implementation of cognitive radio system physical layer modulation technology to multi-carrier modulation.Multi-carrier modulation technology commonly used comprises: OFDM (Orthogonal Frequency Division Multiplexing, OFDM), the modulation of filtering multitone (Filtered Multi-tone, FMT) etc.Because can being one group of parallel flat fading channel with the serial channel equivalence, multi-carrier modulation declines with effective contrary frequency selectivity, the inventive method has increased Vandermonde Vandermonde precoder on the basis of cognition wireless network orthogonal frequency division multiplexi, with Cyclic Prefix (the Cyclic Prefix that makes full use of OFDM symbol, CP) redundancy forms a kind of new frequency beam-shaper, the frequency beam-shaper that uses this method to constitute can effectively be eliminated the interference of cognitive user to main user, thereby realizes cognitive user and main user's frequency spectrum share.This method at home and abroad cognitive radio research field still belongs to the first time.

For achieving the above object, the technical scheme that the present invention takes is: a kind of Vandermonde frequency-division multiplexing method based on multi-carrier modulation technology, it is characterized in that: at first based on symbol cyclic prefix redundancy in the cognition wireless network ofdm system model, structure Vandermonde pre-coding matrix, the Vandermonde pre-coding matrix that satisfies orthogonality condition constitutes the Vandermonde precoder, the Vandermonde precoder is combined with existing cognitive radio OFDM, utilize the Cyclic Prefix redundancy and the selectivity of channel frequency of OFDM symbol to obtain the system multiplexing gain, to eliminate the interference of cognitive user to main telex network, on this basis, adopt frequency domain water injection power distribution method to obtain the full spatial multiplexing gain of system, can reach transmission rate with the maximum that obtains cognitive user, realize cognitive user and main user's frequency spectrum share.Can realize according to the following steps:

(1) structure Vandermonde pre-coding matrix and Vandermonde precoder.

At first, according to 2 * 2 cognition wireless electric models (as shown in Figure 1) under the frequency selective fading channels, main user transmitter use authority frequency band and main receiver user communicate, and the cognitive user transmitter uses this frequency band to send information to corresponding cognitive user receiver simultaneously.When two transmitters are not shared mutual information, and between two transmitters not mutually during cooperation, cognitive user is unknown with respect to main user, therefore, and the prior information of the unknown main user transmitter of cognitive user transmitter; Make h ^(ij)Expression to channel coefficients the receiver j, is supposed h from transmitter i ^(ij)Element (every footpath) is obeyed the multiple Gaussian Profile N of independent same distribution circulation symmetry _c(0, σ _Ij/ (L+1)), and for any i, j, channel is independent identically distributed.

Suppose main user transmitter known channel state h ⁽¹¹⁾, the known local channel state of cognitive user transmitter h ⁽²¹⁾And h ⁽²²⁾, receiver i accurately estimates its channel status h ⁽ⁱⁱ⁾Employing has the intersymbol interference that the multi-carrier modulation technology of N subcarrier can effectively avoid the frequency selective fading channels multipath to cause, the data packet length of each OFDM transmission is the N symbol, inserting length before each OFDM packet is the symbol cyclic prefix of L, receiving terminal extracts the effective information of N symbol in the grouping from (N+L) symbol, therefore this frequency-selective channel can be modeled as the Toeplitz matrix of (N+L) input, N output, and then main user and cognitive user received signal can be expressed as respectively

y _PU＝F(T(h ⁽¹¹⁾)x _PU+T(h ⁽²¹⁾)x _SU+n ₁)

(1)

y _SU＝F(T(h ⁽²²⁾)x _SU+T(h ⁽¹²⁾)x _PU+n ₂)

Wherein, T (h ^(ij)) expression contains the dimension toeplitz matrix of the N of (L+1) footpath Gauss independent same distribution channel fading coefficient * (N+L), note is done

F () is the fast Fourier transform matrix, is expressed as

$F=\left(\begin{array}{cccc}1& 1& \&CenterDot;\&CenterDot;\&CenterDot;& 1\\ 1& e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009102346200E0000011.png,H2009102346200E0000021.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{N}}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009102346200E0000011.png,H2009102346200E0000021.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{N}(N-1)}\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ 1& e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009102346200E0000011.png,H2009102346200E0000021.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{N}(N-1)}& \&CenterDot;\&CenterDot;\&CenterDot;& e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009102346200E0000011.png,H2009102346200E0000021.png"\; state="\{\{state\}\}">j</figure-callout>}{\frac{2\mathrm{\&pi;}}{N}(N-1)}^2}\end{array}\right)---\left(3\right)$

x _PUWith x _SUBe respectively main user transmitter and cognitive user transmitter output vector, its constraints is that power output is limited, promptly

$\mathrm{tr}\left(E\right[x_{\mathrm{PU}}{x}_{\mathrm{PU}}^H\left]\right)\&le;(N+L)P_{\mathrm{PU}}$

(4)

$\mathrm{tr}\left(E\right[x_{\mathrm{SU}}{x}_{\mathrm{SU}}^H\left]\right)\&le;(N+L)P_{\mathrm{SU}}$

N in the formula (1) _k～N _c(0, I _N), k=1,2 is additive white Gaussian noise, considers that the discrete Fourier transform modulation symbol of main user transmitter transmission sequence is

x _PU＝AF ^Hs _PU (5)

Wherein, A is a pre-coding matrix, s _PUFor the N dimension sends sequence vector, therefore, x _PUInclude (N+L) individual symbol, its protection gap length L for the cognitive user transmitter, considers to send vector x greater than coherence time _SU=Vs _SU, wherein V is the linear predictive coding device, s _SUFor cognitive user sends symbolic vector, linear predictive coding device and pre-coding matrix satisfy V=AF ^H, the conjugate transpose of subscript H representing matrix.At the cognition wireless network actual conditions, consider main receiver user is not produced the cognitive user transmission policy of interference, promptly linear predictive coding device V should satisfy orthogonality condition

T(h ⁽²¹⁾)Vs _SU＝0 (6)

If precoder V is (N+L) * L dimension Vandermonde precoder, then it can effectively utilize CP redundancy L.It is as follows promptly to construct the Vandermonde precoder structure that satisfies formula (6)

$V=\left(\begin{array}{cccc}1& 1& \&CenterDot;\&CenterDot;\&CenterDot;& 1\\ a_1& {\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="H2009102346200E0000011.png,H2009102346200E0000021.png"\; state="\{\{state\}\}">a</figure-callout>}}_2& \&CenterDot;\&CenterDot;\&CenterDot;& a_{\mathrm{<figure-callout\; id="1"\; label="L\; a"\; filenames="H2009102346200E0000021.png,H2009102346200E0000022.png"\; state="\{\{state\}\}">L</figure-callout>}}& \\ a_{}^{}{}_1^2& {\mathrm{<figure-callout\; id="2"\; label="a"\; filenames="H2009102346200E0000011.png,H2009102346200E0000021.png"\; state="\{\{state\}\}">a</figure-callout>}}_2^2& \&CenterDot;\&CenterDot;\&CenterDot;& a_{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="H2009102346200E0000011.png,H2009102346200E0000021.png"\; state="\{\{state\}\}">L</figure-callout>}}^2\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ a_1^{N+L-1}& a_2^{N+L-1}& & a_L^{N+L-1}\end{array}\right)---\left(7\right)$

Wherein, { a _l, l=1,2 ..., L is a multinomial

Root.h _i ⁽²¹⁾, i=0,1 ..., L is h ⁽²¹⁾(L+1) dimension channel coefficient vector, V and h ⁽²¹⁾Between orthogonality can guarantee that main user and cognitive user transmit information without interfering with each other in same frequency band, promptly main user and cognitive user satisfy the orthogonality condition shown in the formula (6), utilize the feature of frequency-selective channel to constitute a kind of new frequency beam-shaper, Vandermonde precoder V is determined by vandermonde matrix A, because precoder V and channel h ⁽²¹⁾Orthogonality, when cognitive user sends the Cyclic Prefix sequence of being made up of L symbol, will main user not produced interference.

(2) the Vandermonde precoder is combined with existing cognitive radio OFDM, utilize the Cyclic Prefix redundancy of OFDM symbol and selectivity of channel frequency to obtain the system multiplexing gain.

With formula (5), formula (6) substitution formula (1), can obtain main user equivalence parallel channel and be

$y_{\mathrm{PU}}=H_{\mathrm{diag}}^{\left(11\right)}{s}_{\mathrm{PU}}+v_1---\left(8\right)$

Wherein,

Be diagonalization frequency domain channel matrix, its element is the independent same distribution Gaussian random variable, satisfies H _i ⁽¹¹⁾～N _c(0, σ ₁₁), i=1,2 ..., N, v ₁=Fn ₁For Gauss's additive white noise, satisfy v ₁～N _c(0, I _N), same, the cognitive user received signal can be expressed as

$y_{\mathrm{SU}}=H_2{s}_{\mathrm{SU}}+H_{\mathrm{diag}}^{\left(12\right)}{s}_{\mathrm{PU}}+v_2---\left(9\right)$

Wherein, H ₂=FT (h ⁽²²⁾) V,

Be diagonalization frequency domain channel matrix, its element is independent same distribution Gaussian random variable H _i ⁽¹²⁾～N _c(0, σ ₁₂), i=1,2 ..., N, and v ₂=Fn ₂For Gauss's additive white noise, satisfy v ₂～N _c(0, I _N).

According to formula (8) and formula (9), easily know H ₂For N * L ties up channel matrix, main user's received signal is the zero N row parallel sub-channels signal that disturbs.Its expression Vandermonde frequency-division multiplexing method can be converted into the frequency selectivity interference channel monolateral interference channel vector, and promptly main user's received signal is the zero N row parallel sub-channels signal that disturbs, and the interference of cognitive user received signal is only come from main user.Next step, input covariance (power) design with inquiring into when cognitive user produces zero interference to main user makes cognitive user reach the speed optimization.

(3) cognitive user to the noiseless condition of main user under, cognitive user can obtain maximum achievable rate in the Vandermonde frequency-division multiplexing system, realizes cognitive user and main user's frequency spectrum share.

When the cognitive user receiver carries out single user when decoding, the cognitive user receiver will come from main user's signal as interference, by formula (9), and definition

It is approximately the zero-mean Gaussian random variable, and its covariance is

Because power limited in the formula (4), under the average power, cognitive user input covariance is

$S_{\mathrm{SU}}=\frac{(N+L)P_{\mathrm{SU}}}{\mathrm{tr}\left(V^{H}V\right)}{I}_L---\left(10\right)$

Under the average power allocation strategy, the cognitive user achievable rate is

$R_{\mathrm{SU}}^{\mathrm{eq}}=\frac{1}{\mathrm{<figure-callout\; id="2"\; label="N\; log"\; filenames="H2009102346200E0000011.png,H2009102346200E0000021.png"\; state="\{\{state\}\}">N</figure-callout>}}{\log }_{}{}_2|I_L+\frac{(N+L)P_{\mathrm{SU}}}{\mathrm{tr}\left(V^{H}V\right)}{V}^{H}V|---\left(11\right)$

Wherein, L is the parallel sub-channels number in the Vandermonde frequency-division multiplexing.

When vandermonde matrix V line number (N+L) increases, the V degree of freedom will influence the root range value of multinomial S (z) | a _l|, l=1,2 ..., L, when Vandermonde pre-coding matrix V ranks parameter L, N → ∞ and

When (0＜c≤1), the range value of S (z) root | a _l|, l=1,2 ..., L is positioned at unit circle, the degree of freedom of definition V

$d_V^{\mathrm{eq}}=\underset{P_{\mathrm{SU}}\&RightArrow;\&infin;}{\lim }\frac{{\mathrm{NR}}_{\mathrm{SU}}^{\mathrm{eq}}}{{\log }_{2}P}=\underset{P_{\mathrm{SU}}\&RightArrow;\&infin;}{\lim }\frac{{\mathrm{<figure-callout\; id="2"\; label="log"\; filenames="H2009102346200E0000011.png,H2009102346200E0000021.png"\; state="\{\{state\}\}">log</figure-callout>}}_2|I_L+\frac{(N+L)P_{\mathrm{SU}}}{\mathrm{tr}\left(V^{H}V\right)}{V}^{H}V|}{{\log }_{2}P}---\left(12\right)$

Suppose that the cognitive user transmitter can obtain S _ηAccurately estimated information is worked as s _SUBe variance S _SUThe gaussian random input signal time, cognitive user can reach maximum data rate.At this moment, this optimization problem can be write as following form

$\left\{\begin{array}{c}{R}_{\mathrm{SU}}^{\mathrm{opt}}=\arg \max \frac{1}{\mathrm{<figure-callout\; id="2"\; label="N\; log"\; filenames="H2009102346200E0000011.png,H2009102346200E0000021.png"\; state="\{\{state\}\}">N</figure-callout>}}{\log }_{}{}_2|I_N+S_{\mathrm{\&eta;}}^{-\frac{1}{2}}{H}_2{S}_{\mathrm{SU}}{\left(S_{\mathrm{\&eta;}}^{-\frac{1}{2}}{H}_2\right)}^H|\\ \mathrm{subject\; to\; tr}\left(V^H{\mathrm{VS}}_{\mathrm{SU}}\right)\&le;(N+L)P_{\mathrm{SU}}\end{array}\right.---\left(13\right)$

When the water flood optimal power allocation, the cognitive user achievable rate is

$R_{\mathrm{SU}}^{\mathrm{opt}}=\frac{1}{N}{\mathrm{<figure-callout\; id="2"\; label="log"\; filenames="H2009102346200E0000011.png,H2009102346200E0000021.png"\; state="\{\{state\}\}">log</figure-callout>}}_2|I_L+\frac{(N+L)}{L}{P}_{\mathrm{SU}}{I}_L|---\left(14\right)$

Similar with formula (12) definition, the Vandermonde pre-coding matrix V degree of freedom under the water flood optimal power allocation, promptly the spatial multiplexing gain on the whole frequency band is expressed as

$d_V^{\mathrm{opt}}=\underset{P_{\mathrm{SU}}\&RightArrow;\&infin;}{\lim }\frac{{\mathrm{NR}}_{\mathrm{SU}}^{\mathrm{opt}}}{{\log }_{2}P}=\underset{P_{\mathrm{SU}}\&RightArrow;\&infin;}{\lim }\frac{{\log }_2|I_L+\frac{(N+L)}{L}{P}_{\mathrm{SU}}{I}_L|}{{\log }_{2}P}---\left(15\right)$

Therefore, the utilization frequency beam-shaper that this method constituted can effectively be eliminated the interference of cognitive user to main user, thereby realizes cognitive user and main user's frequency spectrum share.When cognitive user produces zero interference to main user, adopt frequency domain water filling optimal power allocation method can obtain the full spatial multiplexing gain of system, thereby make cognitive user reach maximum data rate.

Cognitive user, comprises with lower module and link successively with the Vandermonde frequency-division multiplexing multi-carrier modulation that adopts Vandermonde precoder and OFDM to constitute per family with main:

Transmitting terminal: bits of user data enters the symbolic coding module, digital modulation module, insert pilot module, string and modular converter, invert fast fourier transformation module, Vandermonde precoder module, parallel serial conversion module, insert Cyclic Prefix and windowing module, D/A converter module is connected to antenna behind the radio frequency sending module;

Receiving terminal: the reception antenna signal enters Receiver Module, analog-to-digital conversion module, timing and frequency synchronization module, remove cyclic prefix module, string and modular converter, fast fourier transform module, parallel serial conversion module, the channel correction module, the digital demodulation module generates receiving data sequence after the symbol decode module.

Advantage of the present invention and remarkable result: the inventive method has increased the Vandermonde precoder on the basis of cognition wireless network orthogonal frequency division multiplexi, form a kind of new frequency beam-shaper with the Cyclic Prefix redundancy that makes full use of OFDM symbol, the frequency beam-shaper that uses this method to constitute can effectively be eliminated the interference of cognitive user to main user.When producing zero interference to main user, cognitive user carries out optimum input covariance (power) design, adopt frequency domain water filling optimal power allocation method can obtain the full spatial multiplexing gain of system, can make cognitive user reach maximum data rate, thereby realize cognitive user and main user's frequency spectrum share.

Description of drawings

Fig. 1 is 2 * 2 cognition wireless electric models under the frequency selective fading channels;

The Vandermonde frequency-division multiplexing system block diagram that Fig. 2 proposes for the present invention based on multi-carrier modulation;

Fig. 3 is the average degree of freedom of vandermonde matrix under the different ratio c values;

Fig. 4 is the spatial multiplexing gain under the average and optimal power allocation strategy of Vandermonde frequency-division multiplexing system;

When Fig. 5 is circulating prefix-length L=16, the relation between cognitive user received signal to noise ratio and the achievable rate;

Fig. 6 is for as Cyclic Prefix value L=16, and during ratio c=1, the relation between cognitive user achievable rate and the main ownership goal speed.

Embodiment

Fig. 1 has represented 2 * 2 cognition wireless electric models under the frequency selective fading channels.Wherein, s _PU, x _PURepresent main user transmitter input signal and output vector respectively; s _SU, x _SURepresent cognitive user transmitter input signal and output vector respectively.h ⁽¹¹⁾, h ⁽¹²⁾Represent that respectively main user transmitter is to the channel coefficients between main user, the cognitive user receiver; h ⁽²¹⁾, h ⁽²²⁾Represent that respectively the cognitive user transmitter is to the channel coefficients between main user, the cognitive user receiver, n _k～N _c(0, I _N), k=1,2 is additive white Gaussian noise, y _PU, y _SURepresent main user and cognitive user receiver signal respectively.

The Vandermonde frequency-division multiplexing system block diagram that Fig. 2 proposes for the present invention based on multi-carrier modulation.On the basis of existing cognitive radio orthogonal FDM modulation system, this block diagram has increased Vandermonde precoder module at the orthogonal frequency division multiplexing modulator transmitting terminal, it combines with existing cognitive radio OFDM, can effectively utilize the Cyclic Prefix redundancy and the selectivity of channel frequency of OFDM symbol to obtain the system multiplexing gain, to eliminate the interference of cognitive user to main telex network.

Systematic function based on the Vandermonde frequency-division multiplexing method of multi-carrier modulation technology can adopt the execution mode of numerical computations and simulation study to analyze, and research does not produce cognitive user maximum achievable rate when disturbing to main user when cognitive user.

Circulating prefix-length L with the ratio of information symbol block length N is

(0＜c≤1), this ratio directly influence the design of Vandermonde precoder and the performance of Vandermonde frequency-division multiplexing system.In actual IEEE 802.11a WLAN standard physical layer OFDM multi-carrier modulating system, the value of ratio c is usually

It is as follows that simulation parameter is set:

● circulating prefix-length (or parallel channel number): L=[2: 2: 24];

● ratio parameter c:

● the absolute value of multinomial S (z) root | a _l|＜1, l=1,2 ..., L, they are the symmetrical impulse response of linear phase fir system, its value all is positioned at unit circle;

● main user transmitter and cognitive user transmitter power: P=1024;

● cognitive user transmitter signal to noise ratio (snr): SNR=[0: 2: 40] dB;

● actual IEEE 802.11a WLAN standard physical layer ofdm system symbol packets and circulating prefix-length parameter are provided with: N=64, L=16;

● main ownership goal speed: [0: 0.5: 3] bps/Hz.

Fig. 3 has represented the average degree of freedom of vandermonde matrix under the different c values.Among the figure, curve (1), (2), (3), (4) represent respectively ratio c=1,

The time, the relation between the average degree of freedom of vandermonde matrix and the L.As can be seen from the figure, along with the increase of circulating prefix-length L, the degree of freedom obviously increases.When L＞2, with respect to less L value, the degree of freedom raises rapidly.Yet when L＞10, degree of freedom curve increases trend and slows down gradually.On the other hand, for less c (promptly bigger vandermonde matrix line number), when identical L value, the V degree of freedom with less c value is far above the V degree of freedom under other c value.For example, when identical L=20,

The V degree of freedom during than c=1 high about 30%.

Fig. 4 has represented when main user transmitter the cognitive user receiver not to be produced interference (σ ₁₂=0) time, the spatial multiplexing gain under different c values and the average/optimal power allocation strategy (the average degree of freedom) curve.Curve (1), (2), (3), (4) represent respectively ratio c=1,

During average power allocation, the relation between system multiplexing gain and the L; (5), (6), (7), (8) represent respectively ratio c=1,

During optimal power allocation, the relation between system multiplexing gain and the L.Although the diagonalization restriction, the degree of freedom that the optimal power allocation strategy can make full use of new channel G ' of carrying.For example, as circulating prefix-length L=16,

The time, when the spatial multiplexing gain under the optimal power allocation strategy is about the average power allocation strategy 3.5 times, it is illustrated in cognitive user main user is produced under zero prerequisite of disturbing, and water flood optimal power allocation strategy can make cognitive user obtain full spatial multiplexing gain.As shown in Figure 4, the Vandermonde frequency division increase linear growth of the spatial multiplexing gain of system under the optimal power allocation strategy along with circulating prefix-length L.

When Fig. 5 has provided circulating prefix-length L=16, the relation between cognitive user achievable rate and the received signal to noise ratio.Curve (1), (2), (3), (4) represent respectively ratio c=1,

During average power allocation, concern between cognitive user achievable rate and the signal to noise ratio; Curve (5), (6), (7), (8) then represent respectively ratio c=1,

During optimal power allocation, concern between cognitive user achievable rate and the signal to noise ratio.According to Fig. 5, water flood optimal power allocation strategy can make cognitive user obtain significant achievable rate gain.When circulating prefix-length L increased, the achievable rate gain then became more obvious.For L=N=16, SNR=30dB, the cognitive user achievable rate under the optimal power allocation strategy are near 11bps/Hz, and the cognitive user speed under the average power allocation only is 3bps/Hz.And circulating prefix-length L directly influences the cognitive user achievable rate.In the high s/n ratio zone (sNR＞30dB), under the average power allocation strategy c=1 with

The time cognitive user achievable rate be higher than under the optimal power allocation respectively

With

The time the cognitive user achievable rate.Along with the increase of length of the cycle L, the cognitive user achievable rate performance under the various c values is basic identical, and it has shown that the length value of Cyclic Prefix only influences the cognitive user achievable rate under the less c value under high s/n ratio zone and optimal power allocation strategy.

It is R that Fig. 6 has provided main ownership goal speed _PU ^*, main user transmitter power limited P _PU+ P _SUDuring≤P, the relation between cognitive user achievable rate and the main ownership goal speed.Curve (1), (2) represent that respectively signal to noise ratio is 5dB, average/during optimal power allocation, and the relation between cognitive user achievable rate and the main ownership goal speed; Curve (3), (4) represent that respectively signal to noise ratio is 10dB, average/during optimal power allocation, and the relation between cognitive user achievable rate and the main ownership goal speed; Curve (5), (6) are represented signal to noise ratio 15dB respectively, average/during optimal power allocation, and the relation between cognitive user achievable rate and the main ownership goal speed; Curve (7), (8) represent that respectively signal to noise ratio is 20dB, average/during optimal power allocation, and the relation between cognitive user achievable rate and the main ownership goal speed.As Cyclic Prefix value L=16, when c=1, the cognitive user achievable rate is along with the increase of cognitive user received signal to noise ratio sharply raises, and the optimal power allocation strategy obviously is better than traditional average power allocation scheme.Yet (SNR＜10dB), cognitive user speed descends along with the increase of main ownership goal speed, but (SNR＞10dB), this downward trend is also not obvious in the high s/n ratio zone in the low signal-to-noise ratio zone.According to IEEE 802.11a WLAN standard Vandermonde frequency-division multiplexing system emulation parameter is set, gets circulating prefix-length L=16, when

The time, can find to change to from 1 when the c value

The time, the cognitive user achievable rate sharply descends, and it shows that circulating prefix-length has remarkable influence to the cognitive user achievable rate.For example, at main ownership goal speed R _PU ^*Under 1.5bps/Hz, c=1, the peak rate of cognitive user is 7.5bps/Hz during SNR=20dB optimal power allocation strategy, The peak rate of cognitive user but is 2.2bps/Hz during the SNR=20dB optimal power allocation.Yet, under identical c value, increase circulating prefix-length L, or under the identical cyclic prefix length L, increase c value, the cognitive user achievable rate in the time of all can significantly improving optimal power allocation.

Above numerical computations and simulation analysis show, under the cognition wireless network frequency selective fading channels, what this patent proposed can not obtain full spatial multiplexing gain based on the Vandermonde frequency-division multiplexing method of multi-carrier modulation technology cognitive user does not produce the prerequisite of interference to main user under, and under the optimal power allocation strategy, make cognitive user acquisition maximum can reach transmission rate, finally realize the frequency spectrum share of main user and cognitive user.

Claims (3)

1. Vandermonde frequency-division multiplexing method based on multi-carrier modulation technology, it is characterized in that: at first based on symbol cyclic prefix redundancy in the cognition wireless network ofdm system model, structure Vandermonde pre-coding matrix, the Vandermonde pre-coding matrix that satisfies orthogonality condition constitutes the Vandermonde precoder, the Vandermonde precoder is combined with existing cognitive radio OFDM, utilize the Cyclic Prefix redundancy and the selectivity of channel frequency of OFDM symbol to obtain the system multiplexing gain, to eliminate the interference of cognitive user to main telex network, on this basis, adopt frequency domain water injection power distribution method to obtain the full spatial multiplexing gain of system, can reach transmission rate with the maximum that obtains cognitive user, realize cognitive user and main user's frequency spectrum share.

2. according to the described Vandermonde frequency-division multiplexing method of claim 1, it is characterized in that comprising following concrete steps based on multi-carrier modulation technology:

(1) structure Vandermonde pre-coding matrix and Vandermonde precoder

According to 2 * 2 cognition wireless electric models under the frequency selective fading channels, main user transmitter use authority frequency band and main receiver user communicate, the cognitive user transmitter uses this frequency band to send information to corresponding cognitive user receiver simultaneously, when two transmitters are not shared mutual information, and when not cooperating mutually between two transmitters, cognitive user is unknown with respect to main user, therefore, and the prior information of the unknown main user transmitter of cognitive user transmitter; Make h ^(ij)The channel coefficients of expression from transmitter i to (L+1) footpath decline the receiver j supposed h ^(ij)Element (every footpath) is obeyed the multiple Gaussian Profile N of independent same distribution circulation symmetry _c(0, σ _Ij/ (L+1)), and for any i, j, channel is independent identically distributed;

Suppose main user transmitter known channel state h ⁽¹¹⁾, the known local channel state of cognitive user transmitter h ⁽²¹⁾And h ⁽²²⁾, receiver i accurately estimates its channel status h ⁽ⁱⁱ⁾Employing has the intersymbol interference that the multi-carrier modulation technology of N subcarrier can effectively avoid the frequency selective fading channels multipath to cause, the data packet length of each OFDM transmission is the N symbol, inserting length before each OFDM packet is the symbol cyclic prefix of L, receiving terminal extracts the effective information of N symbol in the grouping from (N+L) symbol, therefore this frequency-selective channel can be modeled as the Toeplitz matrix of (N+L) input, N output, and then main user and cognitive user received signal can be expressed as respectively

y _PU＝F(T(h ⁽¹¹⁾)x _PU+T(h ⁽²¹⁾)x _SU+n ₁)

(1)

y _SU＝F(T(h ⁽²²⁾)x _SU+T(h ⁽¹²⁾)x _PU+n ₂)

Wherein, T (h ^(ij)) expression contains the dimension toeplitz matrix of the N of (L+1) footpath Gauss independent same distribution channel fading coefficient * (N+L), note is done

F () is the fast Fourier transform matrix, is expressed as

$F=\left(\begin{array}{cccc}1& 1& ...& 1\\ 1& e^{-j\frac{2\mathrm{\&pi;}}{N}}& ...& e^{-j\frac{2\mathrm{\&pi;}}{N}(N-1)}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ 1& e^{-j\frac{2\mathrm{\&pi;}}{N}(N-1)}& ...& e^{-j\frac{2\mathrm{\&pi;}}{N}{(N-1)}^2}\end{array}\right)---\left(3\right)$

x _PUWith x _SUBe respectively main user transmitter and cognitive user transmitter output vector, its constraints is that power output is limited, promptly

$\mathrm{tr}\left(E\right[x_{\mathrm{PU}}{x}_{\mathrm{PU}}^H\left]\right)\&le;(N+L)P_{\mathrm{PU}}$ (4)

$\mathrm{tr}\left(E\right[x_{\mathrm{SU}}{x}_{\mathrm{SU}}^H\left]\right)\&le;(N+L)P_{\mathrm{SU}}$

N in the formula (1) _k～N _c(0, I _N), k=1,2 is additive white Gaussian noise, considers that the discrete Fourier transform modulation symbol of main user transmitter transmission sequence is

x _PU＝AF ^Hs _PU (5)

Wherein, A is a pre-coding matrix, s _PUFor the N dimension sends sequence vector, therefore, x _PUInclude (N+L) individual symbol, its protection gap length L for the cognitive user transmitter, considers to send vector x greater than coherence time _SU=Vs _SU, wherein V is the linear predictive coding device, s _SUFor cognitive user sends symbolic vector, linear predictive coding device and pre-coding matrix satisfy V=AF ^H, the conjugate transpose of subscript H representing matrix at the cognition wireless network actual conditions, is considered main receiver user is not produced the cognitive user transmission policy of interference, and promptly linear predictive coding device V should satisfy orthogonality condition

T(h ⁽²¹⁾)Vs _SU＝0 (6)

If precoder V be (N+L) * L dimension Vandermonde precoder, then it can effectively utilize CP redundancy L, and it is as follows promptly to construct the Vandermonde precoder structure that satisfies formula (6)

$V=\left(\begin{array}{cccc}1& 1& ...& 1\\ a_1& a_2& ...& a_L\\ a_1^2& a_2^2& ...& a_L^2\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ a_1^{N+L-1}& a_2^{N+L-1}& & a_L^{N+L-1}\end{array}\right)---\left(7\right)$

Wherein, { a _l, l=1,2 ..., L is a multinomial Root.h _i ⁽²¹⁾, i=0,1 ..., L is h ⁽²¹⁾(L+1) dimension channel coefficient vector, V and h ⁽²¹⁾Between orthogonality can guarantee that main user and cognitive user transmit information without interfering with each other in same frequency band, promptly main user and cognitive user satisfy the orthogonality condition shown in the formula (6), utilize the feature of frequency-selective channel to constitute a kind of new frequency beam-shaper, Vandermonde precoder V is determined by vandermonde matrix A, because precoder V and channel h ⁽²¹⁾Orthogonality, when cognitive user sends the Cyclic Prefix sequence of being made up of L symbol, will main user not produced interference;

(2) the Vandermonde precoder is combined with existing cognitive radio OFDM, utilize the Cyclic Prefix redundancy of OFDM symbol and selectivity of channel frequency to obtain the system multiplexing gain

With formula (5), formula (6) substitution formula (1), can obtain main user equivalence parallel channel and be

$y_{\mathrm{PU}}=H_{\mathrm{diag}}^{\left(11\right)}{s}_{\mathrm{PU}}+v_1---\left(8\right)$

Wherein,

Be diagonalization frequency domain channel matrix, its element is the independent same distribution Gaussian random variable, satisfies H _i ⁽¹¹⁾～N _c(0, σ ₁₁), i=1,2 ..., N, v ₁=Fn ₁For Gauss's additive white noise, satisfy v ₁～N _c(0, I _N), same, the cognitive user received signal can be expressed as

$y_{\mathrm{SU}}=H_2{s}_{\mathrm{SU}}+H_{\mathrm{diag}}^{\left(12\right)}{s}_{\mathrm{PU}}+v_2---\left(9\right)$

Wherein, H ₂=FT (h ⁽²²⁾) V,

Be diagonalization frequency domain channel matrix, its element is independent same distribution Gaussian random variable H _i ⁽¹²⁾～N _c(0, σ ₁₂), i=1,2 ..., N, and v ₂=Fn ₂For Gauss's additive white noise, satisfy v ₂～N _c(0, I _N);

According to formula (8) and formula (9), easily know H ₂For N * L ties up channel matrix, main user's received signal is the zero N row parallel sub-channels signal that disturbs.Its expression Vandermonde frequency-division multiplexing method can be converted into the frequency selectivity interference channel monolateral interference channel vector, and promptly main user's received signal is the zero N row parallel sub-channels signal that disturbs, and the interference of cognitive user received signal is only come from main user; Next step, the input covariance power designs with inquiring into when cognitive user produces zero interference to main user makes cognitive user reach the speed optimization;

(3) cognitive user to the noiseless condition of main user under, cognitive user can obtain maximum achievable rate in the Vandermonde frequency-division multiplexing system, realizes cognitive user and main user's frequency spectrum share

When the cognitive user receiver carries out single user when decoding, the cognitive user receiver will come from main user's signal as interference, by formula (9), and definition It is approximately the zero-mean Gaussian random variable, and its covariance is

Because power limited in the formula (4), under the average power, cognitive user input covariance is

$S_{\mathrm{SU}}=\frac{(N+L)P_{\mathrm{SU}}}{\mathrm{tr}\left(V^{H}V\right)}{I}_L---\left(10\right)$

Under the average power allocation strategy, the cognitive user achievable rate is

$R_{\mathrm{SU}}^{\mathrm{eq}}=\frac{1}{N}{\log }_2|I_L+\frac{(N+L)P_{\mathrm{SU}}}{\mathrm{tr}\left(V^{H}V\right)}{V}^{H}V|---\left(11\right)$

Wherein, L is the parallel sub-channels number in the Vandermonde frequency-division multiplexing.

When vandermonde matrix V line number (N+L) increases, the V degree of freedom will influence the root range value of multinomial S (z) | a _l|, l=1,2 ..., L, when Vandermonde pre-coding matrix V ranks parameter L, N → ∞ and

The time, the range value of S (z) root | a _l|, l=1,2 ..., L is positioned at unit circle, the degree of freedom of definition V

$d_V^{\mathrm{eq}}=\underset{P_{\mathrm{SU}}\&RightArrow;\&infin;}{\lim }\frac{{\mathrm{NR}}_{\mathrm{SU}}^{\mathrm{eq}}}{{\log }_{2}P}=\underset{P_{\mathrm{SU}}\&RightArrow;\&infin;}{\lim }\frac{{\log }_2|I_L+\frac{(N+L)P_{\mathrm{SU}}}{\mathrm{tr}\left(V^{H}V\right)}{V}^{H}V|}{{\log }_{2}P}---\left(12\right)$

Suppose that the cognitive user transmitter can obtain S _ηAccurately estimated information is worked as s _SUBe variance S _SUThe gaussian random input signal time, cognitive user can reach maximum data rate.At this moment, this optimization problem can be write as following form

$\left\{\begin{array}{c}{R}_{\mathrm{SU}}^{\mathrm{opt}}=\arg \max \frac{1}{N}{\log }_2|I_N+S_{\mathrm{\&eta;}}^{-\frac{1}{2}}{H}_2{S}_{\mathrm{SU}}{\left(S_{\mathrm{\&eta;}}^{-\frac{1}{2}}{H}_2\right)}^H|\\ \mathrm{subject\; to\; tr}\left(V^{H}V{S}_{\mathrm{SU}}\right)\&le;(N+L)P_{\mathrm{SU}}\end{array}\right.---\left(13\right)$

When the water flood power division, the cognitive user achievable rate is

$R_{\mathrm{SU}}^{\mathrm{opt}}=\frac{1}{N}{\log }_2|I_L+\frac{(N+L)}{L}{P}_{\mathrm{SU}}{I}_L|---\left(14\right)$

Similar with formula (12) definition, the Vandermonde pre-coding matrix V degree of freedom under the water flood power division, promptly the spatial multiplexing gain on the whole frequency band is expressed as

$d_V^{\mathrm{opt}}=\underset{P_{\mathrm{SU}}\&RightArrow;\&infin;}{\lim }\frac{{\mathrm{NR}}_{\mathrm{SU}}^{\mathrm{opt}}}{{\log }_{2}P}=\underset{P_{\mathrm{SU}}\&RightArrow;\&infin;}{\lim }\frac{{\log }_2|I_L+\frac{(N+L)}{L}{P}_{\mathrm{SU}}{I}_L|}{{\log }_{2}P}---\left(15\right)$

3. according to the described Vandermonde frequency-division multiplexing method of claim 2 based on multi-carrier modulation technology, it is characterized in that cognitive user and the main Vandermonde frequency-division multiplexing multi-carrier modulation that adopts Vandermonde precoder and OFDM to constitute per family of using, comprise with lower module and link successively:

Transmitting terminal: bits of user data enters the symbolic coding module, digital modulation module, insert pilot module, string and modular converter, invert fast fourier transformation module, Vandermonde precoder module, parallel serial conversion module, insert Cyclic Prefix and windowing module, D/A converter module is connected to antenna behind the radio frequency sending module;

Receiving terminal: the reception antenna signal enters Receiver Module, analog-to-digital conversion module, timing and frequency synchronization module, remove cyclic prefix module, string and modular converter, fast fourier transform module, parallel serial conversion module, the channel correction module, the digital demodulation module generates receiving data sequence after the symbol decode module.

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