CN103647740A

CN103647740A - Multi-carrier modulation and demodulation method of orthogonal non-uniform multi-carrier spacing based on Ramanujan summation

Info

Publication number: CN103647740A
Application number: CN201310606989.6A
Authority: CN
Inventors: 王祖林; 周丽娜; 黄勤
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2013-11-25
Filing date: 2013-11-25
Publication date: 2014-03-19
Anticipated expiration: 2033-11-25
Also published as: CN103647740B

Abstract

The invention discloses a multi-carrier modulation and demodulation method of orthogonal non-uniform multi-carrier spacing based on Ramanujan summation. The method comprises the following steps that step 1, a sending terminal determines non-uniform spacing carriers according to the current channel state, determines positions of the carriers through searching a frequency point distribution table of the Ramanujan summation, and then determining modulation bases; step 2, carrying out inverse Ramanujan Fourier transformation and data modulation by adopting the modulation bases obtained in the step 1; and step 3, a receiving terminal carries out demodulation by using Ramanujan Fourier transformation. The multi-carrier modulation and demodulation method disclosed by the invention carries out carrier spacing allocation according to channel state information, the orthogonality of carriers is kept, and interferences among the carriers are reduced. The modulation bases can realize differential protection for different carriers, and can also carry out difference mapping at the sending terminal to acquire equal data protection. The multi-carrier modulation and demodulation method is low in implementation complexity, and can a lower transmission bit error rate than that of uniformly distributed carriers in a non-uniform channel.

Description

Based on La Manujin and the multi-carrier modulation demodulation method of the non-homogeneous multicarrier spacing of quadrature

Technical field

The present invention relates to a kind of based on La Manujin and the multi-carrier modulation demodulation method of the non-homogeneous multicarrier spacing of quadrature, belong to communication technical field.

Background technology

Multi-carrier modulation technology is as a kind of parallel data processing mode, can be effectively to anti-multipath fading, and improve the message transmission rate of wireless bandwidth efficient channel.As the modulator approach of multi-carrier modulation main flow, traditional OFDM (Orthogonal Frequency Division Multiplexing, OFDM) technology adopts the uniform subcarrier of spacing to modulate.Do not consider the difference of channel to different carrier attenuation degree this equally spaced cutting apart.When the decay of a certain channel is larger, the rising of the subchannel error rate will affect the transmission performance of whole system.

The main thought of non-homogeneous spacing multi-carrier modulation is to utilize channel condition information (Channel State Information, CSI), adjusts the spacing of subcarrier by choosing different transformation matrixs, changes the distribution of subcarrier on frequency spectrum.In the hope of using more subcarrier-modulated in the good frequency range of channel quality, the frequency range of bad channel quality is used less carrier wave even not use carrier wave.Like this, the subcarrier that makes to adjust after spacing has better channel response, improves the energy that receives signal, and then improves the signal to noise ratio of receiving terminal.

For high-speed mobile communication system, modulation-transmission technology faces two subject matters: 1) large multidiameter delay expansion causes frequency selective fading; 2) time selective fading that large Doppler effect (being mainly doppler spread) brings.OFDM evenly divides sub-carrier channels, obtains the optimum bit error rate of Unknown Channel.If there be the auxiliary of channel condition information, adopt non-homogeneous multi-carrier modulation distributing carrier wave to arrive the little channel position of decay, receiving terminal obtains higher channel capacity, improves the signal to noise ratio of receiving terminal.The implementation of non-homogeneous multicarrier is the key factor of its development of restriction always.Employing based on La Manujin and multi-carrier modulation heterogeneous, adopt on the one hand non-uniform spacing modulation and La Manujin and the frequency resonance characteristic of self to resist the frequency decline in channel; The orthogonality that has a similar OFDM due to signal transmission on the other hand reduces the interference that time selective fading is brought.In addition, based on La Manujin and multi-carrier modulation heterogeneous can change easily the modulation base of choosing, and then change transmission spectrum of carrier and distribute.And this is configured in and only needs to change a parameter in the realization of software radio, so meet the simple reconfigurable requirement of 4G communication system to modulation system completely.Patent about multicarrier mainly contains:

Name is called Chinese patent application that " to the method for the stream allocated subbands of the multichannel chain-line in multicarrier modulation communication system ", application number are 200680017456.2 and proposes in multicarrier modulation communication system the method to a plurality of streams of multichannel chain-line by a plurality of allocation of subbands.Name is called the adaptive channel allocation method that Chinese patent that " random sub carrier wave distributing method in multi-user OFDM system ", the patent No. are 200710160371.6 relates to multi-carrier modulation WiMAX mobile communication system.These two schemes are all the realizations to the method for channel allocation of the even carrier distance of tradition.Name is called the method that Chinese patent that " method and device thereof that the impulsive noise of multicarrier modulated signal reduces ", the patent No. are 200410079402.1 proposes noise in a kind of reduction multi-carrier modulation (MCM) signal.Name is called the peak-to-average power ratio problem that Chinese patent that " a kind of method that reduces height power ratio in multi-carrier system ", the patent No. are 200710120181.1 is paid close attention to multicarrier system.Name is called the phase deviation problem that Chinese patent that " multi-carrier modulation and demodulation method and apparatus and carry out the method and apparatus of associated phase of echo offset correction ", the patent No. are 98814047.0 is paid close attention to multicarrier system.Above-mentioned three patents are all the corrective measures at the multi-carrier modulation method of the even intercarrier distance of tradition, do not change the modulation of core and intercarrier apart from allocation algorithm.There is inherent shortcoming in fixing even distribution of carriers, when channel is uneven, the error rate of the subchannel that corresponding decline is large rises, and then affects the performance of whole system.Name is called the multi-carrier modulation demodulation method that Chinese patent that " the multi-carrier modulation demodulation method with non-homogeneous intercarrier distance ", the patent No. are 200910039059.0 proposes to have non-homogeneous intercarrier distance.Although should realize intercarrier apart from modulating, calculation of complex, and lost the orthogonality of intercarrier, has increased the impact of inter-carrier interference.

Summary of the invention

The object of the invention is in order to address the above problem, propose a kind of based on La Manujin and the multi-carrier modulation demodulation method of the non-homogeneous multicarrier spacing of quadrature.The present invention uses and the communication system that has feedback channel, and the receiving terminal of system can be by current information feedback to transmitting terminal, and transmitting terminal is modulated the adjustment of base again according to state.

Based on La Manujin and the multi-carrier modulation demodulation method of the non-homogeneous multicarrier spacing of quadrature, comprise following step:

Step 1: transmitting terminal is determined non-homogeneous spacing carrier wave according to current channel condition, by search La Manujin and frequency distribution table determine carrier position, and then determine modulation base;

Specifically comprise:

(1.1) channel magnitude response and frequency are normalized, after removal normalization, amplitude response is lower than the frequency range of setting threshold;

(1.2) according to La Manujin and frequency distribution table, determine the modulation base choose; La Manujin and frequency distribute by La Manujin and definition obtain;

Step 2: the modulation base that transmitting terminal adopts step 1 to obtain, carries out contrary La Manujin Fourier transform and carries out Data Modulation;

Specifically comprise:

(2.1) according to modulation base, build modulation matrix;

The structure of modulation matrix: the element of modulation matrix be La Manujin and, La Manujin and the sequence of every behavior modulation base, length be the least common multiple of individual modulation base;

(2.2) parallel transmission data and modulation matrix multiplies each other, and obtains modulation signal, sends to channel;

Step 3: receiving terminal is used La Manujin Fourier transform to carry out demodulation;

Specifically comprise:

(3.1) build demodulation matrix, first according to modulation base, ask the Euler's function of modulation base, each Euler's function value is built to diagonal matrix as diagonal element, the transposition of diagonal matrix and modulation matrix multiplies each other and obtains demodulation matrix;

(3.2) reception data are converted to parallel data by serial data, the least common multiple that parallel line number is modulation base, every row receives data and demodulation matrix multiplies each other, least common multiple divided by modulation base obtains demodulating data again, and each row demodulating data is the recovery of receiving terminal to the parallel cell data sending of transmitting terminal.

The invention has the advantages that:

(1) the present invention carries out the distribution of intercarrier distance according to channel condition information, and each carrier wave keeps orthogonality, reduces inter-carrier interference;

(2) the present invention respectively modulates base and can realize the differentially protected of different carrier, also can carry out difference mapping at transmitting terminal and obtain impartial data protection;

(3) implementation complexity of the present invention is low;

(4) the present invention can obtain the transmission bit error rate lower than equally distributed carrier wave in non-homogeneous channel.

Accompanying drawing explanation

Fig. 1 is channel amplitude-frequency response and the carrier spectrum comparison diagram in embodiment of the present invention;

Fig. 2 is the differentially protected bit error rate figure in embodiment of the present invention;

Fig. 3 is the bit error rate curve analogous diagram contrasting with OFDM in embodiment of the present invention;

Fig. 4 is method flow diagram of the present invention.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

The present invention be a kind of based on La Manujin and the multi-carrier modulation demodulation method of the non-homogeneous multicarrier spacing of quadrature, flow process as shown in Figure 4, comprises following step:

Step 1: transmitting terminal is determined non-homogeneous spacing carrier wave according to current channel condition, the carrier position of choosing, can by search La Manujin and frequency distribution table determine, and then determine modulation base.

Specifically comprise:

(1.1) channel magnitude response and frequency are normalized, after removal normalization, amplitude response is lower than the frequency range of setting threshold.

(1.2) according to La Manujin and frequency distribution table, determine the modulation base choose;

La Manujin and frequency distribute by La Manujin and definition obtain.

Step 2: the modulation base that transmitting terminal adopts step 1 to obtain, carries out contrary La Manujin Fourier transform and carries out Data Modulation.

Specifically comprise:

(2.1) according to modulation base, build modulation matrix.

The structure of modulation matrix: the element of modulation matrix be La Manujin and, La Manujin and the sequence of every behavior modulation base, length be the least common multiple of individual modulation base.

(2.2) parallel transmission data and modulation matrix multiplies each other, and obtains modulation signal, sends to channel.

Step 3: receiving terminal is used La Manujin Fourier transform to carry out demodulation.

Specifically comprise:

(3.1) build demodulation matrix, first according to modulation base, ask the Euler's function of modulation base, each Euler's function value is built to diagonal matrix as diagonal element, the transposition of diagonal matrix and modulation matrix multiplies each other and obtains demodulation matrix.

(3.2) reception data are converted to parallel data by serial data, the least common multiple that parallel line number is modulation base, every row receives data and demodulation matrix multiplies each other, least common multiple divided by modulation base obtains demodulating data again, and each row demodulating data is the recovery of receiving terminal to the parallel cell data sending of transmitting terminal;

Embodiment:

Below in conjunction with accompanying drawing, specific embodiment of the invention is described further.The present invention determines intercarrier distance according to channel response, to avoid the excessive frequency band of noise in channel.As accompanying drawing 1, light color is interchannel noise distribution, and dark is the carrier spectrum after normalization.

Specifically comprise:

To the proportional spacing carrier spacing, by the frequency distribution decision of modulating base, the frequency of modulation base distributes in Table 1.Adopt 4 channel parallel data transmission meanss.According to the amplitude-frequency response of channel, choose the frequency that is greater than π/4 apart from normalization frequency π, therefore the sequence number of choice of modulation base is 1,3,4,6.Corresponding frequency position is [0, ± π/3, ± pi/2, ± 2 π/3].

Table 1 La Manujin and frequency analysis

(2.1) according to modulation base, build modulation matrix.

Modulation matrix R _selement be La Manujin and, La Manujin and be defined as the q rank primitive root on unit circle n power with, can be expressed as:

c_{q} (n) = Σ_{\underset{(p, q) = 1}{p = 1}}^{q} \exp (2 iπn \frac{p}{q})

Wherein: (p, q)=1 represents that p and q are relatively prime.Q is La Manujin and c _q(n) sequence number, n be La Manujin and sequence number, p is all positive integers that are less than q relatively prime with q, i is imaginary unit, c _q(n) have periodically, the cycle is q.If the modulation base of choosing is { q ₁, q ₂..., q _m, q ₁< q ₂... < q _m, the least common multiple of all modulation bases is L, modulation matrix is:

Wherein: q _ifor La Manujin and sequence number, 1,2 ..., L be La Manujin and sequence number,

for La Manujin and value, 1≤i≤M, 1≤n≤L.

Suppose to treat that modulating data is x _q, at transmitting terminal, with modulation matrix, data are modulated:

(X_{1}, X_{2}, . . . X_{L}) = (x_{q_{1}}, x_{q_{2}}, . . ., x_{q_{M}}) \cdot R_{s}

Wherein:

for original data to be sent, 1≤i≤M, X _nfor the data after modulation, 1≤n≤L.Obtain modulation signal, send to channel.

(3.1) build demodulation matrix, first according to modulation base, ask the Euler's function of modulation base, each Euler's function value is built to diagonal matrix as diagonal element, the transposition of diagonal matrix and modulation matrix multiplies each other and obtains demodulation matrix R _d:

Wherein, for Euler's function, 1≤i≤M.

(3.2) reception data are converted to parallel data by serial data, the least common multiple that parallel line number is modulation base, every row receives data and demodulation matrix multiplies each other, again divided by the least common multiple of modulating base, obtain demodulating data, each row demodulating data is the recovery of receiving terminal to the parallel cell data sending of transmitting terminal.

Reception vector is use the transposed matrix of modulation matrix to carry out demodulation, obtain demodulating data

({\hat{x}}_{q_{1}}, {\hat{x}}_{q_{2}}, . . ., {\hat{x}}_{q_{M}}) = \frac{1}{L} ({\hat{X}}_{1}, {\hat{X}}_{2}, . . . {\hat{X}}_{L}) \cdot R_{d}

Wherein:

for receiving data, 1≤n≤L,

for demodulating data, 1≤i≤M, is that receiving terminal is to sending the recovery of data.

According to channel condition information, modulate choosing of base, adjust intercarrier apart from only needing to change modulation and demodulation matrix, realize simple.In addition, for different modulation bases, because the integer number relatively prime from it is different, bring different modulation energy, make different modulation bases there is different modulation energy, and then the channel of different modulating base has brought different bit error rates.

The modulation system of use based on La Manujin Fourier transform, modulation and demodulation step is simple, and computation complexity is low, compares with the complexity of OFDM, the multiplier of La Manujin Fourier transform is about 1/3rd of the required multiplier of butterfly fast Fourier transform, is shown in Table 2.

Table 2 La Manujin Fourier transform and the comparison of butterfly fast Fourier transform multiplication computation amount

Computational length N	La Manujin Fourier transform modulation (demodulation)	OFDM modulating/demodulating multiplier number
			2	1(0)	2
4	5(2)	8
			8	14(6)	24
16	34(18)	64
			32	76(44)	160
64	172(108)	384
			128	380(252)	896
256	834(578)	2048
			512	1810(1298)	4608
1024	3912(2888)	10240

The error rate of the communication system of the modulator approach that employing the present invention proposes compares with the bit error rate performance index that adopts even intercarrier apart from the system of modulator approach, as shown in Figure 2, modulator approach more even carrier modulation mode under non-homogeneous fading channel that the present invention proposes has reduced the error rate of system.Fig. 3 is the bit error rate curve of multicarrier system each subchannel under Gaussian white noise channel of the non-homogeneous intercarrier distance based on La Manujin Fourier transform,

modulation base

3,4,6 corresponding subchannel bit error rates are close, lower than the corresponding subchannel bit error rate of modulation base 1.

Main feature of the present invention is according to channel status, adopts suitable modulation base to carry out quadrature modulation, under non-Gaussian white noise channel, can obtain the performance that is better than even modulating system.The present invention compares apart from modulator approach with even intercarrier, has reduced the error rate of system of system under non-Gaussian white noise channel, and has the computation complexity lower than fast Fourier transform.

Claims

Based on La Manujin and the multi-carrier modulation demodulation method of the non-homogeneous multicarrier spacing of quadrature, comprise following step:

Step 1: transmitting terminal is determined non-homogeneous spacing carrier wave according to current channel condition, by search La Manujin and frequency distribution table determine carrier position, and then determine modulation base;

Specifically comprise:

(1.1) channel magnitude response and frequency are normalized, after removal normalization, amplitude response is lower than the frequency range of setting threshold;

(1.2) according to La Manujin and frequency distribution table, determine the modulation base choose; La Manujin and frequency distribute by La Manujin and definition obtain;

Step 2: the modulation base that transmitting terminal adopts step 1 to obtain, carries out contrary La Manujin Fourier transform and carries out Data Modulation;

Specifically comprise:

(2.1) according to modulation base, build modulation matrix;

The structure of modulation matrix: the element of modulation matrix be La Manujin and, La Manujin and the sequence of every behavior modulation base, length be the least common multiple of individual modulation base;

(2.2) parallel transmission data and modulation matrix multiplies each other, and obtains modulation signal, sends to channel;

Step 3: receiving terminal is used La Manujin Fourier transform to carry out demodulation;

Specifically comprise:

(3.1) build demodulation matrix, first according to modulation base, ask the Euler's function of modulation base, each Euler's function value is built to diagonal matrix as diagonal element, the transposition of diagonal matrix and modulation matrix multiplies each other and obtains demodulation matrix;

(3.2) reception data are converted to parallel data by serial data, the least common multiple that parallel line number is modulation base, every row receives data and demodulation matrix multiplies each other, least common multiple divided by modulation base obtains demodulating data again, and each row demodulating data is the recovery of receiving terminal to the parallel cell data sending of transmitting terminal.
According to claim 1 a kind of based on La Manujin and the multi-carrier modulation demodulation method of the non-homogeneous multicarrier spacing of quadrature, step 2 is specially:

(2.1) according to modulation base, build modulation matrix;

Modulation matrix R _selement be La Manujin and, La Manujin and be defined as the q rank primitive root on unit circle n power with, be expressed as:

$c_{q} (n) = Σ_{\underset{(p, q) = 1}{p = 1}}^{q} \exp (2 iπn \frac{p}{q})$

Wherein: (p, q)=1 represents that p and q are relatively prime; Q is La Manujin and c _q(n) sequence number, n be La Manujin and sequence number, p is all positive integers that are less than q relatively prime with q, i is imaginary unit,
c _q(n) have periodically, the cycle is q; If the modulation base of choosing is { q ₁, q ₂..., q _m, q ₁< q ₂... < q _m, the least common multiple of all modulation bases is L, modulation matrix is:

Wherein: q _ifor La Manujin and sequence number, 1,2 ..., L be La Manujin and sequence number,
for La Manujin and value, 1≤i≤M, 1≤n≤L;

(2.2) parallel transmission data and modulation matrix multiplies each other, and obtains modulation signal, sends to channel;

Suppose that data to be sent are x _q, at transmitting terminal, with modulation matrix, data are modulated:

$(X_{1}, X_{2}, . . . X_{L}) = (x_{q_{1}}, x_{q_{2}}, . . ., x_{q_{M}}) \cdot R_{s}$

Wherein: for original data to be sent, 1≤i≤M, X _nfor the data after modulation, 1≤n≤L, obtains modulation signal, sends to channel;
According to claim 1 a kind of based on La Manujin and the multi-carrier modulation demodulation method of the non-homogeneous multicarrier spacing of quadrature, in step 3, be specially:

(3.1) build demodulation matrix, first according to modulation base, ask the Euler's function of modulation base, each Euler's function value is built to diagonal matrix as diagonal element, the transposition of diagonal matrix and modulation matrix multiplies each other and obtains demodulation matrix R _d:

Wherein,
for Euler's function, 1≤i≤M;

(3.2) reception data are converted to parallel data by serial data, the least common multiple that parallel line number is modulation base, every row receives data and demodulation matrix multiplies each other, again divided by the least common multiple of modulating base, obtain demodulating data, each row demodulating data is the recovery of receiving terminal to the parallel cell data sending of transmitting terminal;

Reception vector is use the transposed matrix of modulation matrix to carry out demodulation, obtain demodulating data:

$({\hat{x}}_{q_{1}}, {\hat{x}}_{q_{2}}, . . ., {\hat{x}}_{q_{M}}) = \frac{1}{L} ({\hat{X}}_{1}, {\hat{X}}_{2}, . . . {\hat{X}}_{L}) \cdot R_{d}$

Wherein:
for receiving data, 1≤n≤L,
for demodulating data, 1≤i≤M, is that receiving terminal is to sending the recovery of data.