CN103647740B - Multi-carrier modulation and demodulation method of orthogonal non-uniform multi-carrier spacing based on Ramanujan summation - Google Patents
Multi-carrier modulation and demodulation method of orthogonal non-uniform multi-carrier spacing based on Ramanujan summation Download PDFInfo
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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
Technical field
The present invention relates to a kind of multi-carrier modulation demodulation side of the orthogonal non-uniform overloading wave space based on Ramanujan summation sum
Method, belongs to communication technical field.
Background technology
Multi-carrier modulation technology, as a kind of parallel data processing mode, can be effective against 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 is carried out using the uniform subcarrier of spacing
Modulation.This equidistant segmentation does not consider the difference to different carrier attenuation degree for the channel.When the decay of a certain channel is larger
When, the rising of the subchannel bit 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）, adjust the spacing of subcarrier by choosing different transformation matrixs, change subcarrier on frequency spectrum
Distribution.Use more subcarrier-modulated in the hope of the frequency range good in channel quality, the frequency range of bad channel quality is using less
Carrier wave is not even using carrier wave.So so that the subcarrier after adjustment spacing has more preferable channel response, improve receipt signal
Energy, and then improve the signal to noise ratio of receiving terminal.
For high-speed mobile communication system, modulation-transmission technology faces two subject matters：1）Big multi-path delay spread draws
Play frequency selective fading；2）Large doppler effect（Mainly doppler spread）The time selective fading brought.OFDM is equal
Even division sub-carrier channels, obtain the optimum bit error rate of Unknown Channel.If there being the auxiliary of channel condition information, using non-equal
Even multi-carrier modulation can obtain higher channel capacity with distributing carrier wave to little channel position of decaying, receiving terminal, improve and receive
The signal to noise ratio at end.The implementation of non-homogeneous multicarrier always restricts the key factor of its development.Using based on Ramanujan summation
The multi-carrier modulation heterogeneous of sum, on the one hand adopts non-uniform spacing modulation and Ramanujan summation and the frequency resonance of itself
Characteristic come to resist the frequency in channel decline；On the other hand reduce the time because transmission signal has the orthogonality of similar OFDM
The interference that Selective intensity is brought.Additionally, the multi-carrier modulation heterogeneous based on Ramanujan summation sum can be convenient
Change the modulation base chosen, and then change transmission spectrum of carrier distribution.And this only configures in the realization of software radio
A parameter need to be changed, therefore fully meet the simply reconfigurable requirement to modulation system for the 4G communication system.With regard to many
The patent of carrier wave mainly has：
Entitled " to the method for the stream allocated subbands of the multichannel chain-line in multicarrier modulation communication system ", Application No.
200680017456.2 Chinese patent application proposes, in multicarrier modulation communication system, multiple subbands are assigned to multichannel
The method of multiple streams of link.Entitled " random sub carrier wave distributing method in multi-user OFDM system ", Patent No.
200710160371.6 Chinese patent be related to the adaptive channel allocation side of multi-carrier modulation WiMAX mobile communication system
Method.This two schemes are all the realizations of the method for channel allocation to conventional uniform carrier distance.Entitled " multicarrier modulated signal
The method that reduces of impulsive noise and its device ", the Chinese patent of Patent No. 200410079402.1 propose a kind of reduce many
The method of noise in carrier modulation (MCM) signal.Entitled " a kind of method reducing height power ratio in multi-carrier system ",
The Chinese patent of Patent No. 200710120181.1 pays close attention to the peak-to-average power ratio problem of multicarrier system.Entitled " multicarrier
Modulation and demodulation method and apparatus and the method and apparatus executing associated phase of echo offset correction ", Patent No.
98814047.0 Chinese patent pays close attention to the phase offset problem of multicarrier system.Above three patent is all to carry in conventional uniform
The corrective measure of the multi-carrier modulation method of wave space, the modulation of change core and intercarrier be not away from allocation algorithm.Fixing
Uniformly there is inherent shortcoming in distribution of carriers, and when channel is uneven, the bit error rate of the big subchannel of corresponding decline rises, Jin Erying
Ring the performance of whole system.Entitled " have non-homogeneous intercarrier away from multi-carrier modulation demodulation method ", Patent No.
200910039059.0 Chinese patent propose have non-homogeneous intercarrier away from multi-carrier modulation demodulation method.Although should realize
Intercarrier is away from can modulate, but calculates complicated, and loses the orthogonality of intercarrier, increased the shadow of inter-carrier interference
Ring.
Content of the invention
The invention aims to solving the above problems, a kind of orthogonal non-uniform overloading based on Ramanujan summation sum is proposed
The multi-carrier modulation demodulation method of wave space.The present invention uses and the communication system that there is feedback channel, and the receiving terminal of system can
So that by current information feedback, to transmitting terminal, transmitting terminal is modulated the adjustment of base further according to state.
A kind of multi-carrier modulation demodulation method of the orthogonal non-uniform overloading wave space based on Ramanujan summation sum, including following
Several steps：
Step one：Transmitting terminal determines non-homogeneous spacing carrier wave according to current channel condition, by searching Ramanujan summation sum
Frequency distribution table determines carrier position, and then determines modulation base；
Specifically include：
（1.1）Channel magnitude response and frequency are normalized, remove the response of normalization amplitude and be less than given threshold
Frequency range；
（1.2）According to the frequency distribution table of Ramanujan summation sum, determine the modulation base chosen；The frequency distribution of Ramanujan summation sum
Obtained by the definition of Ramanujan summation sum；
Step 2：The modulation base that transmitting terminal is obtained using step one, carries out inverse Ramanujan summation Fourier transformation and carries out data
Modulation；
Specifically include：
（2.1）According to modulation base, build modulation matrix；
The construction of modulation matrix：The element of modulation matrix is Ramanujan summation with Ramanujan summation and the sequence of base is modulated in every behavior
Row, length is the least common multiple of a modulation base；
（2.2）Parallel transmission data is multiplied with modulation matrix, obtains modulated signal, is sent to channel；
Step 3：Receiving terminal is demodulated using Ramanujan summation Fourier transformation；
Specifically include：
（3.1）Build demodulation matrix, first seek the Euler's function of modulation base according to modulation base, using each Euler's function value as right
Angle element builds diagonal matrix, and diagonal matrix is multiplied with the transposition of modulation matrix and obtains demodulation matrix；
（3.2）Receiving data is converted to parallel data by serial data, parallel line number is the least common multiple of modulation base,
Often row receiving data is multiplied with demodulation matrix, then obtains demodulating data divided by the least common multiple modulating base, each row demodulating data
Recovery for the cell data to transmitting terminal transmitted in parallel for the receiving terminal.
It is an advantage of the current invention that：
（1）The present invention according to channel condition information carry out intercarrier away from distribution, each carrier wave keeps orthogonality, reduces carrier wave
Between disturb；
（2）The present invention respectively modulates base and can realize the differentially protected of different carrier to be reflected it is also possible to carry out difference in transmitting terminal
Penetrate the data protection obtaining equalization；
（3）Implementation complexity of the present invention is low；
（4）The present invention can obtain the transmission bit error rate less than equally distributed carrier wave in non-homogeneous channel.
Brief description
Fig. 1 is channel amplitude-frequency response and 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 in embodiment of the present invention with OFDM contrast；
Fig. 4 is method of the present invention flow chart.
Specific embodiment
Below in conjunction with drawings and Examples, the present invention is described in further detail.
The present invention is a kind of multi-carrier modulation demodulation method of the orthogonal non-uniform overloading wave space based on Ramanujan summation sum,
Flow process is as shown in figure 4, include following step：
Step one：Transmitting terminal determines non-homogeneous spacing carrier wave, the carrier position of selection, Ke Yitong according to current channel condition
Cross the frequency distribution table searching Ramanujan summation sum determining, and then determine modulation base.
Specifically include：
（1.1）Channel magnitude response and frequency are normalized, remove the response of normalization amplitude and be less than given threshold
Frequency range.
（1.2）According to the frequency distribution table of Ramanujan summation sum, determine the modulation base chosen；
The frequency distribution of Ramanujan summation sum is obtained by the definition of Ramanujan summation sum.
Step 2：The modulation base that transmitting terminal is obtained using step one, carries out inverse Ramanujan summation Fourier transformation and carries out data
Modulation.
Specifically include：
（2.1）According to modulation base, build modulation matrix.
The construction of modulation matrix：The element of modulation matrix is Ramanujan summation with Ramanujan summation and the sequence of base is modulated in every behavior
Row, length is the least common multiple of a modulation base.
（2.2）Parallel transmission data is multiplied with modulation matrix, obtains modulated signal, is sent to channel.
Step 3：Receiving terminal is demodulated using Ramanujan summation Fourier transformation.
Specifically include：
（3.1）Build demodulation matrix, first seek the Euler's function of modulation base according to modulation base, using each Euler's function value as right
Angle element builds diagonal matrix, and diagonal matrix is multiplied with the transposition of modulation matrix and obtains demodulation matrix.
（3.2）Receiving data is converted to parallel data by serial data, parallel line number is the least common multiple of modulation base,
Often row receiving data is multiplied with demodulation matrix, then obtains demodulating data divided by the least common multiple modulating base, each row demodulating data
Recovery for the cell data to transmitting terminal transmitted in parallel for the receiving terminal；
Embodiment：
Below in conjunction with accompanying drawing to the present invention be embodied as be described further.The present invention determines carrier wave according to channel response
Spacing, the frequency band excessive to avoid noise in channel.As accompanying drawing 1, light color is interchannel noise distribution, and dark color is the load after normalization
Wave frequency is composed.
Step one：Transmitting terminal determines non-homogeneous spacing carrier wave, the carrier position of selection, Ke Yitong according to current channel condition
Cross the frequency distribution table searching Ramanujan summation sum determining, and then determine modulation base.
Specifically include：
（1.1）Channel magnitude response and frequency are normalized, remove the response of normalization amplitude and be less than given threshold
Frequency range.
（1.2）According to the frequency distribution table of Ramanujan summation sum, determine the modulation base chosen；
Proportional spacing carrier wave interval is determined by the frequency distribution of modulation base, the frequency distribution of modulation base is shown in Table 1.Using 4
Channel parallel data transmission means.According to the amplitude-frequency response of channel, choose the frequency being more than π/4 away from normalization frequency π, therefore choose and adjust
The serial number 1,3,4,6 of base processed.Corresponding frequency position is [0, ± π/3, ± pi/2, ± 2 π/3].
The frequency analysis of table 1 Ramanujan summation sum
Step 2：The modulation base that transmitting terminal is obtained using step one, carries out inverse Ramanujan summation Fourier transformation and carries out data
Modulation.
（2.1）According to modulation base, build modulation matrix.
Modulation matrix RsElement be Ramanujan summation and, the definition of Ramanujan summation sum is n time of the q rank primitive root on unit circle
The sum of power, can be expressed as：
Wherein：It is relatively prime that (p, q)=1 represents p and q.Q is Ramanujan summation and cqThe sequence number of (n), n be Ramanujan summation and
Serial number, p is all positive integers less than q relatively prime with q, i be imaginary unit,cqN () has the cycle
Property, the cycle is q.If the modulation base chosen is { q1,q2,...,qM,q1＜ q2... ＜ qM, the least common multiple of all modulation bases
For L, modulation matrix is：
Wherein：qiFor the sequence number of Ramanujan summation sum, 1,2 ..., L are the serial number of Ramanujan summation sum,For La Manu
The value of golden sum, 1≤i≤M, 1≤n≤L.
（2.2）Parallel transmission data is multiplied with modulation matrix, obtains modulated signal, is sent to channel.
Assume that data to be modulated is xq, in transmitting terminal modulation matrix, data is modulated：
Wherein：For original data to be sent, 1≤i≤M, XnFor the data after modulation, 1≤n≤L.Obtain modulation letter
Number, it is sent to channel.
Step 3：Receiving terminal is demodulated using Ramanujan summation Fourier transformation.
（3.1）Build demodulation matrix, first seek the Euler's function of modulation base according to modulation base, using each Euler's function value as right
Angle element builds diagonal matrix, and diagonal matrix is multiplied with the transposition of modulation matrix and obtains demodulation matrix Rd：
Wherein,For Euler's function, 1≤i≤M.
（3.2）Receiving data is converted to parallel data by serial data, parallel line number is the least common multiple of modulation base,
Often row receiving data is multiplied with demodulation matrix, then the least common multiple divided by modulation base, obtains demodulating data, each row demodulating data
Recovery for the cell data to transmitting terminal transmitted in parallel for the receiving terminal.
Receiving vector isTransposed matrix using modulation matrix is demodulated, and obtains demodulating data
Wherein：For receiving data, 1≤n≤L,For demodulating data, 1≤i≤M, it is receiving terminal to transmission data
Recover.
Be modulated the selection of base according to channel condition information, adjustment intercarrier away from only modulation and demodulation matrix need to be changed,
Realize simple.In addition, for different modulation bases, because the integer number relatively prime from it is different, different tune are brought
Energy processed is so that different modulation bases has different modulation energy, and then the channel of different modulating base brings different mistake ratios
Special rate.
Using the modulation system based on Ramanujan summation Fourier transformation, modulation and demodulation step is simple, and computation complexity is low,
Compared with the complexity of OFDM, the multiplier of Ramanujan summation Fourier transformation is about multiplier needed for butterfly fast Fourier transform
1/3rd, be shown in Table 2.
Table 2 Ramanujan summation Fourier transformation is compared with butterfly fast Fourier transform multiplication computation amount
| Computational length N | Ramanujan summation Fourier transformation modulates (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 |
Using modulator approach proposed by the present invention communication system the bit error rate with using uniform intercarrier away from modulator approach
The bit error rate performance index of system be compared, as shown in Fig. 2 modulator approach proposed by the present invention is in non-homogeneous fading channel
Under more uniform multi-carrier modulation scheme reduce the bit error rate of system.Fig. 3 is the non-homogeneous load based on Ramanujan summation Fourier transformation
The bit error rate curve of the multicarrier system of wave space each subchannel under Gaussian white noise channel, modulates base 3, corresponding to 4,6
Subchannel bit error rate close, less than modulation base 1 corresponding to subchannel bit error rate.
The present invention is mainly characterized by according to channel status, carries out orthogonal modulation using suitable modulation base, in non-gaussian
Under white noise channel, it is possible to obtain better than the performance of homogeneous modulation system.The present invention and uniform intercarrier away from modulator approach compared with,
Reduce error rate of system under non-gaussian white noise channel for the system, and it is multiple to have the calculating lower than fast Fourier transform
Miscellaneous degree.
Claims (3)
1. a kind of multi-carrier modulation demodulation method of the orthogonal non-uniform overloading wave space based on Ramanujan summation sum, including following several
Individual step：
Step one：Transmitting terminal determines non-homogeneous spacing carrier wave according to current channel condition, by searching the frequency of Ramanujan summation sum
Distribution table determines carrier position, and then determines modulation base；
Specifically include：
(1.1) channel magnitude response and frequency are normalized, remove the frequency that the response of normalization amplitude is less than given threshold
Section；
(1.2) the frequency distribution table according to Ramanujan summation sum, determines the modulation base chosen；The frequency distribution of Ramanujan summation sum is passed through
The definition of Ramanujan summation sum obtains；
Step 2：The modulation base that transmitting terminal is obtained using step one, carries out inverse Ramanujan summation Fourier transformation and carries out data modulation；
Specifically include：
(2.1) according to modulation base, build modulation matrix；
The construction of modulation matrix：The element of modulation matrix is Ramanujan summation with Ramanujan summation and the sequence of base is modulated in every behavior, long
Spend the least common multiple for modulating base；
(2.2) parallel transmission data is multiplied with modulation matrix, obtains modulated signal, is sent to channel；
Step 3：Receiving terminal is demodulated using Ramanujan summation Fourier transformation；
Specifically include：
(3.1) build demodulation matrix, first seek the Euler's function of modulation base according to modulation base, using each Euler's function value reciprocal as
Diagonal element builds diagonal matrix, and the transposition of modulation matrix is multiplied with diagonal matrix and obtains demodulation matrix；
(3.2) receiving data is converted to parallel data by serial data, parallel line number is the least common multiple of modulation base, often goes
Receiving data is multiplied with demodulation matrix, then obtains demodulating data divided by the least common multiple modulating base, and each row demodulating data is to connect
The recovery of the cell data to transmitting terminal transmitted in parallel for the receiving end.
2. the multi-carrier modulation of a kind of orthogonal non-uniform overloading wave space based on Ramanujan summation sum according to claim 1
Demodulation method, step 2 is specially：
(2.1) according to modulation base, build modulation matrix；
Modulation matrix RsElement be Ramanujan summation and, the definition of Ramanujan summation sum is the n power of q rank primitive root on unit circle
Be expressed as：
Wherein：It is relatively prime that (p, q)=1 represents p and q；Q is Ramanujan summation and cqN the sequence number of (), n is the sequence of Ramanujan summation sum
Row number, p is all positive integers less than q relatively prime with q, and i is imaginary unit,cqN () has periodically, its cycle
Numerically identical with its sequence number q；If the modulation base chosen is { s1,s2,...,sM,s1＜ s2... ＜ sM, modulation matrix is：
Wherein：qjFor constituting this transmission data corresponding modulating base sjRamanujan summation sum sequence number, 1,2 ...,For drawing horse
Exert the value of gold sum, L is the least common multiple of all modulation bases, 1≤j≤M, 1≤n≤L；
(2.2) parallel transmission data is multiplied with modulation matrix, obtains modulated signal, is sent to channel；
Assume that data to be sent is xq, in transmitting terminal modulation matrix, data is modulated：
Wherein：For original data to be sent, 1≤j≤M, qjFor constituting this transmission data corresponding modulating base sjRamanujan summation and
Sequence number, XnFor the data after modulation, 1≤n≤L, obtain modulated signal, be sent to channel.
3. the multi-carrier modulation of a kind of orthogonal non-uniform overloading wave space based on Ramanujan summation sum according to claim 1
Demodulation method, is specially in step 3：
(3.1) build demodulation matrix, first seek the Euler's function of modulation base according to modulation base, using each Euler's function value reciprocal as
Diagonal element builds diagonal matrix, and the transposition of modulation matrix is multiplied with diagonal matrix and obtains demodulation matrix Rd：
Wherein,For Euler's function, 1≤j≤M, modulation base is { s1,s2,...,sM,s1＜ s2... ＜ sM}；
(3.2) receiving data is converted to parallel data by serial data, parallel line number is the least common multiple of modulation base, often goes
Receiving data is multiplied with demodulation matrix, then the least common multiple divided by modulation base, obtains demodulating data, and each row demodulating data is to connect
The recovery of the cell data to transmitting terminal transmitted in parallel for the receiving end；
Receiving vector isTransposed matrix using modulation matrix is demodulated, and obtains demodulating data：
Wherein：For receiving data, 1≤n≤L,For demodulating data, 1≤j≤M, it is the recovery to transmission data for the receiving terminal, its
Middle qjFor constituting Ramanujan summation and the sequence number of this transmission data corresponding modulating base.
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| 郭旭静，王祖林.有限长Ramanujan-Fourier快速变换及频率估计.《北京航空航天大学学报》.2011,第37卷(第10期),第1317-1320、1325页. * |
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