CN107135057A - An Efficient Frequency Division Multiplexing Waveform Generation Method Based on Zero-Tailing DFT Extension - Google Patents

Abstract

The invention provides a high-efficiency frequency division multiplexing waveform generation method based on zero-tailing DFT expansion, which has high spectral efficiency, low out-of-band leakage and low peak-to-average ratio, and belongs to the technical field of information and communication. The invention comprises the following steps: the method comprises the following steps: zero padding is carried out on the head and the tail of a modulation symbol at a sending end to obtain a time domain sending symbol sequence, and N-point DFT expansion transformation is carried out on the time domain sending symbol sequence to obtain a frequency domain signal vector; step two: supplementing (1-alpha) N/alpha zeros at the tail of the obtained frequency domain signal vector, and performing subcarrier mapping on the frequency domain signal vector after zero padding; step three: performing K-point IFFT on the signal vector after subcarrier mapping, discarding the last (1-alpha) N/alpha data of the frequency domain signal vector obtained after transformation, wherein the remaining N data are time domain transmission symbol vectors with zero trailing characteristics, and the formed waveform is the generated high-efficiency frequency division multiplexing waveform; where α represents a spectral compression factor, α ═ N/K.

Description

An Efficient Frequency Division Multiplexing Waveform Generation Method Based on Zero-Tailing DFT Extension

technical field

The invention relates to a method for generating high-efficiency frequency-division multiplexing waveforms, in particular to a method for generating high-efficiency frequency-division multiplexing waveforms based on zero-tailing DFT expansion, and the invention belongs to the technical field of information and communication.

Background technique

In the 5G era, higher transmission rates are required to meet machine-to-machine communication, IoT data transmission, and integration of traditional mobile communications. Spectrum resources are becoming scarcer, and OFDM (orthogonal frequency division multiplexing) ensures orthogonality between subcarriers. Deploying sub-carrier spectrum resource division at the minimum interval has high spectrum utilization efficiency. However, in the face of faster data transmission rate requirements in the future, the sub-carrier orthogonal transmission scheme is no longer fully applicable. In the case of the same transmission rate, the non-orthogonal SEFDM (High Efficiency Frequency Division Multiplexing) transmission scheme proposed by IzzatDarwazeh et al. can further compress the subcarrier spacing on the basis of the OFDM spectrum structure to save spectrum resources. As a non-orthogonal multi-carrier transmission scheme, SEFDM has attracted much attention in the design of 5G candidate waveforms.

Recently, Izzat Darwazeh conducted some SEFDM experiments in wireless communication systems and optical communication systems. In the wireless communication system, CA-SEFDM (Joint Carrier Aggregation CA and SEFDM) further increases the data transmission rate on the basis of a given bandwidth. At the same time, the system error performance and frequency efficiency performance are tested and analyzed. The research shows that CA-SEFDM It has error performance close to CA-OFDM, but compared with CA-OFDM, CA-SEFDM has higher spectral efficiency; in optical communication, 3.75Gbit/s 60GHz millimeter-wave radio frequency fiber is used for testing and testing, O- Compared with O-OFDM (optical OFDM), SEFDM (optical SEFDM) saves about 25% in bandwidth, and can achieve the same error performance as O-OFDM, and further tests under the same spectral efficiency conditions show that low-order modulation can replace high-order Modulation can achieve better performance. AndreyRashich et al. gave the design scheme of SEFDM receiver based on FFT, and proposed an algorithm based on FFT and max-log-MAP and an iterative receiving algorithm. Tongyang Xu and Izzat Darwazeh further proposed a new waveform design, Nyquist-SEFDM, which utilizes sub-carrier spacing below the symbol rate to compress bandwidth to improve spectral efficiency, and uses a root-raised cosine filter for each sub-carrier for pulse-shaping suppression Spectrum leakage, but root-raised cosine filter pulse shaping also re-introduced inter-subcarrier interference, and the sub-carrier deployment of SEFDM itself lower than the symbol rate carried inter-sub-carrier interference, so Nyquist-SEFDM double inter-sub-carrier interference Increased receiver design complexity. SergeyV.Zavjalov et al. optimized the SEFDM signal envelope, and gave the best signal envelope design method to increase the duration of each sub-carrier signal to achieve the purpose of sub-band bandwidth compression. The research shows that compared with OFDM, it can reduce the occupied bandwidth by 32%.

To sum up, SEFDM, as an efficient frequency division multiplexing scheme, uses non-orthogonal transmission system to reduce subcarrier spacing to compress spectrum and further improve spectrum efficiency. However, inter-subcarrier interference that non-orthogonal system cannot bring is to a certain extent It deteriorates the sideband leakage of signal transmission, which is not conducive to energy concentration, and on the other hand leads to a higher signal peak-to-average ratio.

Contents of the invention

In view of the above problems, the present invention proposes an efficient frequency division multiplexing waveform generation method based on zero-smearing DFT expansion with high spectral efficiency, low out-of-band leakage and low peak-to-average ratio.

A kind of high-efficiency frequency-division multiplexing waveform generation method based on zero-smearing DFT expansion of the present invention comprises the following steps:

Step 1: Padding the head and tail of the modulated symbols at the transmitting end with zeros to obtain the transmitted symbol sequence in the time domain, and performing N-point DFT extension transformation on the transmitted symbol sequence in the time domain to obtain a signal vector in the frequency domain;

Step 2: add (1-α) N/α zeros at the end of the obtained frequency-domain signal vector, and perform subcarrier mapping on the frequency-domain signal vector after zero-filling;

Step 3: Carry out K-point IFFT transformation on the signal vector after subcarrier mapping, discard the last (1-α)N/α data of the frequency domain signal vector obtained after the transformation, and the remaining N data have zero tailing The characteristic time-domain transmission symbol vector, the waveform formed by it is the generated high-efficiency frequency division multiplexing waveform;

Wherein, α represents the spectrum compression factor, α=N/K.

The time domain transmission symbol vector with zero smearing feature is:

x=[x ₀ ,...,x _n ,...,x _N-1 ] ^T ;

Among them, the time domain transmission symbol sequence with zero tailing characteristics X _k is the data in the frequency domain signal vector X after zero padding.

The peak-to-average ratio of the time-domain transmission symbol sequence with zero smearing characteristics is:

Among them, E[·] represents the expectation function.

The power spectral density of the time domain transmission symbol sequence with zero smearing characteristics is:

where the power spectrum of the pulse shaping function Among them, T _S represents the symbol period, R (m) represents the delay as an autocorrelation function of m, and f represents the frequency.

The above technical features can be combined in various suitable ways or replaced by equivalent technical features, as long as the purpose of the present invention can be achieved.

The beneficial effect of the present invention is that the present invention is a non-orthogonal high-efficiency frequency-division multiplexing waveform generation method with high spectral efficiency, low out-of-band leakage and low peak-to-average ratio. Subcarrier intervals below the symbol rate are deployed to occupy the bandwidth of the signal, thereby improving spectrum utilization, using the DFT extension method to reduce the peak-to-average ratio of the transmitted signal, and further adopting the method of padding the head and tail of the transmitted data symbol to construct a time-domain transmitted signal with power The tailing towards zero reduces the peak-to-average ratio of the transmitted signal, which effectively speeds up the sideband attenuation.

Description of drawings

Fig. 1 is a schematic diagram of the principle of generating an efficient frequency division multiplexing waveform based on zero tailing DFT expansion in a specific embodiment;

Fig. 2 is the single zero-smearing DFT expansion high-efficiency frequency division multiplexing time-domain signal waveform generated in the specific embodiment;

Fig. 3 is the high-efficiency frequency division multiplexing signal time-domain waveform of a plurality of zero tailing DFT expansions generated in the specific embodiment;

Figures 4a to 4d are schematic diagrams of the power spectral density of SEFDM signals generated when the compression factors are 0.5, 0.7, 0.9, and 1, respectively, where SEFDM refers to conventional SEFDM signals, and DFT-SEFDM refers to SEFDM signals generated by existing methods with DFT transform , the SEFDM signal generated by the present invention of ZT-DFT-s-SEFDM;

Fig. 5 is a schematic diagram of the ZT-DFT-s-SEFDM signal peak-to-average ratio complementary cumulative probability density function generated when the compressibility factor is 0.5 and 0.8 in a specific embodiment.

detailed description

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

It should be noted that, in the case of no conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but not as a limitation of the present invention. A high-efficiency frequency division multiplexing waveform generation method based on zero-smearing DFT expansion described in this embodiment includes the following steps:

Step 1: Pad the head and tail of the modulation symbol at the transmitting end to obtain the time-domain transmission symbol sequence, perform N-point DFT expansion transformation on the time-domain transmission symbol sequence, and obtain the frequency domain signal vector:

This implementation mode is implemented at the transmitter, as shown in Figure 1, the bit information transmission sequence is generated by the modulator to modulate the symbol group d=[d ₀ ,...,d _m ,...,d _M-1 ] ^T , M is the length of the modulation symbol group, which is obtained by padding the head and tail of the modulation symbol Among them, N _h is the number of zero padding at the head, N _t is the number of zero padding at the tail, and the symbol vector s after zero padding is transformed by N points to obtain S=[S ₀ ,...,S _k ,.. .S _N-1 ] ^T :

S＝F _N s (1)

Among them, F _N represents a normalized N-point discrete Fourier transform matrix, where the nth row and kth column of F _N are expressed as:

Step 2: Add (1-α)N/α zeros at the end of the obtained frequency domain signal vector to obtain Carry out subcarrier mapping on the frequency domain signal vector X after zero padding; Step 3: Carry out K-point IFFT transformation on the signal vector after subcarrier mapping, and the IFFT output signal is expressed as: in, Represents the normalized inverse fast Fourier transform matrix of K, discards the last (1-α)N/α data of the frequency domain signal vector obtained after the transformation, and the remaining N data are time domain with zero tailing characteristics Sending symbol vector: x=[x ₀ ,...,x _n ,...,x _N-1 ] ^T where, the time-domain sending symbol sequence with zero tailing feature X _k is the data in the frequency domain signal vector X after zero padding, α represents the spectrum compression factor, α=N/K. The waveform formed by the time-domain transmission symbol sequence with zero smearing feature in this embodiment is the high-efficiency frequency division multiplexing waveform generated in this embodiment.

FIG. 2 and FIG. 3 show time-domain waveforms of zero-tailing DFT extended high-efficiency frequency division multiplexing signals formed in this embodiment. Among them, Fig. 2 is a single zero-tailing DFT extended high-efficiency frequency division multiplexing time-domain signal waveform, and Fig. 3 is a multiple zero-tailing DFT extended high-efficiency frequency-division multiplexing time-domain signal waveform. It can be seen from FIG. 3 that each symbol carries a tail with power close to zero. Compared with the conventional SEFDM signal waveform, this embodiment has better receiver synchronization characteristics. At the same time, compared with OFDM CP In this embodiment, the length of zero smear can be adaptively set to be greater than the multipath delay of the wireless channel in this embodiment, so as to resist multipath channel fading. The calculation of the zero-smearing time-domain signal is expressed as:

in,

Q _DFT represents an N×M DFT extended subcarrier mapping matrix, and Q _IFFT represents a K×N IFFT matrix. Therefore, the power calculation for a zero-smearing time-domain signal is expressed as:

Assuming that the energy of the transmitted modulation symbol is normalized, the mth element in the matrix _Ph is expressed as:

It can be seen from formula (4) that 0≤m≤N _h -1, M/N≤n≤(N-1)/N, therefore, 0≤m/K≤α(N _h -1)/N, where m/K≠n, So P _h (m), m=0, . . . , N _h -1 will get a smaller power distribution close to zero.

The power spectral density of the time domain transmission symbol sequence with zero smearing characteristic generated in this embodiment is:

Among them, the power spectrum of the time-domain transmitted symbol sequence with zero smearing characteristics

Power Spectrum of Pulse Shaping Function Among them, T _S represents the symbol period, R (m) represents the delay as an autocorrelation function of m, and f represents the frequency.

This embodiment takes a rectangular pulse as an example;

For convenience of comparison and description, SEFDM is used to represent a conventional SEFDM signal, DFT-SEFDM is used to represent a SEFDM signal generated by an existing method with DFT transform, and ZT-DFT-s-SEFDM is a SEFDM signal generated by the present invention;

Figure 4a to Figure 4d show the power spectral density comparison of ZT-DFT-s-SEFDM, DFT-SEFDM, and SEFDM when the compression factors are 0.5, 0.7, 0.9 and 1, respectively. Figure 4 shows the four ZT -DFT-s-SEFDM and DFT-SEFDM, SEFDM signal power spectral density comparison shows that the zero-smearing DFT extended SEFDM waveform generation method in this embodiment has better out-of-band suppression effect. Wherein, DFT-SEFDM represents a special case of ZT-DFT-s-SEFDM when N _h =0, N _t =0. The simulation settings are as follows, the number of SEFDM subcarriers is 512, the modulation method is QPSK, and the zero padding design of ZT-DFT-s-SEFDM is N _h =5, N _t =7.

The peak-to-average ratio of ZT-DFT-s-SEFDM in the present embodiment is:

Among them, E[ ] represents the expected function;

The complementary cumulative probability density function calculation of the peak-to-average ratio is expressed as:

PAPR _CCDF = Pr(λ>PAPR) (8)

Among them, Pr(·) represents the probability statistics operator.

Fig. 5 has provided the ZT-DFT-s-SEFDM signal peak-to-average ratio complementary cumulative probability density function of the present embodiment, has provided two groups of curves in Fig. 5, represents the present embodiment when the compression factor is 0.5 and 0.8 respectively Complementary cumulative probability density functions of ZT-DFT-s-SEFDM and DFT-SEFDM, SEFDM peak-to-average ratio. In the case of the same compression factor, the comparison of the three curves in each group of curves shows that ZT-DFT-s-SEFDM has a signal peak-to-average ratio lower than that of SEFDM, and the peak-to-average ratio suppression method based on DFT orthogonal transformation is relatively common and effective. effective method, while ZT-DFT-s-SEFDM has a signal peak-to-average ratio close to that of DFT-SEFDM. The simulation parameter settings are the same as above.

This embodiment is a new zero-smearing DFT extended high-efficiency frequency division multiplexing waveform generation method. This method uses non-orthogonal sub-carriers to allocate signal bandwidth. When the symbol rate is given, compared with orthogonal multi-carrier modulation The scheme has higher spectral efficiency. At the same time, this embodiment adopts the zero-smearing DFT expansion method in the transmitter, which can effectively suppress the out-of-band leakage of the signal waveform, and at the same time ensure that the signal is transmitted with a lower peak-to-average ratio, saving hardware amplifier design.

Although the invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It is therefore to be understood that numerous modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the invention as defined by the appended claims. It shall be understood that different dependent claims and features described herein may be combined in a different way than that described in the original claims. It will also be appreciated that features described in connection with individual embodiments can be used in other described embodiments.

Claims (4)

1. A high-efficiency frequency division multiplexing waveform generation method based on zero-tailing DFT expansion is characterized by comprising the following steps:

the method comprises the following steps: zero padding is carried out on the head and the tail of a modulation symbol at a sending end to obtain a time domain sending symbol sequence, and N-point DFT expansion transformation is carried out on the time domain sending symbol sequence to obtain a frequency domain signal vector;

step two: supplementing (1-alpha) N/alpha zeros at the tail of the obtained frequency domain signal vector, and performing subcarrier mapping on the frequency domain signal vector after zero padding;

step three: performing K-point IFFT on the signal vector after subcarrier mapping, discarding the last (1-alpha) N/alpha data of the frequency domain signal vector obtained after transformation, wherein the remaining N data are time domain transmission symbol vectors with zero trailing characteristics, and the formed waveform is the generated high-efficiency frequency division multiplexing waveform;

where α represents a spectral compression factor, α ═ N/K.

2. The method according to claim 1, wherein the time-domain transmission symbol vector with zero-tail characteristic is:

x＝[x₀,...,x_n,...,x_N-1]^T；

wherein, the time domain with zero tailing characteristic sends the symbol sequenceX_kThe data in the zero-padded frequency domain signal vector X.

3. The method according to claim 2, wherein the time-domain transmission symbol sequence with zero tail feature has a peak-to-average ratio of:

<mrow> <mi>P</mi> <mi>A</mi> <mi>P</mi> <mi>R</mi> <mo>=</mo> <mfrac> <mrow> <munder> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> <mrow> <mn>0</mn> <mo>&amp;le;</mo> <mi>n</mi> <mo>&amp;le;</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munder> <mo>|</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <mrow> <mi>E</mi> <mo>&amp;lsqb;</mo> <mo>|</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> </mrow> </mfrac> </mrow>

wherein E [. cndot. ] represents an expectation function.

4. The method according to claim 2, wherein the power spectral density of the time-domain transmission symbol sequence with the zero-tail characteristic is:

<mrow> <msub> <mi>P</mi> <mi>L</mi> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mi>G</mi> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <msub> <mi>T</mi> <mi>S</mi> </msub> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mi>&amp;infin;</mi> </munderover> <mi>R</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mn>2</mn> <msub> <mi>&amp;pi;mfT</mi> <mi>S</mi> </msub> </mrow> </msup> </mrow>

wherein the power spectrum of the pulse shaping functionWherein T is_SRepresents the symbol period, r (m) represents the autocorrelation function with a delay of m, and f represents the frequency.