CN108234102A - A kind of SM-GFDM systems with low complex degree detection algorithm - Google Patents
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Abstract
The present invention relates to a kind of SM GFDM systems with low complex degree detection algorithm, belong to mobile communication technology field.The characteristics of system combination spatial modulation system and GFDM technologies, include the following steps：Step 1：A part of bit information is carried first with the aerial position of spatial modulation；Step 2：Spatial modulation with multi-transceiver technology GFDM is combined, a cyclic prefix can be only used before every frame using GFDM, so as to improve the spectrum utilization efficiency of SM GFDM systems；Step 3：At SM GFDM Demodulation Systems end, using the openness of matrix, decomposed by constructing the docking collection of letters number of Fourier transform block matrix, so as to reduce the complexity in calculating process.The invention can effectively promote the utilization ratio to scattered frequency spectrum, while can also obtain relatively low detection complexity.
Description
Technical Field
The invention relates to the technical field of 5G candidate modulation schemes, in particular to a GFDM-combined spatial modulation system and a low-complexity detection method.
Background
With the arrival of the 5G era, higher requirements are put on the utilization of spectrum resources, since a Cyclic Prefix (CP) needs to be added in front of each section of spectrum in the conventional OFDM technology, a great waste is caused on the Frequency band resources, and in order to solve the problem of spectrum resource shortage, many novel 5G Multicarrier transmission technologies, such as Filter Bank Multicarrier (FBMC), Universal Filtering Multicarrier (UFMC), and Generalized Frequency Division Multiplexing (GFDM), have appeared in recent years, so that scattered spectrum resources can be utilized, and thus the OFDM technology is more suitable for future 5G mobile communication systems, wherein the GFDM technology only needs to use one Cyclic Prefix in front of each frame, so that the utilization efficiency of spectrum resources is improved, and the OFDM technology is one of the 5G new technologies with potential.
In order to further improve the utilization of spectrum resources, the concept of MIMO (Multiple input Multiple output) technology has been proposed and has received increasing attention. In order to solve the problem, the concept of a Spatial Modulation (SM) technology is provided, and under the premise that a plurality of antennas are configured at a transmitting end and a receiving end, only one transmitting antenna is activated at the same time at the transmitting end, so that the problems of inter-channel interference, inter-antenna synchronization and the like of the MIMO system are effectively solved, and meanwhile, the Spatial modulation can utilize information carried by an antenna serial number per se, so that the information quantity carried by a signal is increased in the Spatial dimension. At the receiving end of the SM system, common signal detection algorithms include Maximum Likelihood detection (ML), Sphere Decoding detection (SD), Matched Filtering detection (MF), and the like, where although the ML detection algorithm has a higher complexity, it can search all possible combinations of active antenna indexes and constellation modulation symbols in an exhaustive manner, so that a lower Bit Error Rate (BER) can be achieved.
Based on the above advantages of the spatial modulation technique, in order to further improve the transmission efficiency of the spatial modulation technique, a concept of a multi-carrier spatial modulation technique is proposed. The multi-carrier spatial modulation technology combines spatial modulation and OFDM technology, and utilizes the OFDM technology to distribute single-path data to parallel multi-path subcarriers for parallel transmission, thereby improving the frequency spectrum utilization rate of the system; however, the conventional OFDM technology needs to add a cyclic prefix before each timeslot, which causes a large waste of frequency spectrum, and OFDM also has the disadvantages of inter-subcarrier interference, high out-of-band leakage, strict synchronization requirement, low flexibility, and the like. Therefore, in order to be better suitable for the future 5G communication system, the invention combines the characteristics of the GFDM technology and provides a spatial modulation (SM-GFDM) system combined with GFDM.
Meanwhile, in consideration of the problem of high system complexity after combination, the invention designs a low-complexity SM-GFDM receiving end detection algorithm, so that the algorithm can be more suitable for practical application. Considering the non-orthogonality of GFDM subcarrier, the performance is slightly lost compared with OFDM technology, in order to solve the problem, in SM-GFDM system, ML detection algorithm with best performance is adopted at the space modulation end to improve the system performance, meanwhile, at the GFDM receiving end, the characteristic that the sparsity of matrix does not influence the system performance is utilized, the invention provides MF, ZF and MMSE detection algorithm based on the sparsity of matrix to reduce the complexity of the whole system, and simultaneously, the system keeps better performance.
Disclosure of Invention
The invention aims to design a GFDM combined spatial modulation system and a low-complexity signal detection algorithm. The space modulation system and the GFDM system are two independent systems, in the space modulation system, a transmission information bit is firstly divided into two parts according to a space mapping table, one part is used for transmitting information, the other part is used for selecting and activating an antenna index, the transmission bit sequence is firstly converted into a parallel bit sequence after serial-parallel conversion, according to the space mapping table, the mapped transmission data integrates two parts of information, an original real signal is converted into a complex signal, and the complex signal enters a GFDM modulator to carry out GFDM modulation by utilizing the multi-carrier characteristic of GFDM, wherein the space mapping part is equivalent to the process of carrying out QAM modulation. In the GFDM system, the original GFDM needs to perform serial-to-parallel conversion on the bit sequence after M-QAM mapping to each sub-carrier, perform K-fold up-sampling on the signal on each sub-carrier, filter and modulate the sampled data, and finally superimpose the data and transmit the data through a channel. Therefore, the QAM mapping in the GFDM modulation step can be replaced by spatial modulation in the combined system, thereby constituting the transmitting end of the SM-GFDM system. The combined system avoids the problem of interference between antennas in the MIMO-GFDM system due to the combination of the advantages of spatial modulation, and meanwhile, by utilizing the GFDM characteristic, the scattered frequency spectrum can be utilized in the application facing 5G.
At a receiving end of the SM-GFDM system, a received signal is firstly subjected to GFDM demodulation, and then a demodulated signal is subjected to frequency domain equalization and then spatial demodulation, so that an original input bit vector is obtained. Suppose that in an SM-GFDM system, an originating terminal and a receiving terminal are respectively configured with NtAnd NrRoot aerial, using MaryQAM modulation, where K subcarriers are used in GFDM modulation, M time slots, and the total number of samples N ═ KM, since the number of bits N ═ log that can be transmitted by the spatial modulation part2Mary+log2NtA bit, input data source at spatial modulation moduleMapping the bit sequence into constellation symbols and antenna indexes according to a space mapping table, and performing serial-parallel conversion to generate space modulation symbolsWherein d isk＝[dk(0)，dk(1)，…，dk(M-1)]TThen, after passing through a GFDM modulator, a GFDM signal is generated:
wherein,and xk＝[xk(0)，xk(1)，…，xk(M-1)]TMatrix ofIn order to modulate the matrix, the modulation matrix,is a KM x KM diagonal matrix,k is 0, …, K-1, i.e.G is the unit impulse response G ═ G from the prototype filter0，…，gn，…，gN-1]TThe KM × M matrix obtained by cyclic shift is used, soWhere the mth (M-0, 1, …, M-1) column of G represents the impulse response of the pulse shaping filter on the mth data symbol. Assuming that the channel is a quasi-static flat rayleigh fading channel, the received signal vector for a particular pair of transmit and receive antennas can be expressed as:
y＝Hx+n (2)
whereinIn order to be a matrix of channels,is a mean value of 0 and a variance ofThe noise signal vector of (2).
In an SM-GFDM system, because an ML detection algorithm with the best performance is used at a spatial modulation end to improve the system performance, the invention aims to design a detection algorithm for reducing the complexity of the system on the premise of not influencing the performance, and based on the detection algorithm, the invention provides MF, ZF and MMSE detection and calculation based on matrix sparsity.
The present invention defines an MF receiver based on matrix sparsity as:
wherein: wNIs a normalized Discrete Fourier Transform (DFT) block matrix with KM x KM dimensions, consisting of K x K sub-matrices omega with M x M dimensionskl(K, l ═ 0, 1, …, K-1), i.e.WhereinEyes of a userThus, it is possible to provideΓ＝WNAHΓ y may be computed using sparsity reduction of Γ, andcan be calculated by means of FFT.
Because of ΓHHas the same sparsity as the gamma, so that the data can be directly subjected to frequency domain transformation (pre-coding) in advance, namely, the data is subjected to pre-codingThe GFDM signal can be expressed as:
are defined in the inventionWherein gamma iskIs a matrix of M × KM, K is 0, …, K-1, then:
from equation (5), Γ is equivalent to a frequency domain demodulator after fourier transform of the GFDM received signal, and since the inner product of two complex exponential signals of different frequencies is zero, that is:
wherein: m, n-0, …, K-1, we can get:
for the purposes of the present invention, h ═ (K-K) modK, then:
whereinIn the form of a diagonal matrix,namely, it isSubstituting equation (8) into equation (7) we can obtain:
thus, combining ΨhBy the expression of (A), we can obtain gammakIn (1) only has M2The columns of the non-zero elements are h, h + K, …, h + (M-1) K, and the rest columns are all zero. So that gamma shares KM2A non-zero element, therefore Γ ═ WNAHHas sparseness.
The invention defines a ZF receiver expression based on matrix sparsity as follows:
we need to analyze the matrix aHAnd (A) characteristics. From the definition of the GFDM modulation matrix we can easily have:
because of the fact thatOrder toThen D is diag { [ D ]0，…，Dk，…，DK-1]Is a block diagonal matrix KM x KM, DkIs an M × M matrix, so there are:
in combination with formula (9), we have:
wherein circ (. sup.). sup. -) represents a circulant matrix of initial behavior, i.e. ifThen C can be abbreviated as C ═ circ (a)0，a1，…an-1) In the form of (a) a (b),representing an M-point cyclic convolution. We define the in-phase component of the prototype filter g as g0，…，gk，…，gK-1Wherein g isk＝[gk，gk+K，…，gk+(M-1)K]T，ghIs the h th in-phase component of g, anIs ghReverse folding and circular shifting the sequence obtained at position 1 to the right. And is composed ofThe estimated signal can be expressed as:
order toyh＝[yh，yh+K，…，yh+K(M-1)]TThen, there are:
therefore, the method comprises the following steps:
in combination with equation (13), (16) can be written as:
the final estimated signal can be expressed as:
because the MMSE receiver based on matrix sparsity is represented in the form:
in conjunction with the above analysis we can easily obtain:
wherein, INIs an NxN identity matrix, orderThen because ofTherefore, the method comprises the following steps:
due to the adoption of the technical scheme, the invention has the following advantages:
1. the invention combines the space modulation and GFDM technical advantages to form an SM-GFDM system, can utilize the multi-carrier characteristic of GFDM to improve the transmission efficiency of space modulation, and can utilize the characteristic of space modulation to carry part of information on the antenna index, thereby improving the spectrum utilization efficiency of the system.
2. The invention provides MF, ZF and MMSE detection algorithms based on the matrix sparsity by utilizing the characteristic that the system performance is not influenced by the sparsity of the matrix, and introduces a normalized discrete Fourier transform block matrix, thereby reducing the complexity of the whole system on the premise of maintaining the performance of the SM-GFDM system.
Drawings
In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
FIG. 1 is a block diagram of a federated system of the present invention;
FIG. 2 is a diagram of a model GFDM transmitter for use with the present invention;
FIG. 3 is a flow chart of an MF receiver based on matrix sparsity according to the present invention;
detailed description of the preferred embodiments
The invention combines the space modulation system and the GFDM technology into the SM-GFDM system by utilizing the advantages of the space modulation system and the GFDM technology, realizes the multi-carrier transmission of the space modulation system, and utilizes the GFDM technology characteristic to utilize the scattered spectrum. In consideration of the complexity of the combined system, the SM-GFDM system detection algorithm based on the matrix sparsity is invented, so that the system complexity is reduced on the premise of maintaining the system performance. The following description of the embodiments of the present invention is provided in connection with the accompanying drawings and the specific examples.
1. System model
In the SM-OFDM system, OFDM has the problems of weak carrier frequency offset resistance, large peak-to-average ratio, serious out-of-band power leakage, and the like, so a spatial modulation system using combined GFDM is considered, and a SM-GFDM system model diagram is shown in fig. 1. A binary data source s firstly performs symbol mapping and selects and activates antenna index through spatial modulation, the modulated signal is then subjected to GFDM modulation, a GFDM modulator model is as shown in fig. 2, the spatial modulation signal is firstly subjected to serial-to-parallel conversion and then distributed to each subcarrier, the data symbol on each subcarrier is subjected to up-sampling operation of K times, then filtered by a pulse shaping filter, and then modulated to each subcarrier, finally all the subcarrier symbols are superposed to generate an SM-GFDM symbol, the SM-GFDM symbol is sent to a receiving end through a channel, at the receiving end of an SM-GFDM system, the received signal is firstly subjected to GFDM demodulation, and as the demodulated signal contains partial channel components, a proper spatial modulation and demodulation algorithm is selected to perform spatial demodulation, and an original transmission bit sequence is recovered.
2. Low-complexity SM-GFDM system detection algorithm
Consider the following example in which the transmit and receive ends in an SM-GFDM system are each configured with NtAnd NrRoot aerial, using MaryQAM modulation, where K subcarriers are used in GFDM modulation, M time slots, and the total number of samples N ═ KM, since the number of bits N ═ log that can be transmitted by the spatial modulation part2Mary+log2NtA bit, input data source at spatial modulation moduleMapping the bit sequence into constellation symbols and antenna indexes according to a spatial mapping table, wherein, taking transmission of 3-bit information (i.e. a frequency band utilization rate of 3 bits/s/Hz) as an example, the spatial mapping table is shown in table 1.
TABLE 1 spatial mapping table
Fig. 3 is a flowchart of the MF transmitter based on matrix sparsity according to the present invention, and as shown in the figure, the MF receiver algorithm based on matrix sparsity according to the present invention includes the following steps:
the method comprises the following steps: computing a diagonal matrix EkAnd modulating matrix A, and generating cyclic matrix G:
after serial-to-parallel conversion, spatial modulation symbols are generatedWherein d isk＝[dk(0)，dk(1)，…，dk(M-1)]TThen, after passing through a GFDM modulator, a GFDM signal is generated:
wherein,and xk＝[xk(0)，xk(1)，…，xk(M-1)]TMatrix ofIn order to modulate the matrix, the modulation matrix,is a KM x KM diagonal matrix,k is 0, …, K-1, i.e.G is the unit impulse response G ═ G from the prototype filter0，…，gn，…，gN-1]TThe KM × M matrix obtained by cyclic shift is used, soWhere the mth (M-0, 1, …, M-1) column of G represents the impulse response of the pulse shaping filter on the mth data symbol. Assuming that the channel is a quasi-static flat rayleigh fading channel, the received signal vector for a particular pair of transmit and receive antennas can be expressed as:
y＝Hx+n (23)
whereinIn order to be a matrix of channels,is a mean value of 0 and a variance ofThe noise signal vector of (2).
In an SM-GFDM system, because an ML detection algorithm with the best performance is used at a spatial modulation end to improve the system performance, the invention aims to design a detection algorithm for reducing the complexity of the system on the premise of not influencing the performance, and based on the detection algorithm, the invention provides an MF detection algorithm based on matrix sparsity.
Step two: computing a Fourier transform block matrix WNAnd Γ ═ WNAHSparsity of (c):
the present invention defines an MF receiver based on matrix sparsity as:
wherein: wNIs a normalized Discrete Fourier Transform (DFT) block matrix with KM x KM dimensions, consisting of K x K sub-matrices omega with M x M dimensionskl(K, l ═ 0, 1, …, K-1), i.e.WhereinAnd isThus, it is possible to provideΓ＝WNAHΓ y may be computed using sparsity reduction of Γ, andcan be calculated by means of FFT.
Because of ΓHHas the same sparsity as the gamma, so that the data can be directly subjected to frequency domain transformation (pre-coding) in advance, namely, the data is subjected to pre-codingThe GFDM signal can be expressed as:
are defined in the inventionWherein gamma iskIs a matrix of M × KM, K is 0, …, K-1, then:
from equation (26), it can be seen that Γ is equivalent to a frequency domain demodulator after fourier transform of the GFDM received signal, and since the inner product of two complex exponential signals at different frequencies is zero, that is:
wherein: m, n-0, …, K-1, we can get:
for the purposes of the present invention, h ═ (K-K) modK, then:
whereinIn the form of a diagonal matrix,namely, it isSubstituting equation (29) into equation (28) we can obtain:
thus, combining ΨhBy the expression of (A), we can obtain gammakIn (1) only has M2The columns of the non-zero elements are h, h + K, …, h + (M-1) K, and the rest columns are all zero. So that gamma shares KM2A non-zero element, therefore Γ ═ WNAHHas sparseness. Obtaining an estimated signal according to an MF receiver implementation equation (24) based on matrix sparsity
Step three: base ofIn the analysis, matrix sparsity is utilized to solve ZF receiver estimation signals based on the matrix sparsity
Since ZF receivers based on matrix sparsity are represented as:
we need to analyze the matrix aHAnd (A) characteristics. From the definition of the GFDM modulation matrix we can easily have:
because of the fact thatOrder toThen D is diag { [ D ]0，…，Dk，…，DK-1]Is a block diagonal matrix KM x KM, DkIs an M × M matrix, so there are:
in combination with formula (30), we have:
wherein circ (. sup.). sup. -) represents a circulant matrix of initial behavior, i.e. ifThen C can be abbreviated as C ═ circ (a)0，a1，…an-1) In the form of (a) a (b),representing an M-point cyclic convolution. We define the in-phase component of the prototype filter g as g0，…，gk，…，gK-1Wherein g isk=[gk，gk+K，…，gk+(M-1)K]T，ghIs the h th in-phase component of g, anIs ghReverse folding and circular shifting the sequence obtained at position 1 to the right. And is composed ofThe estimated signal can be expressed as:
order toyh＝[yh，yh+x，…，yh+K(M-1)]TThen, there are:
therefore, the method comprises the following steps:
in combination with equation (34), equation (37) can be written as:
the final estimated signal can be expressed as:
step four: combining the analysis, and utilizing the matrix sparsity to solve the MMSE receiver estimation signal based on the matrix sparsity
The invention defines the expression form of MMSE receiver based on matrix sparsity as follows:
in conjunction with the above analysis we can easily obtain:
wherein, INIs an NxN identity matrix, orderThen because ofTherefore, the method comprises the following steps:
thus, MF, ZF and MMSE detection schemes based on matrix sparsity are obtained.
In summary, the present solution aims to utilize the advantages of the spatial modulation and GFDM system, combine the spatial modulation technique and the GFDM technique into an SM-GFDM system, and propose MF, ZF, MMSE detection schemes based on the sparsity of the matrix by using the characteristic that the sparsity of the matrix does not affect the performance of the system, but can reduce the complexity of the calculation, so as to reduce the overall complexity of the system while maintaining the better performance of the system. The scheme can overcome the problems of weak carrier frequency offset resistance, large peak-to-average ratio, serious out-of-band power leakage and the like of an SM-OFDM system, can improve the utilization efficiency of frequency spectrum resources by using GFDM characteristics, cannot overcome the problem of interference between antennas of an MIMO-GFDM system, can carry part of information on the antenna index by using the position information of the antennas so as to improve the information transmission efficiency, can relieve the shortage of the frequency spectrum resources of 5G in the future to a certain extent, and becomes one of the candidate modulation schemes of 5G in the future.
Claims (6)
1. An SM-GFDM system with a low-complexity detection algorithm is characterized in that a GFDM technology which is one of 5G candidate waveforms with a relatively high potential overcomes the defects of inter-subcarrier interference, high out-of-band leakage, strict synchronization requirement, low flexibility and the like compared with an OFDM (Orthogonal Frequency Division Multiplexing) system; on the other hand, the spatial modulation is a brand new MIMO transmission technology, the complexity and hardware overhead of a multi-antenna system can be reduced while the transmission efficiency and performance are maintained, the spatial modulation can use the activation state of an antenna as a carrier of information transmission, the problems of inter-channel interference, inter-antenna synchronization, radio frequency cost and the like in the traditional MIMO scheme are effectively simplified, and the spatial modulation is also suitable for large-scale MIMO channels with asymmetric uplink and downlink antenna numbers, so the spatial modulation is a brand new physical layer wireless transmission technology, can skillfully combine digital modulation, coding and multi-antenna to realize high transmission rate and low complexity physics, combines the spatial modulation and GFDM technology to establish an SM-GFDM system model, can improve the spatial modulation transmission efficiency by using the multi-carrier characteristic of GFDM, resulting in greater utilization of the available frequency band resources.
2. The SM-GFDM system with low complexity detection algorithm of claim 1, wherein according to the spatial modulation system principle, the binary bit sequence is subjected to serial-to-parallel conversion and then antenna index selection and constellation modulation are respectively performed according to a spatial mapping table; after the GFDM technology is combined, because the GFDM principle is that GFDM modulation is performed after data streams are QAM mapped, QAM mapping at the GFDM modulation end can be replaced by spatial modulation, thereby combining the SM-GFDM system.
3. The SM-GFDM system with low complexity detection algorithm as claimed in claim 1, wherein at the receiving end of the SM-GFDM system, considering that the performance of the SM-GFDM is slightly reduced due to the non-orthogonality of the GFDM compared with the SM-OFDM system, in order to maintain the overall performance of the system, the maximum likelihood detection with the best performance is considered at the receiving end of the spatial modulation, under the premise that the performance of the system is not affected by the sparsity of the matrix, but the complexity in the calculation process can be reduced, the invention provides an MF, ZF, MMSE detection algorithm based on the sparsity of the matrix to reduce the overall complexity of the system.
4. An SM-GFDM system with low complexity detection algorithm as claimed in claim 1, characterized in that the invention uses the properties of fourier transformWell-defined normalized discrete Fourier transform block matrix WNAnd then it is combined with modulation matrix AHMultiplying to obtain a result after multiplication of Γ ═ WNAHThe final MF receiver model reduces the calculation complexity of system detection by using the sparsity of gamma, and the transmitting end of the SM-GFDM system is configured with NtRoot antenna, receiving end configuration NrRoot aerial, using Mary-QAM modulation, using K subcarriers in GFDM modulation, SM-GFDM system of M time slots, the invention defines a diagonal matrixAnd isObtaining the K (K is 0, …, K-1) th subcarrier in the gammaWhere h is (K-K) modK, gives ΓkIn (1) only has M2Non-zero elements are arranged in columns of h, h + K, …, h + (M-1) K, and the rest columns are all zero, so that the gamma value has KM2A non-zero element, therefore Γ ═ WNAHAnd sparsity is realized, so that the sparse detection of the MF receiver based on matrix sparsity with lower complexity is obtained.
5. An SM-GFDM system with low complexity detection algorithm as claimed in claim 1, characterized by using normalized discrete fourier transform block matrix WNAnd sparsity of the obtained Γ, the present invention defines a KM × KM dimensional block diagonal matrix D { [ D { ] in which D { [ D ] is a diagonalized matrix0，…,Dk，…,DK-1]In which D iskIs a matrix of dimension M x M, so that we obtainIs in the form of a cyclic matrix, and combines the definition of a modulation matrix A to obtain the matrix sparsity-basedZF receiver model isThus, it is possible to provideThe calculation can be performed using the matrix sparsity.
6. An SM-GFDM system with low complexity detection algorithm as claimed in claim 1, characterized in that since MMSE detection algorithm is related to the variance of the noise, since the channel is time varying, real time computation is needed, in combination with normalized dft block matrix WNAnd the block diagonal matrix D can be definedTherefore, in combination with the expression of MMSE detection, the MMSE detection algorithm based on matrix sparsity of the present invention can be expressed asTherefore, by utilizing the sparsity of the matrix, a low-complexity MMSE detection scheme is obtained.
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Cited By (5)
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| CN109039414A (en) * | 2018-08-20 | 2018-12-18 | 西北工业大学 | A kind of spatial polarizations modulator approach of spectral efficient |
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| CN109302240A (en) * | 2018-10-11 | 2019-02-01 | 西北工业大学 | The serial equalization methods of low complex degree OSDM based on double selection fading channels |
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