AU2018451596A1 - 5G multi-carrier spread spectrum underwater acoustic communication method - Google Patents
5G multi-carrier spread spectrum underwater acoustic communication method Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
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- H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
- H04B1/69—Spread spectrum techniques
- H04B1/707—Spread spectrum techniques using direct sequence modulation
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Abstract
The present invention relates to a 5G multi-carrier spread spectrum underwater acoustic communication method, belongs to the field of underwater acoustic communication, and relates to generalized frequency division multiplexing (GFDM) underwater acoustic communication technology and spread spectrum underwater acoustic communication technology. A GFDM spread spectrum underwater acoustic communication system suitable for use in the underwater acoustic field provided by the present invention implements effective information transmission in an underwater acoustic channel of limited bandwidth resources. The present invention aims to provide an effective information transmission method for the field of underwater acoustic communication of limited channel bandwidth resources, and the method has important significance for development of underwater acoustic technology.
Description
Our Ref: OF180851D/P/AU
5G MULTI-CARRIER SPREAD SPECTRUM UNDERWATER ACOUSTIC COMMUNICATION METHOD
The present invention relates to a 5G multi-carrier spread spectrum underwater acoustic communication method, belongs to the field of underwater acoustic communications, and relates to a Generalized Frequency Division Multiplexing (GFDM) underwater acoustic communication technology and a spread spectrum underwater acoustic communication technology.
In radio 5G, the main requirements for communication systems are high network capacity, low cost, and high data transmission rate, and such a high data transmission rate is not only a requirement in radio but also a requirement in high-speed underwater acoustic communications. The key technologies in 5G comprise several aspects such as realization of a large-scale Multiple Input Multiple Output (MIMO) system, an advanced multiple access technology, a full duplex technology, an new multi-carrier technology and an adaptive coding and modulation technology. As a result of such a rapid increase in user demand, the requirement of non-strict synchronization between users among multiple application scenarios, and the requirement of improving devices' processing capabilities, orthogonal multiple access technologies in traditional !0 mobile communication technologies, e.g., a Frequency Division Multiple Access (FDMA) technology, a Time Division Multiple Access (TDMA) technology, a Code Division Multiple Access (CDMA) technology, and an Orthogonal Frequency Division Multiple Access (OFDMA) technology, evolve towards new technologies and new directions. In non-orthogonal transmission technologies, non-orthogonal multiple access technologies and multi-carrier technologies are two main technologies currently developed, in which non-orthogonal multiple access technologies are represented by Pattern Division Multiple Access (PDMA) technologies, and can be divided into several division modes, power domain division, generalized domain division and coding domain
Our Ref: OF180851D/P/AU
division. These emerging multi-carrier technologies have the advantage of high data transmission rate of traditional multi-carrier technologies, and are more flexible and effective than traditional multi-carrier technologies. However, the structure of GFDM based on a filter bank makes its channel estimation a difficult problem, at present there is no relevant literature that effectively solves this problem yet, and in underwater acoustic communications, the influence of an underwater acoustic channel on a communication system cannot be ignored; this disadvantage is the key point that hinders its application in the field of underwater acoustic communications. In view of the above problem, there is proposed herein a multi-carrier spread spectrum underwater acoustic communication technology. The advantages of spread spectrum technologies are used to make up for problems such as channel multi-path time delay.
An object of the present invention is to provide an efficient underwater acoustic communication solution for the field of underwater acoustic communications with limited channel bandwidth resources. The present invention proposes a GFDM spread spectrum underwater acoustic communication system suitable for the field of underwater acoustics, which realizes effective information transmission in an underwater acoustic channel with limited !0 bandwidth resources. The object of the present invention is to provide an effective information transmission method for the field of underwater acoustic communications with limited channel bandwidth resources, which is of great significance for the development of underwater acoustic technologies. The object of the present invention is achieved by a method comprising the !5 following steps: step 1: at a transmitting end, encoding source data, and performing a spread spectrum operation on the encoded serial data by using a spread spectrum sequence; step 2: performing GFDM modulation on data after spread spectrum, and after that, adding a cyclic prefix to the modulated data to obtain transmitted data;
Our Ref.: OF180851D/P/AU
step 3: at a receiving end, performing synchronization and GFDM demodulation on the data, after the modulated signals pass through an underwater acoustic channel; and step 4: despreading the demodulated data, and integrating the obtained signals over a duration and making a judgement to obtain data estimated by the receiving end. Preferably, the present invention further comprises any one or more features selected from the following items 1-4: 1. A spread spectrum process in the step 1 is as below:
the transmitted data is expressed by d(t ), and then the process can be
expressed as:
d(t)= d(n)g(t-nT,)
c(t)= c(n)p(t-nT)
where values of d(n) and a pseudo-random sequence c(n) used for
spreading spectrum are 1 or -1, g(t) and p(t) are rectangular pulses of a unit
amplitude with durations T and T, respectively, N represents a length of the spread
spectrum sequence, and in general, T,=NT,; a sequence after spread spectrum p(t)
is:
p(t)= d(t)c(t)
wherein Table 1 gives responses in a frequency domain of several typical g(t)
filters: Table 1 Responses in a frequency domain of several typical filters Name Response in a frequency domain
RC (Raised Cosine filter) GRC[f 1rI CoS 7ina
RRC (Root-Raised Cosine filter) GRRC[f]= G[f]
where a represents a roll-off factor
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lin" x) = min 1, max 0, a ~2a I+~~l a))
2. A modulation process in the step 2 is expressed as below:
data after GFDM modulation is y(t) , g[-] is used to express a GFDM
modulation process, and then:
y(t)=g[p(t)] = g[d(t)c(t)]
a discrete spread spectrum signal for GFDM adopting a BPSK modulation mode can be expressed as: Ne -1 MGD
SMC-DS (t ) =E E E dk[i]ck[j]pT( -i - jT)cos[2r(f0 +kAf')t] k=0 i=-M j=0
where d[i] is data on a k-th subcarrier,Ck[j] represents a spread spectrum
sequence which is correspondingly multiplied by d[i], Nc represents a number of
subcarriers,and Af'=1/T is a subcarrier spacing.
3. A process of performing the GFDM demodulation on the received signal in the step 3 is as below: at the receiving end, on the premise of correct synchronization, the GFDM
demodulation is performed on the received signal y(t), g-'[-] is used to represent the
GFDM demodulation process, and then a signal r(t) to be despread can be expressed
as:
r(t)=g-i[y'(t)] 4. A process of despreading the received signal in the step 4 is as below: r(t) is despread by utilizing a spread spectrum sequence c,(t) which is
generated locally and the same as that at the transmitting end: m (t)=r(t)c, (t) =g -'[y'(t)]c, (t) =g -'[g[d(t)c(t)]]c,(t)=d(t)c(t)c, (t)
the signal is integrated over the duration:
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q(t) =fm(t)dt
where a pulse duration of the spread spectrum sequence c(t) is T,, namely
Jbc(t)c,(t)dt = T,
and therefore, q(t) can be expressed as:
fT, when d(V=1 -Twhen dMt=-1
5. Analysis of a bit error rate in the step 4 Each sub-block of GFDM is the same as to the number of sub-carriers therein, and thus it has the same bit error performance. With a chaotic spread spectrum sequence taken as an example to analyze the bit error rate performance, since a chaotic sequence has very strong autocorrelation and different chaotic sequences are
mutually independent, there is E[RR,]=0 between different chaotic sequences;
besides, although a chaotic sequence has the characteristic of being noise-like, it is also independent of Gaussian white noise, and a chaotic sequence's mean value is 0, with a variance of 1.
for the demodulated signal dn, at the receiving end, an information
sequence corresponding to it is represented by SI, and the corresponding chaotic
sequence is represented by Ck, ,
S =[dic,+no,d1c +n1,---,dc-,_+n,_
=d1 G +w1
C =[c +n, c + n,---, c,_ +n, =G +w2
where ni and n are mutually independent Gaussian white noises, and they
are noises at the i-th data after spread spectrum in the received signal dnkiand at
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the spread spectrum code, respectively, wi and w2 represent sets of the two
noises, and '=c,,.c,_A is a set of the spread spectrum sequences;
information on the k-th subcarrier and the m-th subsymbol is expressed by
1. = S. x c.", and then the mean value and the variance are, respectively:
=+11=E(G., +w)(G.,+w 2)l=E[Gk +wG +w2G., +W1W2 E[dl"kIdk as noise's mean value is 0, with a variance of 1, the above equation can be simplified as
E (I / di=+1=E [G, =2 Ec = K-IE K
for the same reason, the variance is:
Var /d 1,=+1]=E G +W 1)2(Gk +W2)2 -E2 [(Gk +W)(Gk +W2)
=E(G + +w2+W2+ w+)G,+w
-E2 [Gk +WG,k +w2 G,,,k + Ww2
K-I EN0+2N2 K 4 since the structure of each subblock of GFDM is the same, its bit error rate
can be obtained based on the mean value and the variance:
BE 2 rl < 0 / d k=+1)+2 Pr~lk > k/d =-1)
K-1 E !erfcr E[lI~ d=+t1] 1 KI E1 2 2Var~iId =+1)) 2e2 E + 2 NO K 2
=erfc 2 y -2 2~~~ ~~ [(-K1 -j2
where erfc is an error function, erfc(x)= 2j e-"dp , and y is a
signal-to-noise ratio.
Our Ref: OF180851D/P/AU
A GFDM spread spectrum communication system performs GFDM modulation on N parallel signals on which spread spectrum has been performed, and in general, a number of parallel data is less than a number of subcarriers in an OFDM system. The GFDM-DS system transmits, in parallel, multiple data after direct spread spectrum, in underwater acoustic communications, the spread spectrum signals are limited by a bandwidth, and when the spread spectrum codes are relatively long, transmitting the signals and performing synchronization at the receiving end both require to take a lot of time. As compared with the prior art, the present invention has the following beneficial effects: realizing a GFDM spread spectrum underwater acoustic communication system for the first time, and verifying the system's performance through simulation and experimentation -- in experiments, a 5G multi-carrier spread spectrum underwater acoustic communication system based on a modulator structure of M=2 and K=29 achieved a bit error rate of 0.0119, and a 5G multi-carrier spread spectrum underwater acoustic communication system based on a modulator structure of M=29 and K=2 achieved error-free information transmission, which proves that the GFDM spread spectrum underwater acoustic communication system is a fire-new and efficient underwater acoustic communication system that can flexibly utilize a bandwidth of a transmission channel.
Figure 1: a schematic diagram of anti-interference of a spread spectrum system; Figure 2: a schematic diagram of multi-carrier time-domain spread spectrum; Figure 3: a schematic diagram of multi-carrier frequency-domain spread !5 spectrum; Figure 4: (a) a schematic diagram of a transmitting end of a GFDM spread spectrum underwater acoustic system, and (b) a schematic diagram of a receiving end of the GFDM spread spectrum underwater acoustic system; Figure 5: a comparison diagram of bit error rate performance of GFDM spread
Our Ref: OF180851D/P/AU
spectrum underwater acoustic communication systems with different filter banks and different modulation matrices; Figure 6: an impulse response of an experimental channel; and Figure 7: pictures of transmission and reception in an experiment: (a) a transmitted image, (b) a received image of a GFDM spread spectrum underwater acoustic communication system (M=2, and K=29), and (c) a received image of a GFDM spread spectrum underwater acoustic communication system (M=29, and K=2).
A spread spectrum communication technology is that, at a transmitting end, a spread spectrum sequence is utilized to perform spread spectrum processing on a transmitted signal to spread an original bandwidth occupied by the signal, and at a receiving end, despread processing is performed on the transmitted signal by adopting a correlation inspection method, with a noise signal in the transmission process being spread into a broadband signal; the principle and process of anti-multipath interference thereof are shown in Figure 1. The target signal can be extracted by a narrowband filtering method. Since an interference signal has no coherence, it causes little interference to the useful signal, and there is relatively high signal-to-noise ratio. Due to the correlation detection performed at the receiving end, even if the same type of signal is used for interference, it is difficult for the interference to work relatively greatly as the !0 code pattern of a pseudo-random sequence cannot be accurately obtained, and thus the system's anti-interference performance is effectively improved, which in turn reduces the system's bit error rate. Time-domain spread spectrum: a block diagram of multi-carrier time-domain spread spectrum transmission is as shown in Figure 2. At a transmitting end, !5 serial-to-parallel conversion is performed on a data signal, after that, spread spectrum codes distributed in a time domain are utilized to perform a spread spectrum operation on each data symbol individually, and finally each data after spread spectrum is modulated by using a subcarrier of a different frequency, and ultimately multi-carrier time-domain spread spectrum is realized. It can be seen from the figure that all chips of
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each transmitted data after time-domain spread spectrum are transmitted on one subcarrier, which indicates that the system has a relatively poor ability to resist frequency-selective fading, while a length of the chips of each transmitted data after time-domain spread spectrum is the same as a length of the spread spectrum codes, and therefore the system has a relatively strong ability to resist time-selective fading. A schematic diagram of multi-carrier frequency-domain spread spectrum is as shown in Figure 3: transmitted data symbols are spread respectively using spreading codes distributed in a frequency domain. After spread spectrum, for each data symbol, L chips are obtained, and these L chips are modulated respectively on subcarriers whose number is the same as the number of the chips. In this spread spectrum mode, in a time domain, a duration of the transmitted data and a duration of the OFDM symbol are the same. In this section, a communication system based on multi-carrier time-domain spread spectrum is studied with respect to a multi-carrier system. A GFDM-DS system performs GFDM modulation on N parallel signals on which spread spectrum has been performed, and in general, a number of parallel data is less than a number of subcarriers in an OFDM system. The GFDM-DS system transmits, in parallel, multiple data after direct spread spectrum, in underwater acoustic communications, the spread spectrum signals are limited by a bandwidth, and when the spread spectrum codes are relatively long, transmitting the signals and performing !0 synchronization at the receiving end both require to take a lot of time, and the receiving end of the GFDM-DS spread spectrum system adopts the method introduced above, as shown in Figure 4 (b). Figure 5 shows BER performance of RC and RRC filter banks with different modulation matrices in the case of Gaussian white noise and in a multipath channel, !5 wherein two selected modulation matrices are as below: a number of subblocks M=2 and a number of subcarriers K=29; and, a number of subblocks M=29, and a number of subcarriers K=2. It can be seen from the figure that the bit error rate performance in the case of the number of subcarriers K=2 is significantly better than that of the modulation matrix with the number of subcarriers K=29, whether it is in the Gaussian white noise channel or the multipath channel.
Our Ref: OF180851D/P/AU
The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. An experiment was performed in an anechoic pool in May 2017, the pool having a length of 25 meters, a width of 15 meters, and a height of 10 meters, anechoic wedges being arranged around the pool. A transmitting transducer, having a working frequency band of 3-8kHz, was deployed at a depth of 3 meters, a standard hydrophone was adopted as a receiving hydrophone, which was deployed at a depth of 3 meters, and a horizontal distance between the transmitting transducer and the receiving hydrophone was 5 meters. The actually measured impulse response of a channel was as shown in Figure 6, maximum multipath time delay being about 5.5ms, a sampling frequency being 48kHz, and a situation of roll-off parameter(s) in two types of spread spectrum systems in which a RC filter is combined with a RRC filter bank being taken as an example to perform a comparison of experimental results. Transmission and reception of the GFDM-DS and GFDM-CSS spread spectrum underwater acoustic communication systems are performed by adopting the RC filter and the RRC filter bank. The present invention comprises the following steps: step 1: at a transmitting end, encoding binary source data, and performing a spread spectrum operation on the encoded serial data by using a spread spectrum !0 sequence, Figure 4 (a) is a principle diagram of a transmitting end and a receiving end for spreading spectrum and despreading of a GFDM spread spectrum system, in which time-domain spread spectrum is performed on data undergoing parallel-to-serial conversion by using the spread spectrum sequence, after that, GFDM modulation is !5 performed according to a GFDM modulation method to obtain modulated data, and a cyclic prefix is added to obtain transmitted data. At the receiving end, the received signals are synchronized firstly, on the premise of ensuring correct synchronization, the synchronized signals are demodulated and despread, and after that, the obtained signals are integrated over a duration and judged to obtain data estimated by the
receiving end, where the transmitted data is expressed by d(t ), and then a spread
Our Ref.: OF180851D/P/AU
spectrum process can be expressed as below:
d(t)= d(n)g(t-nT,)
c(t)= c(n)p(t-nT)
where, values of d(n) and a pseudo-random sequence c(n) used for
spreading spectrum are 1 or -1, g(t) and p(t) are rectangular pulses of a unit
amplitude with durations TIand TI, respectively, N represents a length of the spread
spectrum sequence, in general, T=NTc , and a sequence after spread spectrum p(t)
is:
p(t)=d(t)c(t).
step 2: performing GFDM modulation on data after spread spectrum, and after that, adding a cyclic prefix to the modulated data to obtain transmitted data, wherein a modulation process can be expressed as below:
data after GFDM modulation is y(t) , g[.] is used to express a GFDM
modulation process, and then:
y(t)=g[p(t)] = g[d(t)c(t)]
and a discrete spread spectrum signal for GFDM adopting a BPSK modulation mode can be expressed as:
SMc-DS (t)N 1G [i ck[]pT(t-iT -jT)cos[2;r(f-+kAf')t] k=O P=-M j=0
where d[i] is data on a k-th subcarrier,Ck[j] represents a spread spectrum
sequence which is correspondingly multiplied by d[i], Nc represents a number of
W subcarriers,and Af'=1/T is a subcarrier spacing.
step 3: at a receiving end, performing synchronization and GFDM demodulation on the data, after the modulated signals pass through an underwater acoustic channel; at the receiving end, on the premise of correct synchronization, the GFDM
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demodulation is performed on the received signal y(t), g-'[-] is used to represent the
GFDM demodulation process, and then a signal r(t) to bedespread can be expressed
as:
r(t)=g-'[y'(t)]
step 4: despreading the demodulated data, and integrating the obtained signals over a duration and making a judgement to obtain data estimated by the receiving end, wherein a despreading process is as below:
r(t) is despread by utilizing a spread spectrum sequence c,(t) which is
generated locally and the same as that at the transmitting end: 1[y'(t)]C(t) M(t)=r(t)c,(t)=g-
= g 1 [g[d(t)c(t)]]c,(t)=d(t)c(t)c,(t) the signal is integrated over the duration:
q(t) = m(t)dt
where a pulse duration of the spread spectrum sequence c(t) is T, namely
fc(t)c, (t)dt = T and therefore, q(t) can be expressed as:
T, when dWt)=1 --T, when d(t)=-1
Figure 7: (a) is a picture of transmission in an experiment, and (b) is a received image in the case of a modulator structure of M=2 and K=29, a bit error rate of which is 0.0119. (c) is a received image in the case of a modulator structure of M=29 and K=2, a !0 bit error rate of which is 0. According to the experimental results, in the case where a transmitted signal occupies the same bandwidth and channel resources are divided equally by subcarriers included in different modulation matrix structures, as a number of the subcarriers increases, performance of the GFDM spread spectrum system decreases, because when the number of the subcarriers is large, for a non-orthogonal multi-carrier
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technology, main lobe overlap between various subcarriers is serious, which in turn leads to a decrease in bit error performance. Therefore, on the one hand, it is required to design a reasonable subcarrier structure to avoid inter-carrier interference, and on the other hand, it is required to research and design a reasonable channel estimation method for the GFDM's modulator structure to remove influence of the channel on the system and improve performance of the GFDM spread spectrum system. The specific instances described above are only preferred examples of the present invention and do not limit the present invention in any form, and any simple modification and equivalent change made to the above examples according to the technical essence of the present invention falls within the protection scope of the present invention.
Claims (6)
1. A 5G multi-carrier spread spectrum underwater acoustic communication method, characterized in that the method comprises the following steps:
step 1: at a transmitting end, encoding source data , and performing GFDM
modulation on the encoded data c, where X represents a GFDM modulated signal
step 2: adding a cyclic prefix to the GFDM modulated signal;
if To represents a sub-symbol period and Te represents a cyclic prefix length, then a symbol period of one GFDM is:
TGFDM =c + M -TO which uses fewer cyclic prefixes than an OFDM technology, and thus has higher spectrum efficiency; step 3: after the modulated signal passes through an underwater acoustic channel, at a receiving end, synchronizing the data, performing underwater acoustic channel estimation and equalization, and then performing GFDM demodulation; and
step 4: demapping and decoding the GFDM demodulated signal.
2. The 5G multi-carrier spread spectrum underwater acoustic communication method according to claim 1, characterized in that: a GFDM modulation process in the !0 step 1 is as below: T d , ,d->
a modulated data vector d can be expressed as ,- , where
.= a " and dkm represents data transmitted on a k-th sub-carrier and a
m-th sub-symbol, and an impulse response corresponding to the data is:
gkm[n]= g[(n- mK)modN]-exp -j27k-n K]
where n represents a sampling point, and it can be seen from the above equation
that each I nIis obtained by subjecting a prototype filter to transformation of
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different time and frequency;
the transmitted data (Q[n]T can be expressed as:
4o =[A]KI K-I1M-1
x[n]=I gk,.[n].dk,n = 0,--- ,N -1
let Z. - (k,m ) , the equation (4) can be written as
i=Ad
a dimension of a modulation matrix A in GFDM is KM x KM (a number of the
sub-carriers is K, and a number of the sub-symbols is M), which can be expressed as:
A= '' gk, -10go, 1 .. KlM -1)
where Zk,m is generated by shiftinggo,o in a time domain and in a frequency
domain, and k,° =[Ain 2 and ° [A]n,K1 are generated by cyclic shifting of
90,0 [A]" by analogy.
3. The 5G multi-carrier spread spectrum underwater acoustic communication method according to claim 1, characterized in that: methods for selecting the parameter K in the dimension of the GFDM modulation matrix A in the step 1 are classified into two categories, wherein the first category is as below: when the channel conditions are good, a value of the parameter K is first set based on an available bandwidth of the underwater acoustic channel, available bandwidth resources are equally allocated by the number of sub-carriers, the parameter K, and !0 further a value of the number of sub-blocks, the parameter M, is inferred from the data
length N and the relational expression K xM=N.
4. The 5G multi-carrier spread spectrum underwater acoustic communication method according to claim 1, characterized in that: methods for selecting the parameter
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K in the dimension of the GFDM modulation matrix A in the step 1 are classified into two categories, wherein the second category is as below: when the channel conditions are not good or it is desired to use scattered spectrum information, an adaptive method is used to flexibly set the number of sub-carriers, the parameter K, based on a limited range of the channel's bandwidth frequency, and a value of the number of subblocks, the parameter M, is inferred from the data length N
and the relational expression K x M=N.
5. The 5G multi-carrier spread spectrum underwater acoustic communication method according to claim 1, characterized in that: a transmission process through the underwater acoustic channel after the GFDM demodulation in the step 3 is as below: after passing through the underwater acoustic channel, the received signal is:
=Hi+ f
where represents the received signal, X represents the transmitted signal, a transmission function of the underwater acoustic channel is represented by H, and on the assumption that in the case where the presence of Gaussian white noise is
considered, the Gaussian white noise is represented by 4; at the receiving end, after
time-frequency synchronization, the cyclic prefix is removed;
after channel estimation and equalization, the received signal is Z, which can be O expressed as:
i= H9+= H-'HA + H-'f= Ad+
6. The 5G multi-carrier spread spectrum underwater acoustic communication method according to claim 1, characterized in that: a GFDM demodulation process in the step 3 is as below:
d Bi
a dimension of a matrix B used for demodulation is the same as that of the modulation matrix A, and when the receiving end adopts a different equalization mode,
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the matrix B is in a different form -- with three modes of matched filtering, zero-forcing equalization and minimum mean square error criterion taken as an example, in these
equalization modes, the forms of the matrix B are expressed by BMF, BZF, and BMMSE respectively, which can be respectively expressed as:
BMF AH
BZF=A-'
B ~SEI+AHAA n2 H BMMSE
22 where variances of the noise and signal are UZ and Ud, respectively, and the
estimated transmission data b is obtained after final demodulation.
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| CN101534269B (en) * | 2009-04-14 | 2012-05-09 | 华南理工大学 | Underwater sound communication system |
| EP2916506B1 (en) * | 2014-03-07 | 2019-07-31 | Vodafone GmbH | Walsh-Hadamard transformed GFDM radio transmission |
| CN104753638B (en) * | 2015-03-02 | 2017-11-28 | 西安理工大学 | A kind of chaos spread spectrum underwater acoustic communication method |
| CN108933749B (en) * | 2018-06-08 | 2021-01-15 | 天津大学 | Aliasing generalized frequency division multiplexing multi-carrier modulation system |
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