WO2016155244A1

WO2016155244A1 - Signal processing method and wireless signal transceiving device

Info

Publication number: WO2016155244A1
Application number: PCT/CN2015/089266
Authority: WO
Inventors: Yuechao GUO
Original assignee: Lenovo Beijing Ltd
Current assignee: Lenovo Beijing Ltd
Priority date: 2015-04-01
Filing date: 2015-09-09
Publication date: 2016-10-06
Anticipated expiration: 2017-10-01
Also published as: CN106161315B; CN106161315A

Abstract

The present disclosure relates to a signal processing method and a wireless signal transceiving device, the method comprises: modulating a to-be-transmitted baseband signal to at least one subcarrie; determining, for the at least one subcarrier to which the to-be-transmitted baseband signal is modulated, a shaping filter parameter and a spectrum spreading coefficient; performing time domain and frequency domain shift-processing on the shaping filter parameter; filtering the at least one subcarrier based on the shift-processed shaping filter parameter so as to obtain first modulated subcarriers; spectrum-spreading the first modulated subcarriers based on the spectrum spreading coefficient so as to obtain second modulated subcarriers; and transmitting data based on the second modulated subcarriers.

Description

SIGNAL PROCESSING METHOD AND WIRELESS SIGNAL TRANSCEIVING DEVICE

TECHNICAL FIELD

The present disclosure relates to the field of signal processing technique, and more particularly, to a signal processing method and a wireless signal transceiving device.

BACKGROUND

The 5G mobile communication system puts forward higher requirements for air interface technology whose basis is waveform technology. When the subframe data modulated and transmitted later through GFDM waveform, there is non-orthogonality between subcarriers, i.e., there is Inter-Carrier Interference (ICI) . And transmitting data through GFDM may cause a very high complexity of system processing. How to reduce ICI and provide lower processing complexity become technical problems.

SUMMARY

Embodiments of the present disclosure provide a signal processing method and a wireless signal transceiving device.

The technical solutions in the embodiments of the present disclosure are implemented as below.

A signal processing method applied to a wireless signal transceiving device, the method comprising:

modulating a to-be-transmitted baseband signal to at least one subcarrier；

determining, for the at least one subcarrier to which the to-be-transmitted baseband signal is modulated, a shaping filter parameter and a spectrum spreading coefficient；

performing time domain and frequency domain shift-processing on the shaping filter parameter；

filtering the at least one subcarrier based on the shift-processed shaping filter parameter so as to obtain first modulated subcarriers；

spectrum-spreading the first modulated subcarriers based on the spectrum spreading coefficient so as to obtain second modulated subcarriers； and

transmitting data based on the second modulated subcarriers.

A wireless signal transceiving device, comprising a modulating unit, a first determining unit, a shifting unit, a first filtering unit, a spreading unit, and a transmitting unit, wherein:

the modulating unit is for modulating a to-be-transmitted baseband signal to at least one subcarrier；

the first determining unit is for determining, for the at least one subcarrier to which the to-be-transmitted baseband signal is modulated, a shaping filter parameter and a spectrum spreading coefficient；

the shifting unit is for performing time domain and frequency domain shift-processing on the shaping filter parameter；

the filtering unit is for filtering the at least one subcarrier based on the shift-processed shaping filter parameter so as to obtain first modulated subcarriers；

the spreading unit is for spectrum-spreading the first modulated subcarriers based on the spectrum spreading coefficient so as to obtain second modulated subcarriers； and

the transmitting unit is for transmitting data based on the second modulated subcarriers.

In the embodiments of the present disclosure, by means of spreading an interval between subcarriers in the original GFDM system, Power Spectrum Density (PSD) of each subcarrier data channel after being filter-shaped does not overlap at all, thereby ICI interference is eliminated, and in order to improve carrier utilization, by means of designing parameters for FTN modulation compression, bandwidth utilization is improved, a decline of bandwidth utilization of the system caused by spreading the interval between subcarriers in GFDM is counteracted. In the embodiments of the present disclosure, the above described technique of spreading the interval between subcarriers and compressing carrier frequency causes a relatively high complexity of signal transmission, therefore, when filtering the carriers, the spreading coefficient of the frequency domain filtering is usually set to greatly reduce complexity of the filtered signal. The embodiments of the present disclosure reduce interference between carriers without lowering carrier utilization, and control the complexity of wireless signal processing within a reasonable range.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart of a signal processing method in a first embodiment of the present disclosure；

FIG. 2 is a flowchart of a signal processing method in a second embodiment of the present disclosure；

FIG. 3 is a schematic diagram of principle of a wireless signal transmitter according to an embodiment of the present disclosure；

FIG. 4 is a flowchart of a signal processing method in a third embodiment of the present disclosure；

FIG. 5 is another schematic diagram of principle of a wireless signal transmitter according to an embodiment of the present disclosure； and

FIG. 6 is a schematic diagram of component structure of a wireless signal transceiving device according to an embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Hereinafter, in order to more comprehensively understand the features and technical content of the present disclosure, some embodiments will be described with reference to the accompanying drawings, the drawings are for making reference and illustrating, rather than making limitations to the present disclosure.

FIG. 1 is a flowchart of a signal processing method in a first embodiment of the present disclosure, as shown in FIG. 1, the signal processing method is applied to a wireless signal transceiving device in this example. In the embodiment of the present disclosure, the wireless signal transceiving device may be an antenna system applicable to a base station, a mobile terminal or to a wireless transceiving device such as a wireless router, a relay station and so on. The signal processing method comprises the following steps.

Step 101, modulating a to-be-transmitted baseband signal to at least one subcarrier.

In the embodiment of the present disclosure, a to-be-transmitted baseband signal is obtained, and modulated to a corresponding subcarrier.

Step 102, determining, for the at least one subcarrier to which the to-be-transmitted baseband signal is modulated, a shaping filter parameter and a spectrum spreading coefficient.

In the embodiment of the present disclosure, a GFDM signal discrete mathematical model can be expressed as:

It is supposed that s (k, m) is a complex expression of a signal which is already modulated carrying information, the following matrix with K×M order represents a set of modulated complex signals within one subframe:

The subcarrier shaping filter can select SINC function, , a shaping filter on each subcarrier is designed to obtain a shaping filter parameter g (n) and a spectrum spreading coefficient (roll-off factor) a.

Wherein,

g(n) represents a discrete sequence of sub-carrier shaping filter；

a represents a roll-off factor (spectrum spreading coefficient) of g (n) .

Step 103, performing time domain and frequency domain shift-processing on the shaping filter parameter.

In particular, it is supposed that m (m＝0, 1, 2 ... M-1) and k (k＝0, 1, 2 ... K-1) indicate a slot index within one subframe and an index of subcarriers within a predetermined bandwidth, respectively. Corresponding to each time slot at each subcarrier, time domain and frequency domain shift-processing are performed on g (n) . The expression of g (n) after the shift is

Step 104, filtering the at least one subcarrier based on the shift-processed shaping filter parameter so as to obtain first modulated subcarriers.

K≤N, 0≤n≤NM (1)

In this case, K subcarriers are obtained.

Step 105, spectrum-spreading the first modulated subcarriers based on the spectrum spreading coefficient so as to obtain second modulated subcarriers, and transmitting data on the second modulated subcarriers.

After the subcarrier baseband prototype filter is defined, then the roll-off factor a is further determined. And the interval between subcarriers is spread as (1+a) times, that is, the spread interval between subcarriers becomes F_f, meanwhile K_f subcarriers can be accommodated under the pre-designed system bandwidth.

f_gf＝ (1+a) f_c

Selecting appropriately a total bandwidth fc of the system and the value of a to make the number of spread subcarriers as an integer, which eliminates the overlap between spread signals, also the subcarriers, which are completely orthogonal. So ICI interference could be completely eliminated.

FIG. 2 is a flowchart of a signal processing method in a second embodiment of the present disclosure. As shown in FIG. 2, the signal processing method is applied to a wireless signal transceiving device in this example. The wireless signal transceiving device may be an antenna system applicable to a base station, a mobile terminal or to a wireless transceiving device such as a wireless router, a relay station and so on. Comparing to the first embodiment, this embodiment further comprises the following steps before transmitting data.

Step 206, determining, for the second modulated subcarriers, a time domain compression coefficient based on the spectrum spreading coefficient.

It is designed that the FTN (First Than Nquist) time domain compression coefficient on each subcarrier is r, 0<r<1.

While the symbol cycle on the subcarriers is changed into T_gf, by means of artificially introducing ISI, the number of time slots that can be accommodated within each subcarrier in each frame is M_gf.

Relationship between respective coefficients is as follows:

In the embodiment of the present disclosure, in other words, a reciprocal of a sum of the spectrum spreading coefficient and one is regarded as the time domain compression coefficient r.

Step 207, performing time domain compression on the second modulated subcarriers based on the time domain compression coefficient, so as to obtain third modulated subcarriers； transmitting data with the third modulated subcarriers.

The time domain compression is performed to decrease an interval between the second modulated subcarriers.

The modulated data (K×M matrix) within one subframe of the original GFDM is again mapped as a new matrix K_gf×M_gf, it is supposed that s_gf (k, m) indicates one already-modulated complex symbol within the set, then it is obtained:

That is, information amount transmitted within a unit subframe does not change.

And g (n) is the pulse shaping filter, N is an upstream sampling times of prototype filter g (n) , the value of N in the new waveform GFDM-FTN after the transform maintains unchanged, the transmitted signal in GFDM-FTN is represented as:

K_gf≤rN, 0≤n≤NM (NM_gf/r＝NM) (2)

The above formula is a to-be-transmitted signal on which time domain compression has been performed, a transmitter structure directly implemented in time domain by the GFDM-FTN signal can be determined from the above formula, as shown in FIG. 3.

FIG. 4 is a flowchart of a signal processing method in a third embodiment of the present disclosure, as shown in FIG. 4, the signal processing method is applied to a wireless signal transceiving device in this example. In the embodiment of the present disclosure, the wireless signal transceiving device may be an antenna system applicable to a base station, a mobile terminal or to a wireless transceiving device such as a wireless router, a relay station and so on. The signal processing method further comprises the following steps.

Step 401 to step 403 are same as the step 101 to step 103 in FIG. 1.

Step 404, setting a spreading coefficient for a frequency domain filter parameter in the shaping filter to spread the frequency domain response of the shaping filter parameter.

Step 405, performing Fourier transform on the at least one subcarrier, to transform the at least one subcarrier into a frequency domain signal.

Step 406, filtering the frequency domain signal based on the spreading coefficient and the shift-processed shaping filter parameter, performing inverse Fourier transform on a filtered signal to obtain the first modulated subcarriers.

Step 407, spectrum-spreading the first modulated subcarriers based on the spectrum spreading coefficient so as to obtain second modulated subcarriers.

In the embodiment of the present disclosure, based on the subcarrier baseband prototype filter is completed, the roll-off factor a is further determined. And the interval between subcarriers is spread as (1+a) times, that is, the spread interval between subcarriers becomes f_gf, meanwhile K_gf subcarriers can be accommodated under the pre-designed system bandwidth.

f_gf＝ (1+a) f_c

The number of spread subcarriers is also made an integer by appropriately designing a total bandwidth fc of the system and the value of a. There is no overlap between spread signals, the subcarriers, which are completely orthogonal, so it is possible to completely eliminate ICI interference.

Step 408, determining, for the second modulated subcarriers, a time domain compression coefficient based on the spectrum spreading coefficient.

It is designed that the FTB time domain compression coefficient on each subcarrier is r, 0<r<1.

Relationship between respective coefficients is as follows:

In this case, it can be proved that after the above processing, a maximum bandwidth utilization under Nquist theory can be achieved. It is proved by the following reasoning:

when

is optimal, the maximum channel capability under Nquist theory can be reached.

Step 409, performing time domain compression on the second modulated subcarriers based on the time domain compression coefficient, so as to obtain third modulated subcarriers； transmitting data with the third modulated subcarriers.

Data within one GFDM-FNT subframe is represented by matrix K_gf×M_gf, it is supposed that s_gf (k, m) indicates one already-modulated complex symbol within the set, then it is obtained:

K_gf≤rN, 0≤n≤NM (NM_gf/r＝NM)

Usually, complexity is determined based on the number of complex multipliers required during an implementing process, considering the discrete mathematical models of GFDM-FTN signal and OFDM signal, complexity of direct implementation of the two signals can be obtained as:

GFDM-FTN：

The OFDM symbol is represented as:

During the modulated complex signal baseband shaping on subcarriers, linear convolution is usually replaced with circular convolution, the above transmitted signal x_gf (n) is transformed as:

While g (n) is the prototype filter,

indicates an offset position of the corresponding subcarriers on the frequency domain, s_f (k, m) δ (n-rmN) indicates a modulated complex symbol data stream after upstream sampling is performed on each subcarrier. According to the equivalence principle between time domain and frequency domain, the above transmitted signal is equivalent to

In the above formulas, DFT_NM (.) and IDFT_NM (.) indicate discrete Fourier at NM points and discrete Fourier inverse transform, respectively. Their meanings are provided as below:

The result of

FFT transform is equivalent to

which may be understood as the shift of the prototype filter on the frequency domain.

is equivalent to that first

is performed, and then the obtained result is repeated rN times with M_f as a cycle.

DFT_NM (g ( <n> _NM-1) ) indicates the frequency domain transform of the prototype filter.

It can be known from the above transform formulas that, g (n) disperses a spectrum distribution of NM points after being Fourier transformed, most are zero, ideally, g (n) (filter g (n) in a cyclic structure) is effective in the frequency domain after going through NM points FFT transform, the number of non-zero data is (1+a) M＝M_gf.

It is supposed that L is the spreading coefficient of the frequency domain filtering, then 1≤L≤rN. A multiplication length of the frequency domain filtering on each subcarrier is changed into LM_gf, then M_gf≤LM_gf≤rNM_gf＝NM, this case corresponds to the structure of the simplified transmitter, as shown in FIG. 5.

The value of L can be selected according to the size of the designed spreading coefficient a of the prototype pulse shaping filter g (n) , for example, when the value of a is relatively small, the spectrum spreading is relatively small, a relatively small value can be taken for L, and vice versa.

Based on analysis, it can be obtained that the complexity realized in this case (based on FFT) is:

Based on the subframe structure in the current LTE standard, as shown in the following Table 1, respective data parameters in one subframe are as below:

Parameter	Value	Description
Parameter	Value	Description	B	20 MHz	Channel bandwidth
BSC	15 kHz	Interval between subcarriers	B	20 MHz	Channel bandwidth
BSC	15 kHz	Interval between subcarriers	N	2048	Maximum number of subcarriers
K	1200	Number of effective subcarriers	N	2048	Maximum number of subcarriers
K	1200	Number of effective subcarriers	Filter	RRC	Shaping filter
a	0.25	Roll-off factor	Filter	RRC	Shaping filter
a	0.25	Roll-off factor	r	0.8	FTN compression coefficient
BSC_gf	18.75kHz	Spread interval between subcarriers	r	0.8	FTN compression coefficient
BSC_gf	18.75kHz	Spread interval between subcarriers	K_gf	960	Number of spread subcarriers
M_gf	{15, 17.5}	Number of time slots in subframes after time domain compression	K_gf	960	Number of spread subcarriers
M_gf	{15, 17.5}		L
	1≤L≤rN＝1638.4	Spreading coefficient of frequency domain multiplication	L

Table 1

One TTI (Transmission time interval) in the LTE system includes 12 or 14 OFDM symbols, that is, M＝12, 14.

FIG. 6 is a schematic diagram of component structure of a wireless signal transceiving device according to an embodiment of the present disclosure, as shown in FIG. 6, the wireless signal transceiving device comprises a modulating unit 60, a first determining unit 61, a shifting unit 62, a first filtering unit 63, a spreading unit 64, and a transmitting unit 65, wherein:

the modulating unit 60 is for modulating a to-be-transmitted baseband signal to at least one subcarrier；

the first determining unit 61 is for determining, for the at least one subcarrier to which the to-be-transmitted baseband signal is modulated, a shaping filter parameter and a spectrum spreading coefficient；

the shifting unit 62 is for performing time domain and frequency domain shift-processing on the shaping filter parameter；

the filtering unit 63 is for filtering the at least one subcarrier based on the shift-processed shaping filter parameter so as to obtain first modulated subcarriers；

the spreading unit 64 is for spectrum-spreading the first modulated subcarriers based on the spectrum spreading coefficient so as to obtain second modulated subcarriers； and

the transmitting unit 65 is for transmitting data based on the second modulated subcarriers.

Based on the wireless signal transceiving device shown in FIG. 6, the wireless signal transceiving device in the embodiment of the present disclosure further comprises a second determining unit (not shown in FIG. 6) and a compressing unit (not shown in FIG. 6) , in which:

the second determining unit is for determining, for the second modulated subcarriers, a time domain compression coefficient based on the spectrum spreading coefficient；

the compressing unit is for performing time domain compression on the second modulated subcarriers based on the time domain compression coefficient, so as to obtain third modulated subcarriers； the time domain compression is performed to decrease an interval between the second modulated subcarriers；

the transmitting unit is further for transmitting data with the third modulated subcarriers.

The second determining unit described above is further for selecting a reciprocal of a sum of the spectrum spreading coefficient and one as the time domain compression coefficient.

Based on the wireless signal transceiving device shown in FIG. 6, the wireless signal transceiving device in the embodiment of the present disclosure further comprises a setting unit (not shown in FIG. 6) , a first transforming unit (not shown in FIG. 6) , a second filtering unit (not shown in FIG. 6) , and a second transforming unit (not shown in FIG. 6) , wherein:

the setting unit is for setting a spreading coefficient for a frequency domain filter parameter in the shaping filter to spread a frequency band of the shaping filter parameter；

the first transforming unit is for performing Fourier transform on the at least one subcarrier, to transform the at least one subcarrier into a frequency domain signal；

the second filtering unit is for filtering the frequency domain signal based on the spreading coefficient and the shift-processed shaping filter parameter； and

the second transforming unit is for performing inverse Fourier transform on a filtered signal to obtain the first modulated subcarriers.

In the embodiment of the present disclosure, the spectrum spreading coefficient and the spectrum spreading coefficient are in a positive correlation.

As will be appreciated by those skilled in the art, the functions achieved by respective units in the wireless signal transceiving device shown in FIG. 6 may be understood by making reference to the signal processing method described above and the related description of the embodiments thereof. The functions of the respective units in wireless signal transceiving device in FIG. 6 may be implemented by programs running on a processor, and may also be implemented by specific logic circuits.

In case of no conflict, the technical solution in the embodiments described above may be combined.

In the several embodiments provided by present disclosure, it should be understood that the device/apparatus and methods disclosed therein may also be implemented by other manners. The above described device/apparatus embodiments are merely illustrative, for example, the unit division is only a logical function division, there may be other division manners in practical implementation, such as: a plurality of units or components may be combined or may be integrated into another system, or some features may be omitted or not executed. In addition, coupling, or direct coupling, or communicative connection between the shown or discussed respective components may be achieved through some interfaces, indirect coupling or communicative connection between devices or units may be electrical, mechanical, or other forms.

Units described above as separate members may be or may not be physically separated, components showed as units may be or may not be physical units； they may be located at one place or distributed to a plurality of network cells； it is possible to select some or all of the units therein to achieve the purpose of solutions in the embodiments according to the actual needs.

Further, respective functional units in the embodiments of the present disclosure may be all integrated in one processing unit and may also be separated as one unit each, or two or more units may also be integrated in one unit； the aforesaid integrated unit may be implemented in the form of hardware or in the form of hardware plus software functional unit.

As will be appreciated by those of ordinary skill in the art: all or part of the steps of the above method embodiments may be completed by instructing relevant hardware through programs, these programs may be stored in a computer readable storage medium, the steps included in the above method embodiments will be executed when the programs are executed； the aforesaid storage medium includes various mediums capable of storing program codes like a mobile storage device, a Read Only Memory (ROM) , a magnetic disk, or an optical disk.

Alternatively, the above integrated units of the present disclosure may also be stored in a computer readable storage medium when being implemented in the form of a software functional module and sold and used as an independent product. Based on such understanding, the substance or the part that contributes to the prior art of the technical solutions of embodiments of the present disclosure may be reflected in the form of a software product, the computer software product may be stored in a storage medium, and include several instructions for causing a computer apparatus (which may be a personal computer, a server, or a network device) to fully or partially perform the method described in the various embodiments of the present disclosure. The aforesaid storage medium includes various mediums capable of storing program codes like a mobile storage device, a Read Only Memory (ROM) , a magnetic disk, or an optical disk.

The protection scope of the present disclosure is not limited to the above, modifications or replacements that are easily conceivable for those skilled in the art within the technique range disclosed in the present disclosure should all fall into the protection scope of the present disclosure.

The above described are only preferred embodiments of the present disclosure, which are not intended to limit the protection scope of the present disclosure.

Claims

A signal processing method applied to a wireless signal transceiving device, the method comprising:

modulating a to-be-transmitted baseband signal to at least one subcarrier；

determining, for the at least one subcarrier to which the to-be-transmitted baseband signal is modulated, a shaping filter parameter and a spectrum spreading coefficient；

performing time domain and frequency domain shift-processing on the shaping filter parameter；

filtering the at least one subcarrier based on the shift-processed shaping filter parameter to obtain first modulated subcarriers；

spectrum-spreading the first modulated subcarriers based on the spectrum spreading coefficient to obtain second modulated subcarriers； and

transmitting data based on the second modulated subcarriers.
The method as claimed in claim 1, wherein transmitting data based on the second modulated subcarriers comprises:

determining, for the second modulated subcarriers, a time domain compression coefficient based on the spectrum spreading coefficient；

performing time domain compression on the second modulated subcarriers based on the time domain compression coefficient to obtain third modulated subcarriers；

transmitting data with the third modulated subcarriers.
The method as claimed in claim 2, wherein determining, for the second modulated subcarriers, a time domain compression coefficient based on the spectrum spreading coefficient comprises:

selecting a reciprocal of a sum of the spectrum spreading coefficient and one as the time domain compression coefficient.
The method as claimed in claim 1, wherein filtering the at least one subcarrier based on the shift-processed shaping filter parameter to obtain first modulated subcarriers comprises:

setting a spreading coefficient for a frequency domain filter parameter in the shaping filter to spread a frequency band of the shaping filter parameter；

performing Fourier transform on the at least one subcarrier, to transform the at least one subcarrier into a frequency domain signal；

filtering the frequency domain signal based on the spreading coefficient and the shift-processed shaping filter parameter, performing inverse Fourier transform on a filtered signal to obtain the first modulated subcarriers.
The method as claimed in claim 4, wherein the spreading coefficient and the spectrum spreading coefficient are in a positive correlation.
A wireless signal transceiving device, comprising a modulating unit, a first determining unit, a shifting unit, a first filtering unit, a spreading unit, and a transmitting unit, wherein:

the modulating unit is for modulating a to-be-transmitted baseband signal to at least one subcarrier；

the first determining unit is for determining, for the at least one subcarrier to which the to-be-transmitted baseband signal is modulated, a shaping filter parameter and a spectrum spreading coefficient；

the shifting unit is for performing time domain and frequency domain shift-processing on the shaping filter parameter；

the filtering unit is for filtering the at least one subcarrier based on the shift-processed shaping filter parameter so as to obtain first modulated subcarriers；

the spreading unit is for spectrum-spreading the first modulated subcarriers based on the spectrum spreading coefficient so as to obtain second modulated subcarriers； and

the transmitting unit is for transmitting data based on the second modulated subcarriers.
The device as claimed in claim 6, wherein the device further comprises a second determining unit and a compressing unit, in which:

the second determining unit is for determining, for the second modulated subcarriers, a time domain compression coefficient based on the spectrum spreading coefficient；

the compressing unit is for performing time domain compression on the second modulated subcarriers based on the time domain compression coefficient, so as to obtain third modulated subcarriers；

the transmitting unit is further for transmitting data with the third modulated subcarriers.
The device as claimed in claim 7, wherein the second determining unit is further for selecting a reciprocal of a sum of the spectrum spreading coefficient and one as the time domain compression coefficient.
The device as claimed in claim 6, further comprising a setting unit, a first transforming unit, a second filtering unit, and a second transforming unit, wherein:

the setting unit is for setting a spreading coefficient for a frequency domain filter parameter in the shaping filter to spread a frequency band of the shaping filter parameter；

the first transforming unit is for performing Fourier transform on the at least one subcarrier, to transform the at least one subcarrier into a frequency domain signal；

the second filtering unit is for filtering the frequency domain signal based on the spreading coefficient and the shift-processed shaping filter parameter； and

the second transforming unit is for performing inverse Fourier transform on a filtered signal to obtain the first modulated subcarriers.
The device as claimed in claim 9, the spreading coefficient and the spectrum spreading coefficient are in a positive correlation.