CN101729462A - Method for comprehensively measuring and calculating carrier to interference plus noise ratio in orthogonal frequency division multiplexing - Google Patents

Method for comprehensively measuring and calculating carrier to interference plus noise ratio in orthogonal frequency division multiplexing Download PDF

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CN101729462A
CN101729462A CN 200810216976 CN200810216976A CN101729462A CN 101729462 A CN101729462 A CN 101729462A CN 200810216976 CN200810216976 CN 200810216976 CN 200810216976 A CN200810216976 A CN 200810216976A CN 101729462 A CN101729462 A CN 101729462A
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reference symbol
unit group
resource unit
noise ratio
carrier
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CN101729462B (en
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张磊
赵路
郭阳
王晨
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ZTE Corp
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Abstract

The invention discloses a method for comprehensively measuring and calculating carrier to interference plus noise ratio in orthogonal frequency division multiplexing, which comprises the following steps: measuring reference symbols in a resource block, using the reference symbols to constitute a reference symbol resource unit group and calculating the signal channel response value thereof; calculating signal power which corresponds to the reference symbol resource unit group according to the signal channel response value; measuring total power of the reference symbol resource unit group which corresponds to the signal channel reference value and obtaining the corresponding interference plus noise power; and calculating the carrier to interference plus noise ratio according to the ratio of the sum of a plurality of signal powers of the reference symbol resource unit group to the sum of a plurality of interference plus noise powers of the reference symbol resource unit group. The method processes the interference plus noise powers of the reference symbol signals received on the adjacent reference symbol resource units, thereby overcoming the shortcoming of inaccurate measurement and calculation of the carrier to interference plus noise ratio caused by frequency selective fading and signal channel time variation and solving the problem that the measurement and the calculation of the carrier to interference plus noise ratio can not resist the frequency selective fading and the signal channel time variation.

Description

A kind of in OFDM the method for comprehensively measuring and calculating carrier-in-interference noise ratio
Technical field
The present invention relates to the digital transmission technology field, in particular a kind of in OFDM the method improvement of comprehensively measuring and calculating carrier-in-interference noise ratio.
Background technology
In the last few years, OFDM (Orthogonal Frequency Division Multiplexing is hereinafter to be referred as OFDM) orthogonal frequency division multiplexi had been widely used in carrying out high-speed data transmission by the wire/wireless channel.The orthogonal frequency division multiplex OFDM technology converts the serial data of input the data of parallel transmission to, and this parallel data is modulated on a plurality of Resource Units, also promptly has on the subchannel of orthogonality, then the data after the transmission modulation.
This orthogonal frequency division multiplex OFDM technology is widely used in the digital transmission technology field, for example numeral/audio broadcasting, digital TV, WLAN (wireless local area network) WLAN, wireless asynchronous transfer mode WATM or broadband wireless access BWA or the like.
System based on the orthogonal frequency division multiplex OFDM technology, in carrying out the control of adaptive coding and modulating AMC and power, it is exactly CINR (Carrier to Interference+Noise Ratio is hereinafter to be referred as CINR) the carrier-in-interference noise ratio that is used for reflecting channel quality that a very important reference index is arranged.And for the orthogonal frequency division multiplex OFDM symbol that receives, the gross power on each Resource Unit can be divided into two parts, and a part is a signal power, and another part is an interference plus noise power.
Mention a kind of method in the Chinese patent of application number 200610127279.5 " a kind of method of measurement of carrier-in-interference noise ratio and device ", this method is by measuring a plurality of Resource Units and grouping, and the Resource Unit that comprises equal number in each resource unit group is right; Utilize Resource Unit in the resource unit group in each resource unit group to the interference noise power of the domain channel response value of estimating Resource Unit in each resource unit group respectively; According to the rule of the frequency domain channel response linear variation of described Resource Unit, eliminate in the described interference noise power and change the estimation error that is caused by domain channel response; Interference noise power according to the domain channel response value of Resource Unit in the described resource unit group after the elimination error calculates the carrier-in-interference noise ratio.The present invention can terminal through last become or the time during constant channel, accurately measure the carrier-in-interference noise ratio, reach and make full use of the higher subchannel of carrier-in-interference noise ratio, improve the purpose of systematic function.But this invention only is used for descending structure, and purpose of design only is in order to resist time varying channel, and is powerless for frequency selective fading channels, and design complexities is higher, and effect is unsatisfactory in the practical application.
Also mention another kind of method in the patent " WO2007/021159A2 ", this method is by utilizing the rule of Resource Unit upper signal channel response change adjacent on the targeting sequencing, and interference noise is that the thought of the Gaussian random variable of zero-mean comes noise jamming is averaged, make it to trend towards zero, the CINR carrier-in-interference noise ratio that obtains system is estimated.Because this method also only can be used for targeting sequencing, and the default channel response does not change in a big way, and the precision of the measurement of CINR carrier-in-interference noise ratio can be affected, and effect is also relatively poor in frequency selective fading channels.
Therefore, prior art still awaits improving and development.
Summary of the invention
The objective of the invention is to, provide a kind of in OFDM the method for comprehensively measuring and calculating carrier-in-interference noise ratio, in order to solve at LTE (Long Term Evolution, hereinafter to be referred as LTE) in the process of down link comprehensively measuring and calculating carrier-in-interference noise ratio, the problem that becomes when contrary frequency selectivity decline simultaneously and channel.
Technical scheme of the present invention is as follows:
A kind of in OFDM the method for comprehensively measuring and calculating carrier-in-interference noise ratio, may further comprise the steps:
A, in Resource Block the witness mark symbol, and this reference symbol formed the reference symbol resource unit group, calculate its channel response value;
B, calculate the signal power of corresponding reference symbol resource unit group according to described channel response value;
C, the described channel response value corresponding reference sign resources of measurement unit group gross power obtain corresponding interference plus noise power;
D, obtain the carrier-in-interference noise ratio by the ratio calculation of the interference plus noise power sum of the signal power sum of a plurality of reference symbol resource unit group and a plurality of reference symbol resource unit group.
Described method, wherein, the witness mark symbol comprises in the described steps A:
Selective measurement belongs to same OFDM symbol but is positioned at the locational reference symbol of different reference symbol Resource Units in Resource Block.
Described method, wherein, form the reference symbol resource unit group in the described steps A and comprise:
Reference symbol on each OFDM symbol is set at one group of reference symbol resource unit group.
Described method, wherein, the witness mark symbol specifically comprises following at least a mode in the described steps A:
In a Resource Block, choose a plurality of reference symbol resource unit group, form a plurality of reference symbol resource unit group;
In a plurality of Resource Block, choose a reference symbol resource unit group respectively, form a plurality of reference symbol resource unit group;
In a plurality of Resource Block, choose a plurality of reference symbol resource unit group respectively, form a plurality of reference symbol resource unit group.
Described method, wherein, described steps A also comprises:
Two reference symbols on same OFDM symbol in the single Resource Block are P 1And P 2The time, described P 1And P 2On the reference symbol signal Y that receives 1And Y 2Calculate acquisition according to following formula:
Y 1=H 1X 1+N 1+I 1,Y 2=H 2X 2+N 2+I 2
Wherein, channel response value is H 1And H 2, corresponding transmitting terminal the reference symbol signal be X 1And X 2, corresponding interference signal is I 1And I 2, corresponding noise signal is N 1And N 2
Described method, wherein, channel response value H described in the described steps A 1And H 2Obtain according to following formula:
Y 1 X 1 = H 1 + N 1 + I 1 X 1 , Y 2 X 2 = H 2 + N 2 + I 2 X 2 .
Described method, wherein, described steps A also comprises:
As described N 1+ I 1, N 2+ I 2During for the Gaussian random variable of zero-mean, P 1And P 2Channel response value H after the approximate processing 1And H 2Obtain according to following formula:
H 1 ≈ Y 1 X 1 , H 2 ≈ Y 2 X 2 .
Described method, wherein, described step B specifically comprises:
Described P 1And P 2On signal power calculate according to following formula and obtain:
E [ ( Y 1 / X 1 ) · ( Y 2 / X 2 ) * ] =
E [ H 1 H 2 * ] + E [ H 1 · ( N 2 + I 2 X 2 ) * ] + E [ H 2 * · ( N 1 + I 1 X 1 ) ] + E [ ( N 1 + I 1 X 1 ) · ( N 2 + I 2 X 2 ) * ] .
Described method, wherein, described step B also comprises:
Described N 1+ I 1, N 2+ I 2Be the Gaussian random variable of zero-mean, and described channel response value H 1And H 2Value when identical, P 1And P 2Signal power after the approximate processing obtains according to following formula:
E[(Y 1/X 1)·(Y 2/X 2) *]=E[|H 1| 2]。
Described method, wherein, described step D specifically comprises:
Obtain the carrier-in-interference noise ratio according to following formula:
CINR ^ = | Σ m = 1 K / 2 ( Y 1 ( k ) / X 1 ( k ) ) · ( Y 2 ( k ) / X 2 ( k ) ) * | · 2 Σ k = 1 K | Y ( k ) / X ( k ) | 2 - | Σ m = 1 K / 2 ( Y 1 ( k ) / X 1 ( k ) ) · ( Y 2 ( k ) / X 2 ( k ) ) * | · 2 ,
Wherein, CINR is the carrier-in-interference noise ratio, Y 1(k) and Y 2(k) be the reference symbol signal of receiving terminal on two reference symbols on the same OFDM symbol in a plurality of Resource Block, the reference symbol signal of corresponding transmitting terminal is X 1(k) and X 2(k), Y (k)/X (k) is the gross power of each reference symbol resource unit group in a plurality of Resource Block.
Provided by the present invention a kind of in OFDM the method for comprehensively measuring and calculating carrier-in-interference noise ratio, because characteristics according to LTE descending reference allocation of symbols, by reference symbol signal processing interference plus noise power to receiving on the adjacent reference symbol Resource Unit, the carrier-in-interference noise ratio that becomes when having overcome frequency selective fading of the prior art and channel and cause is calculated inaccurate shortcoming, has solved the problem that becomes when the carrier-in-interference noise ratio that exists in the prior art is calculated contrary frequency selectivity decline simultaneously and channel.
Description of drawings
Fig. 1 is the schematic flow sheet of the method for the invention;
Fig. 2 is the distribution schematic diagram of reference symbol in the single Resource Block of the present invention.
Embodiment
Below with reference to shown in accompanying drawing, to the present invention a kind of in OFDM the embodiment and the embodiment of comprehensively measuring and calculating carrier-in-interference noise ratio described in detail.
The present invention a kind of in OFDM the method for comprehensively measuring and calculating carrier-in-interference noise ratio, it is a kind of method of calculating the carrier-in-interference noise ratio of in the LTE down link, measuring, main core point is, interference plus noise power sum in a plurality of resource unit group of the conjugate multiplication that adds up, and calculate the carrier-in-interference noise ratio with value calculating method with appointment; Be well known to those skilled in the art as for knowledge such as LTE, Resource Block, CINR and OFDM technology, do not repeat them here.
Taking it by and large, the embodiment of comprehensively measuring and calculating carrier-in-interference noise ratio is in OFDM, by the composition mode of selective measurement reference symbol, obtains a plurality of reference symbol groups in a plurality of Resource Block; For each reference symbol group, estimate the channel response value of described reference symbol Resource Unit; According to described channel response value, calculate the signal power of the channel response value correspondence of described reference symbol resource unit group again, and interference plus noise power; At last according to a plurality of described signal powers and, and a plurality of described interference plus noise power and, calculate the carrier-in-interference noise ratio.
Specifically, above-mentioned embodiment may further comprise the steps as shown in Figure 1:
Step S110, in a plurality of Resource Block by the composition mode of the one or more reference symbol resource unit group of selective measurement respectively, obtain a plurality of reference symbol resource unit group; Can in single Resource Block, belong to same orthogonal frequency division multiplexed symbol but be positioned at the locational reference symbol of different reference symbol Resource Units by selective measurement, also can in a plurality of Resource Block, carry out the described reference symbol of selective measurement;
Step S120, the reference symbol on each OFDM symbol is set at one group,, estimates the channel response value of reference symbol Resource Unit in the described reference symbol resource unit group for each reference symbol resource unit group;
Step S130, according to described channel response value, calculate the signal power of described channel response value correspondence, and further calculate corresponding interference plus noise power by measuring gross power;
Step S140, according to the signal power of described a plurality of reference symbol resource unit group, and the power of the interference plus noise of described a plurality of reference symbol resource unit group calculates the carrier-in-interference noise ratio.
Give an example, two reference symbol resource unit group of selective measurement in single Resource Block, and two reference symbols in the described reference symbol resource unit group though belong to same OFDM symbol, are positioned on the different reference symbol Resource Units position; Then, will form the reference symbol resource unit group, calculate its channel response value with the reference symbol of above-mentioned selective measurement.
With Fig. 2 is example, laterally is a plurality of orthogonal frequency division multiplex OFDM symbol directions in the single Resource Block.With the reference symbol on each orthogonal frequency division multiplex OFDM symbol is one group.The witness mark symbol packets is the 1st, the 5, the reference symbol on the 8th, the 12 orthogonal frequency division multiplex OFDM symbol.The reference symbol of selective measurement in one group is called P 1And P 2In other words the problem that this kind selective measurement has become when having considered frequency selective fading and channel simultaneously, has laterally considered the frequency selective fading problem, and becomes problem when vertically having considered channel; Can in a Resource Block, choose a plurality of reference symbol resource unit group, form a plurality of reference symbol resource unit group; Also can in a plurality of Resource Block, choose a reference symbol resource unit group respectively, form a plurality of reference symbol resource unit group; More can in a plurality of Resource Block, choose a plurality of reference symbol resource unit group respectively, form a plurality of reference symbol resource unit group.
At length, the channel response value of the described reference symbol resource unit group of calculating specifically comprises among the described step S120:
Step S121: for two reference symbol P of described reference symbol resource unit group 1And P 2If set P 1And P 2On the reference symbol signal that receives be Y 1And Y 2, the reference symbol signal of corresponding transmitting terminal is X 1And X 2, channel response value is H 1And H 2, disturb and to be I 1And I 2, noise is N 1And N 2, then have following formula to set up:
Y 1=H 1X 1+N 1+I 1,Y 2=H 2X 2+N 2+I 2
Step S122: the formula among the step S121 respectively divided by the reference symbol signal of corresponding transmitting terminal, is obtained following formula:
Y 1 X 1 = H 1 + N 1 + I 1 X 1 , Y 2 X 2 = H 2 + N 2 + I 2 X 2 ,
N wherein 1+ I 1, N 2+ I 2It is the Gaussian random variable of zero-mean.
Further, after the approximate processing that the formula among the above-mentioned steps S122 is estimated, obtain the channel response value H of two reference symbol signals 1And H 2, promptly
H 1 ≈ Y 1 X 1 , H 2 ≈ Y 2 X 2 .
At length, described step S130 specifically comprises:
Step S131: for a plurality of reference symbol resource unit group of selective measurement, respectively according to following formula, conjugate multiplication calculates the signal power in the described reference symbol resource unit group,
E [ ( Y 1 / X 1 ) · ( Y 2 / X 2 ) * ] =
E [ H 1 H 2 * ] + E [ H 1 · ( N 2 + I 2 X 2 ) * ] + E [ H 2 * · ( N 1 + I 1 X 1 ) ] + E [ ( N 1 + I 1 X 1 ) · ( N 2 + I 2 X 2 ) * ] ,
By the formula of aforementioned calculation method, to compare with general computational methods, the variation that has become when having taken into account frequency selective fading and channel simultaneously can be calculated the signal power in the described reference symbol resource unit group accurately.
Further, because H 1And H 2Value identical, noise item and distracter are the gaussian variables of zero-mean, then the simplified formula among the above-mentioned steps S131 is:
E[(Y 1/X 1)·(Y 2/X 2) *]=E[|H 1| 2]。
Step S132: the gross power of all Resource Unit respective signal responses in described a plurality of resource unit group that measuring and calculating is obtained, deduct the signal power sum of described a plurality of resource unit group, obtain the interference plus noise power sum in described a plurality of resource unit group.
At length, described step S140 specifically comprises:
According to the signal power sum of described a plurality of reference symbol resource unit group, and the power sum of the interference plus noise of described a plurality of reference symbol resource unit group, calculate the carrier-in-interference noise ratio by the two ratio.
With the comprehensively measuring and calculating of value in can adopt multiple computational methods, basic principle is similar.
Preferably, among the described step S142, described carrier-in-interference noise ratio calculates by following formula:
CINR ^ = | Σ m = 1 K / 2 ( Y 1 ( k ) / X 1 ( k ) ) · ( Y 2 ( k ) / X 2 ( k ) ) * | · 2 Σ k = 1 K | Y ( k ) / X ( k ) | 2 - | Σ m = 1 K / 2 ( Y 1 ( k ) / X 1 ( k ) ) · ( Y 2 ( k ) / X 2 ( k ) ) * | · 2 ,
Wherein, CINR is the carrier-in-interference noise ratio, Y 1(k) and Y 2(k) be the reference symbol signal of receiving terminal on two reference symbols on the same OFDM symbol in a plurality of Resource Block, X 1(k) and X 2(k) be the reference symbol signal of corresponding transmitting terminal, Y (k)/X (k) is the gross power of each reference symbol resource unit group in a plurality of Resource Block, m=1 to K/2, k=1 to K, K>0 and be integer.
By the formula of aforementioned calculation method, compare with general computational methods, under the variation that becomes when taking into account frequency selective fading and channel at the same time, can calculate indeterminable carrier-in-interference noise ratio accurately.
The technology that adopts interference plus noise power to obtain the carrier-in-interference noise ratio in the above specific embodiment can adopt existing various possible schemes according to practical application, is well known to those skilled in the art, and also repeats no more at this.
Provided in the specific embodiment of the invention a kind of in OFDM the method for comprehensively measuring and calculating carrier-in-interference noise ratio, because characteristics according to LTE descending reference allocation of symbols, by reference symbol signal processing interference plus noise power to receiving on the adjacent reference symbol Resource Unit, the carrier-in-interference noise ratio that becomes when having overcome frequency selective fading of the prior art and channel and cause is calculated inaccurate shortcoming, has solved the problem that becomes when the carrier-in-interference noise ratio that exists in the prior art is calculated contrary frequency selectivity decline simultaneously and channel.
Should be understood that; for those of ordinary skills; can be improved according to the explanation of such scheme or conversion, for example with the comprehensively measuring and calculating of value in can adopt multiple computational methods, and all these improve and conversion all should belong to the protection range of claims of the present invention.

Claims (10)

1. the method for a comprehensively measuring and calculating carrier-in-interference noise ratio in OFDM may further comprise the steps:
A, in Resource Block the witness mark symbol, and this reference symbol formed the reference symbol resource unit group, calculate its channel response value;
B, calculate the signal power of corresponding reference symbol resource unit group according to described channel response value;
C, the described channel response value corresponding reference sign resources of measurement unit group gross power obtain corresponding interference plus noise power;
D, obtain the carrier-in-interference noise ratio by the ratio calculation of the interference plus noise power sum of the signal power sum of a plurality of reference symbol resource unit group and a plurality of reference symbol resource unit group.
2. method according to claim 1 is characterized in that, the witness mark symbol comprises in the described steps A:
Selective measurement belongs to same OFDM symbol but is positioned at the locational reference symbol of different reference symbol Resource Units in Resource Block.
3. method according to claim 2 is characterized in that, forms the reference symbol resource unit group in the described steps A and comprises:
Reference symbol on each OFDM symbol is set at one group of reference symbol resource unit group.
4. method according to claim 3 is characterized in that, the witness mark symbol specifically comprises following at least a mode in the described steps A:
In a Resource Block, choose a plurality of reference symbol resource unit group, form a plurality of reference symbol resource unit group;
In a plurality of Resource Block, choose a reference symbol resource unit group respectively, form a plurality of reference symbol resource unit group;
In a plurality of Resource Block, choose a plurality of reference symbol resource unit group respectively, form a plurality of reference symbol resource unit group.
5. method according to claim 4 is characterized in that, described steps A also comprises:
Two reference symbols on same OFDM symbol in the single Resource Block are P 1And P 2The time, described P 1And P 2On the reference symbol signal Y that receives 1And Y 2Calculate acquisition according to following formula:
Y 1=H 1X 1+N 1+I 1,Y 2=H 2X 2+N 2+I 2
Wherein, channel response value is H 1And H 2, corresponding transmitting terminal the reference symbol signal be X 1And X 2, corresponding interference signal is I 1And I 2, corresponding noise signal is N 1And N 2
6. method according to claim 5 is characterized in that, channel response value H described in the described steps A 1And H 2Obtain according to following formula:
Y 1 X 1 = H 1 + N 1 + I 1 X 1 , Y 2 X 2 = H 2 + N 2 + I 2 X 2 .
7. method according to claim 6 is characterized in that, described steps A also comprises:
As described N 1+ I 1, N 2+ I 2During for the Gaussian random variable of zero-mean, P 1And P 2Channel response value H after the approximate processing 1And H 2Obtain according to following formula:
H 1 ≈ Y 1 X 1 , H 2 ≈ Y 2 X 2 .
8. method according to claim 6 is characterized in that, described step B specifically comprises:
Described P 1And P 2On signal power calculate according to following formula and obtain:
E [ ( Y 1 / X 1 ) · ( Y 2 / X 2 ) * ] =
E [ H 1 H 2 * ] + E [ H 1 · ( N 2 + I 2 X 2 ) * ] + E [ H 2 * · ( N 1 + I 1 X 1 ) ] + E [ ( N 1 + I 1 X 1 ) · ( N 2 + I 2 X 2 ) * ] .
9. method according to claim 8 is characterized in that, described step B also comprises:
Described N 1+ I 1, N 2+ I 2Be the Gaussian random variable of zero-mean, and described channel response value H 1And H 2Value when identical, P 1And P 2Signal power after the approximate processing obtains according to following formula:
E[(Y 1/X 1)·(Y 2/X 2) *]=E[|H 1| 2]。
10. method according to claim 9 is characterized in that, described step D specifically comprises:
Obtain the carrier-in-interference noise ratio according to following formula:
CINR ^ = | Σ m = 1 K / 2 ( Y 1 ( k ) / X 1 ( k ) ) · ( Y 2 ( k ) / X 2 ( k ) ) * | · 2 Σ k = 1 K | Y ( k ) / X ( k ) | 2 - | Σ m = 1 K / 2 ( Y 1 ( k ) / X 1 ( k ) ) · ( Y 2 ( k ) / X 2 ( k ) ) * | · 2 ,
Wherein, CINR is the carrier-in-interference noise ratio, Y 1(k) and Y 2(k) be the reference symbol signal of receiving terminal on two reference symbols on the same OFDM symbol in a plurality of Resource Block, the reference symbol signal of corresponding transmitting terminal is X 1(k) and X 2(k), Y (k)/X (k) is the gross power of each reference symbol resource unit group in a plurality of Resource Block.
CN 200810216976 2008-10-24 2008-10-24 Method for comprehensively measuring and calculating carrier to interference plus noise ratio in orthogonal frequency division multiplexing Expired - Fee Related CN101729462B (en)

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CN102201879A (en) * 2011-06-20 2011-09-28 合肥东芯通信股份有限公司 Measurement method and device for interference noise of long term evolution (LTE) system
CN104219180A (en) * 2014-09-24 2014-12-17 京信通信系统(中国)有限公司 Processing method and device for detecting reference signal
CN108736919A (en) * 2017-04-14 2018-11-02 大唐移动通信设备有限公司 A kind of noise power estimation method and device

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KR100800765B1 (en) * 2004-05-27 2008-02-01 삼성전자주식회사 Apparatus and method for estimating carrier to interference and noise ratio in communication system
CN101217526B (en) * 2008-01-17 2010-08-18 中兴通讯股份有限公司 An OFDM system carrier interference noise ratio measurement method
CN101227445B (en) * 2008-01-23 2011-09-21 中兴通讯股份有限公司 Method for computing carrier jamming noise ratio under OFDM

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102201879A (en) * 2011-06-20 2011-09-28 合肥东芯通信股份有限公司 Measurement method and device for interference noise of long term evolution (LTE) system
CN102201879B (en) * 2011-06-20 2013-06-19 合肥东芯通信股份有限公司 Measurement method and device for interference noise of long term evolution (LTE) system
CN104219180A (en) * 2014-09-24 2014-12-17 京信通信系统(中国)有限公司 Processing method and device for detecting reference signal
CN104219180B (en) * 2014-09-24 2017-10-31 京信通信系统(中国)有限公司 The treating method and apparatus of detection reference signal
CN108736919A (en) * 2017-04-14 2018-11-02 大唐移动通信设备有限公司 A kind of noise power estimation method and device
CN108736919B (en) * 2017-04-14 2020-05-26 大唐移动通信设备有限公司 Noise power estimation method and device

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