CN101729486B - Method and system for double-antenna receiving diversity in single carrier frequency domain equalization system - Google Patents

Method and system for double-antenna receiving diversity in single carrier frequency domain equalization system Download PDF

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CN101729486B
CN101729486B CN200910243888.0A CN200910243888A CN101729486B CN 101729486 B CN101729486 B CN 101729486B CN 200910243888 A CN200910243888 A CN 200910243888A CN 101729486 B CN101729486 B CN 101729486B
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CN101729486A (en
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吴南润
任琦
郑波浪
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BEIJING VIGA Co Ltd
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Abstract

The invention discloses a method and a system for double-antenna receiving diversity in a single carrier frequency domain equalization system. The method comprises the following steps: synchronously processing receiving signals of two receiving antennas; performing channel estimation for the synchronized receiving signals to acquire frequency domain responses H1 and H2 and simultaneously acquire noise estimation values sigma 12 and sigma 22 of the receiving signals; when the noise estimation value sigma 12 or sigma 22 is greater than the preset threshold value K, calculating an equalization coefficient by adopting a lowest estimation noise criterion, and performing equalization; and when both the noise estimation values sigma 12 and sigma 22 are not greater than the threshold value K, calculating the equalization coefficient by adopting a maximum merging criterion, and performing equalization. By adopting different criterions to calculate the equalization coefficient so as to perform the equalization process aiming at different conditions, the defect of performance deterioration possibly caused by diversity technology based on the maximum merging criterion under the condition of deep decline is avoided, and the best diversity grain also can be acquired even if one receiving antenna cannot synchronize normally.

Description

Double-antenna receiving diversity method and system in single carrier frequency domain equalization system
Technical Field
The invention relates to the technical field of single carrier frequency domain equalization, in particular to a double-antenna receiving diversity method and system in a single carrier frequency domain equalization system based on noise estimation self-adaption.
Background
In wireless communication systems, in addition to being interfered by various types of noise, multipath propagation of the transmitted signal also affects data transmission. With the increase of the signal transmission rate, the higher and higher transmission bandwidth causes severe time dispersion, and the received signal contains multipath waves undergoing attenuation and time delay, which causes frequency selective fading, thereby causing severe intersymbol interference, deep fading and other problems. A Single Carrier-Frequency Domain Equalization (SC-FDE) is an effective method for resisting multipath interference in broadband wireless transmission, and can better solve the above problems.
The SC-FDE technology needs to insert a cyclic prefix and perform frequency domain equalization, and meanwhile, the method transmits signals in a symbol block structure, has high requirements on synchronization of a receiving end and is quite sensitive to frequency deviation. General SC-FDE system data is transmitted in frames, each frame consisting of n data blocks and 1 preamble block, as shown in fig. 1.
The multi-antenna technology is an important way for improving the signal transmission quality of a mobile communication system, is one of the major breakthroughs in the modern communication technology, and the most effective method for resisting deep fading is to use the multi-antenna technology. The multi-antenna receiving technology is to receive signals through multiple antennas of a receiving end, so as to improve the signal transmission quality of the receiving end. For a single-antenna receiving system, due to the time-varying characteristic of a wireless channel, a deep fading condition necessarily occurs at some time, and at this time, energy reaching a receiving end is very low, which affects transmission quality of signals. The dual-antenna receiving technology utilizes two antennas to receive signals simultaneously, and the possibility that the two antennas receive deep fading signals simultaneously is much lower than that of a single antenna, so that diversity gain is introduced.
In the SC-FDE system, a general multi-antenna reception employs a dual-antenna reception. The double-antenna receiving system mainly comprises a synchronization module, a channel estimation module and a frequency domain equalization module. Channel estimation can be performed only if accurate synchronization is obtained, and then frequency domain equalization is performed. The method for receiving diversity by two antennas mainly aims at a frequency domain equalization module, a general SC-FDE system adopts a maximum combination criterion, as shown in FIG. 2, a transmitted signal is x, two antennas respectively receive signals r1 and r2 at a certain time, channel estimation is respectively carried out after synchronization is respectively carried out to obtain H1 and H2, and the obtained H1 and H2 simultaneously enter the frequency domain equalization module to calculate an equalization coefficient according to the maximum combination criterion and carry out equalization processing.
For the double-antenna receiving diversity method in the single carrier frequency domain equalization system adopting the maximum combination criterion, firstly, the receiving end of each antenna is ensured to complete accurate synchronization, namely timing synchronization and carrier synchronization. However, due to the deep fading condition, the energy of the received signal at a certain antenna receiving end is very low, and correct synchronization cannot be completed, so that the channel estimation result at the antenna receiving end is completely wrong, and at this time, the equalization coefficient is calculated and equalized by using the maximum combination criterion, which may deteriorate the data transmission quality and reduce the reliability of the receiver. The maximum combining criterion is therefore based on the fact that the receiving ends of the individual antennas are already perfectly synchronized correctly.
Disclosure of Invention
The invention provides a double-antenna receiving diversity method and system in a single carrier frequency domain equalization system based on noise estimation self-adaptation, which are used for solving the problem that the double-antenna receiving diversity method in the single carrier frequency domain equalization system adopting the maximum combination criterion can deteriorate the data transmission quality when signals are deeply faded in the prior art.
To achieve the above object, in one aspect, the present invention provides a dual antenna receive diversity method in a single carrier frequency domain equalization system, where the method includes the following steps:
carrying out synchronous processing on the received signals of the two receiving antennas;
performing channel estimation on the synchronized received signal to obtain frequency domain response H1、H2And simultaneously obtaining a noise estimation value sigma of the received signal1 2、σ2 2
When the noise estimate value sigma1 2Or σ2 2When the noise is larger than a preset threshold value K, calculating an equalization coefficient by adopting a minimum estimation noise criterion, and equalizing; when the noise estimate value sigma1 2And σ2 2And when the sum of the.
Further, a preamble block sequence used for channel estimation at a transmitting end for transmitting signals to the two receiving antennas is a UW sequence, u ═ u (1)]The Fourier change value of which is Ufft=[U(1)...U(M)]。
Further, before performing channel estimation on the synchronized received signal, the method further includes:
extracting pilot data for channel estimation from the received signal(i ═ 1, 2); wherein, the pilot frequency data total length is 2M,consists of two UW data of length M, and i denotes the number of antennas.
Further, a frequency domain response H is obtained1、H2And noise estimate σ1 2、σ2 2The method comprises the following steps:
for pilot frequency dataPerforming fast Fourier transform to obtain Obtaining pilot dataFrequency domain information of (a);
the noise estimation value of the received signal of each receiving antenna is obtained by the following formula:
<math> <mrow> <msup> <msub> <mi>&sigma;</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mi>M</mi> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
<math> <mrow> <msup> <msub> <mi>&sigma;</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mi>M</mi> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
the frequency domain response H is obtained by the following formula1、H2
<math> <mrow> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
<math> <mrow> <msub> <mi>H</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>h</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>h</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
Wherein R is1(2)、R1(4)、......、R1(M) is a vector: the value of; r2(2)、R2(4)、......、R2(M) is a vectorThe value of; u (n) is a vector UfftThe value of (b).
Further, calculating an equalization coefficient by using a maximum merging criterion, and performing equalization, specifically comprising:
obtaining the equalization coefficient W corresponding to each receiving antenna by the following formulai
<math> <mrow> <msub> <mi>W</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <mfrac> <msubsup> <mi>H</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>&sigma;</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
Obtaining the balance coefficient WiAnd then, carrying out equalization processing through the following equalization algorithm formula:
Z(k)=W1(k)·R1(k)+W2(k)·R2(k);
wherein Hi *Is a vector HiConjugation of (1); | HiL is vector HiThe mold of (4); i is the number of the antenna, (i ═ 1, 2); k 1.., M; r1(k)、R2(k) Are respectively a vectorThe value of; w1(k)、W2(k) Are respectively a vector W1、W2The value of (b).
Further, calculating an equalization coefficient by using a minimum estimation noise criterion, and performing equalization, specifically comprising: obtaining the equalization coefficient W corresponding to each receiving antenna by the following formulai
<math> <mrow> <msub> <mi>W</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <mfrac> <msubsup> <mi>H</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>H</mi> <mi>i</mi> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>&sigma;</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
Judging the noise estimation value sigma1 2Whether or not less than sigma2 2If so, then W is selected1As an equalization coefficient, z (k) ═ W1(k)·R1(k) Carrying out equalization processing for an equalization algorithm formula; if not, selecting W2As an equalization coefficient, z (k) ═ W2(k)·R2(k) Carrying out equalization processing for an equalization algorithm formula;
wherein Hi *Is a vector HiConjugation of (1); | HiL is vector HiThe mold of (4); i is the number of the antenna, (i ═ 1, 2); k 1.., M; r1(k)、R2(k) Are respectively a vectorThe value of; w1(k)、W2(k) Are respectively a vector W1、W2The value of (b).
In another aspect, the present invention further provides a dual-antenna receive diversity system in a single carrier frequency domain equalization system, where the system includes:
the synchronous processing unit is used for carrying out synchronous processing on the received signals of the two receiving antennas;
a channel estimation unit for performing channel estimation on the synchronized received signal to obtain a frequency domain response H1、H2And simultaneously obtaining a noise estimation value sigma of the received signal1 2、σ2 2
An equalization processing unit for processing the noise estimation value sigma1 2Or σ2 2When the noise is larger than a preset threshold value K, calculating an equalization coefficient by adopting a minimum estimation noise criterion, and equalizing; when the noise estimate value sigma1 2And σ2 2And when the average value is not more than the threshold value K, calculating an equalization coefficient by adopting a maximum merging criterion, and equalizing.
The invention has the following beneficial effects:
the invention calculates the equalization coefficient by adopting different criteria according to different conditions to perform equalization processing, avoids the defect of performance deterioration possibly caused by diversity technology based on the maximum merging criterion under the condition of deep fading, and ensures that the optimal diversity gain can be obtained even under the condition that one receiving antenna cannot be normally synchronized.
Drawings
FIG. 1 is a diagram illustrating a structure of a data frame in a SC-FDE system in the prior art;
FIG. 2 is a flow chart of a method for performing dual antenna receive diversity in a single carrier frequency domain equalization system in the prior art;
fig. 3 is a flowchart of a method for performing dual antenna receive diversity in a single carrier frequency domain equalization system according to embodiment 1 of the present invention;
fig. 4 is a schematic diagram of a structure of pilot data according to embodiment 1 of the present invention;
fig. 5 is a schematic structural diagram of a dual-antenna receive diversity system in a single carrier frequency domain equalization system according to embodiment 2 of the present invention.
Detailed Description
The present invention will be described in further detail below with reference to the drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
As shown in fig. 3, embodiment 1 of the present invention relates to a dual antenna receive diversity method in a single carrier frequency domain equalization system, which includes the following steps:
step S101 is to perform synchronization processing on the received signals of the two receiving antennas. The method for performing the synchronization processing may be any method in the prior art, and since the method for performing the synchronization processing already exists in the prior art, the detailed description of the patent is omitted.
Step S102, channel estimation is carried out on the synchronized received signal to obtain frequency domain response H1、H2And simultaneously obtaining a noise estimation value sigma of the received signal1 2、σ2 2
And respectively carrying out energy normalization processing on current received signal frames of the two receiving antennas. The energy normalization process may be performed by an existing digital AGC (automatic GAIN CONTROL) chip.
A preamble block sequence used for channel estimation at a transmitting end for transmitting signals to the two receiving antennas is a UW sequence, u ═ u (1),.. mu.u (m)]The Fourier change value of which is Ufft=[U(1)...U(M)]. UW sequences, i.e. Unique Word (Unique Word) sequences, are generally chu sequences, frank-zadaff sequences, PN sequences specified by the ieee802.16a standard.
Extracting pilot data for channel estimation from the received signal(i ═ 1, 2); the pilot data total length is 2M, and the pilot data total length is composed of UW data with two M lengths (the structure is shown in fig. 4). i denotes the number of the antenna.
For pilot frequency dataPerforming fast Fourier transform to obtain Obtaining pilot dataFrequency domain information of (a);
the noise estimation value of the received signal of each receiving antenna is obtained by the following formula:
<math> <mrow> <msup> <msub> <mi>&sigma;</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mi>M</mi> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
<math> <mrow> <msup> <msub> <mi>&sigma;</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mi>M</mi> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
the frequency domain response H is obtained by the following formula1、H2
<math> <mrow> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
<math> <mrow> <msub> <mi>H</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>h</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>h</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
Wherein R is1(2)、R1(4)、......、R1(M) is a vectorThe value of; r2(2)、R2(4)、......、R2(M) is a vectorThe value of; u (n) is a vector UfftThe value of (b).
Step S103, judging whether sigma is1 2And σ2 2If no, turning to step S104; otherwise, go to step S105. The threshold K may be set according to experience and the specific signal transmission environment. Or experimental setting may be performed first, and then, adjustment may be performed according to the quality of signal transmission, so as to finally obtain an appropriate threshold.
Step S104, when the noise estimation value sigma1 2And σ2 2And when the sum of the.
First, an equalization coefficient W corresponding to each receiving antenna is obtained by the following formulai
<math> <mrow> <msub> <mi>W</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <mfrac> <msubsup> <mi>H</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>&sigma;</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
Then, based on the obtained equalization coefficient WiCarrying out equalization processing through the following equalization algorithm formula:
Z(k)=W1(k)·R1(k)+W2(k)·R2(k);
wherein Hi *Is a vector HiConjugation of (1); | HiL is vector HiThe mold of (4); i is the number of the antenna, (i ═ 1, 2); k 1.., M; r1(k)、R2(k) Are respectively a vectorThe value of; w1(k)、W2(k) Are respectively a vector W1、W2The value of (b).
Step S105, when the noise estimation value sigma1 2Or σ2 2When the value is larger than the threshold value K, the minimum estimation noise criterion is adopted to calculate the equilibrium systemCounting and equalizing.
First, an equalization coefficient W corresponding to each receiving antenna is obtained by the following formulai
<math> <mrow> <msub> <mi>W</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <mfrac> <msubsup> <mi>H</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>H</mi> <mi>i</mi> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>&sigma;</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
Then, the noise estimation value σ is judged1 2Whether or not less than sigma2 2If so, then W is selected1As an equalization coefficient, z (k) ═ W1(k)·R1(k) Carrying out equalization processing for an equalization algorithm formula; if not, selecting W2As an equalization coefficient, z (k) ═ W2(k)·R2(k) And carrying out equalization processing for the equalization algorithm formula. Through the selection, the antenna corresponding to the minimum noise can be selected to receive data for equalization, and further the optimal diversity gain is obtained.
Wherein Hi *Is a vector HiConjugation of (1); | HiL is vector HiThe mold of (4); i is the number of the antenna, (i ═ 1, 2); k 1.., M; r1(k)、R2(k) Are respectively a vectorThe value of; w1(k)、W2(k) Are respectively a vector W1、W2The value of (b).
On the other hand, embodiment 2 of the present invention relates to a dual antenna receive diversity system in a single carrier frequency domain equalization system, the system includes:
a synchronization processing unit 201, configured to perform synchronization processing on the received signals of the two receiving antennas;
a channel estimation unit 202 connected to the synchronization processing unit 201 and configured to perform channel estimation on the synchronized received signal to obtain a frequency domain response H1、H2And simultaneously obtaining a noise estimation value sigma of the received signal1 2、σ2 2
An equalization processing unit 203 connected to the channel estimation unit 202 for estimating the noise estimation value σ1 2Or σ2 2When the noise is larger than a preset threshold value K, calculating an equalization coefficient by adopting a minimum estimation noise criterion, and equalizing; when the noise estimate value sigma1 2And σ2 2And when the average value is not more than the threshold value K, calculating an equalization coefficient by adopting a maximum merging criterion, and equalizing.
The method of performing equalization processing in the dual antenna receive diversity system of the present embodiment is the same as the method according to embodiment 1, and therefore, detailed description thereof is omitted in the present embodiment.
The accuracy of the synchronization module is determined by the signal-to-noise ratio of the received signal. In a wireless mobile communication channel, there must be a deep fading time, and at this time, the signal-to-noise ratio of the received signal is very low, which inevitably results in inaccurate synchronization, which seriously affects the accuracy of channel estimation, and at this time, a diversity technique using the maximum combining criterion is not feasible. Because the noise estimation value calculated by the invention is obtained by using the synchronization information, the obtained noise estimation value is completely deviated from a normal value when the front-end data is not synchronized. Based on this, it can be roughly determined whether the receiving end obtains better synchronization. After a certain receiving end is judged not to obtain accurate synchronization, the balance coefficient is calculated by adopting the minimum estimation noise criterion and balanced, and the receiving antenna with the wrong synchronization can be excluded from participating in diversity. Therefore, the defect of performance deterioration possibly caused by diversity technology based on the maximum combination criterion under the condition of deep fading is avoided, and the optimal diversity gain can be obtained even under the condition that one receiving antenna cannot be normally synchronized.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (4)

1. A dual-antenna receiving diversity method in a single carrier frequency domain equalization system is characterized by comprising the following steps:
carrying out synchronous processing on the received signals of the two receiving antennas;
performing channel estimation on the synchronized received signal to obtain frequency domain response H1、H2And simultaneously obtaining a noise estimation value sigma of the received signal1 2、σ2 2
When the noise estimate value sigma1 2Or σ2 2When the noise is larger than a preset threshold value K, calculating an equalization coefficient by adopting a minimum estimation noise criterion, and equalizing; when the noise estimate value sigma1 2And σ2 2When the sum of the sum;
wherein, the sequence of the preamble block used for channel estimation in the transmitting end for transmitting signals to the two receiving antennas is UW sequence, u ═ u (1), …, u (m)]The Fourier change value of which is Ufft=[U(1)…U(M)];
Before performing channel estimation on the synchronized received signal, the method further includes: extracting pilot data for channel estimation from the received signalThe pilot frequency data total length is 2M and consists of two UW data with the length of M, and i represents the number of an antenna;
obtaining a frequency domain response H1、H2And noise estimate σ1 2、σ2 2The method specifically comprises the following steps:
for pilot frequency dataPerforming fast Fourier transform to obtain <math> <mrow> <msub> <mover> <mi>R</mi> <mo>&RightArrow;</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <mi>FFT</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> Obtaining pilot dataFrequency domain information of (a);
the noise estimation value of the received signal of each receiving antenna is obtained by the following formula:
<math> <mrow> <msup> <msub> <mi>&sigma;</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mi>M</mi> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
<math> <mrow> <msup> <msub> <mi>&sigma;</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mi>M</mi> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
the frequency domain response H is obtained by the following formula1、H2
<math> <mrow> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
<math> <mrow> <msub> <mi>H</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>h</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>h</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
Wherein R is1(2)、R1(4)、……、R1(M) is a vectorThe value of; r2(2)、R2(4)、……、R2(M) is a vectorThe value of; u (n) is a vector UfftThe value of (b).
2. The method for dual-antenna receive diversity in a single-carrier frequency domain equalization system according to claim 1, wherein the calculating of the equalization coefficient using the maximum combining criterion and the equalizing are performed specifically comprises:
obtaining the equalization coefficient W corresponding to each receiving antenna by the following formulai
<math> <mrow> <msub> <mi>W</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <mfrac> <msubsup> <mi>H</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>&sigma;</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
Obtaining the balance coefficient WiAnd then, carrying out equalization processing through the following equalization algorithm formula:
Z(k)=W1(k)·R1(k)+W2(k)·R2(k);
wherein,is a vector HiConjugation of (1); | HiL is vector HiThe mold of (4); i is the number of the antenna, (i ═ 1, 2); k 1.., M; r1(k)、R2(k) Are respectively a vectorThe value of; w1(k)、W2(k) Are respectively a vector W1、W2The value of (b).
3. The method for dual-antenna receive diversity in a single-carrier frequency domain equalization system according to claim 1, wherein the equalization coefficient is calculated using a lowest estimated noise criterion and equalized, specifically comprising:
obtaining the equalization coefficient W corresponding to each receiving antenna by the following formulai
<math> <mrow> <msub> <mi>W</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>W</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <mfrac> <msubsup> <mi>H</mi> <mi>i</mi> <mo>*</mo> </msubsup> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>H</mi> <mi>i</mi> </msub> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>&sigma;</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
Judging the noise estimation value sigma1 2Whether or not less than sigma2 2If so, then W is selected1As an equalization coefficient, z (k) ═ W1(k)·R1(k) Carrying out equalization processing for an equalization algorithm formula; if not, selecting W2As an equalization coefficient, z (k) ═ W2(k)·R2(k) Carrying out equalization processing for an equalization algorithm formula;
wherein,is a vector HiConjugation of (1); | HiL is vector HiThe mold of (4); i is the number of the antenna, (i ═ 1, 2); k 1.., M; r1(k)、R2(k) Are respectively a vectorThe value of; w1(k)、W2(k) Are respectively a vector W1、W2The value of (b).
4. A dual antenna receive diversity system in a single carrier frequency domain equalization system, the system comprising:
the synchronous processing unit is used for carrying out synchronous processing on the received signals of the two receiving antennas;
a channel estimation unit for performing channel estimation on the synchronized received signal to obtain a frequency domain response H1、H2And simultaneously obtaining a noise estimation value sigma of the received signal1 2、σ2 2
An equalization processing unit for processing the noise estimation value sigma1 2Or σ2 2When the noise is larger than a preset threshold value K, calculating an equalization coefficient by adopting a minimum estimation noise criterion, and equalizing; when the noise estimate value sigma1 2And σ2 2When the average value is not greater than the threshold K, calculating an equalization coefficient by adopting a maximum merging criterion, and equalizing;
wherein, the sequence of the preamble block used for channel estimation in the transmitting end for transmitting signals to the two receiving antennas is UW sequence, u ═ u (1), …, u (m)]The Fourier change value of which is Ufft=[U(1)…U(M)];
Before performing channel estimation on the synchronized received signal, the method further includes: extracting pilot data for channel estimation from the received signalThe pilot frequency data total length is 2M and consists of two UW data with the length of M, and i represents the number of an antenna;
the channel estimation unit obtains a frequency domain response H1、H2And noise estimate σ1 2、σ2 2The method specifically comprises the following steps:
for pilot frequency dataPerforming fast Fourier transform to obtain <math> <mrow> <msub> <mover> <mi>R</mi> <mo>&RightArrow;</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <mi>FFT</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> Obtaining pilot dataFrequency domain information of (a);
the noise estimation value of the received signal of each receiving antenna is obtained by the following formula:
<math> <mrow> <msup> <msub> <mi>&sigma;</mi> <mn>1</mn> </msub> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mi>M</mi> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
<math> <mrow> <msup> <msub> <mi>&sigma;</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>+</mo> <msup> <mrow> <mo>|</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mi>M</mi> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
the frequency domain response H is obtained by the following formula1、H2
<math> <mrow> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
<math> <mrow> <msub> <mi>H</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>[</mo> <msub> <mi>h</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>h</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> <mo>]</mo> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>
Wherein R is1(2)、R1(4)、……、R1(M) is a vectorThe value of; r2(2)、R2(4)、……、R2(M) is a vectorThe value of; u (n) is a vector UfftThe value of (b).
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