CN112260811B - Pilot frequency distribution method of multi-input multi-output orthogonal frequency division multiplexing system - Google Patents

Pilot frequency distribution method of multi-input multi-output orthogonal frequency division multiplexing system Download PDF

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CN112260811B
CN112260811B CN202011113737.6A CN202011113737A CN112260811B CN 112260811 B CN112260811 B CN 112260811B CN 202011113737 A CN202011113737 A CN 202011113737A CN 112260811 B CN112260811 B CN 112260811B
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pilot
pilot frequency
frequency distribution
measurement matrix
rate
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CN112260811A (en
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李涛泳
孙莉
郑培清
张国和
丁莎
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Beijing Xingyan Boshang Technology Co ltd
Jiangsu Siyuan Integrated Circuit And Intelligent Technology Research Institute Co ltd
Shenzhen Research Institute Of Xi'an Jiaotong University
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Beijing Xingyan Boshang Technology Co ltd
Jiangsu Siyuan Integrated Circuit And Intelligent Technology Research Institute Co ltd
Shenzhen Research Institute Of Xi'an Jiaotong University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00—Arrangements affording multiple use of the transmission path
    • H04L5/003—Arrangements for allocating sub-channels of the transmission path
    • H04L5/0048—Allocation of pilot signals, i.e. of signals known to the receiver
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems

Abstract

The invention provides a pilot frequency distribution method of a multi-input multi-output orthogonal frequency division multiplexing system, which calculates the Welch lower bound according to the actual parameters of the system, randomly generates an initial pilot frequency distribution scheme, generates OFDM symbols which are sent by a transmitting antenna and consist of subcarriers, optimizes the initial pilot frequency distribution scheme by adopting an extended simulated annealing algorithm, and obtains the optimized final pilot frequency distribution scheme. The invention can effectively reduce the calculation complexity, enables the measurement matrix with higher potential to have higher updating and optimizing probability, effectively improves the convergence rate of the algorithm and improves the optimizing efficiency of the pilot frequency distribution scheme.

Description

Pilot frequency distribution method of multi-input multi-output orthogonal frequency division multiplexing system
Technical Field
The invention relates to a pilot frequency distribution method, in particular to a pilot frequency distribution method of an orthogonal frequency division multiplexing system.
Background
With the development of modern wireless communication technology, people have more and more strong demands on large-capacity data transmission. Since a Multi-Input Multi-Output (MIMO) Ultra Wide Band (UWB) Orthogonal Frequency Division Multiplexing (OFDM) system has advantages of large capacity, low power consumption, and the like, the system is considered as one of key technologies for realizing large-capacity data transmission. In the practical application of MIMO UWB OFDM systems, channel estimation is one of the major problems to be solved. Only accurate channel estimation can guarantee high-speed transmission of data, and in order to accurately estimate a channel, an OFDM system generally employs a pilot-assisted method for channel estimation. However, if conventional channel estimation methods such as Least Squares (LS), minimum Mean-Squared Error (MMSE), etc. are used, the required pilot frequency will increase dramatically, resulting in a decrease in the effective data transmission rate.
Because the ultra-wideband channel has the characteristic of sparsity, compressed sensing is widely used for estimation of the ultra-wideband channel, so that the number of pilot frequencies required by the channel is reduced. For the channel estimation method based on compressed sensing, the measurement matrix with lower coherence can provide more accurate channel estimation results. In the prior art, when a measurement matrix is designed, the number of pilots used for estimating each sub-channel is generally assumed to be the same (see Wang Nina, "sparse channel estimation method of MIMO-OFDM system based on compressed sensing", university of electronic technology, 2013, first stage; he Xueyun, "research on pilot optimization method in structured compressed sensing channel estimation of large-scale MIMO OFDM system", signal processing, 2017, first stage; zhou Yucheng, "pilot design scheme in MIMO-OFDM channel estimation based on compressed sensing", data acquisition and processing, 2019, fourth stage). The methods prove that the accuracy of channel estimation can be effectively improved through pilot frequency design, so that the system performance is improved.
Due to the high computational complexity of the prior art method and the adoption of a random method for updating and optimizing the pilot frequency allocation scheme, the method has two disadvantages: firstly, the complexity of pilot frequency design is too high, and the reduction of the efficiency of pilot frequency design becomes an obstacle to the practical application of the method in the prior art; secondly, the pilot frequency scheme is updated in a random mode, and the potential of each measurement matrix cannot be effectively explored, so that the optimization efficiency of the pilot frequency design scheme is low.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a pilot frequency allocation method of an input multi-output orthogonal frequency division multiplexing system, which can reduce the calculation complexity and improve the optimization efficiency of a pilot frequency allocation scheme.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step one, inputting the number N of subcarriers and the number N of transmitting antennas according to actual parameters of a system t The number N of receiving antennas r Number of pilot carriers
Figure BDA0002729527210000021
Sub-channels
Figure BDA0002729527210000022
Length of (2)
Figure BDA0002729527210000023
Calculating Welch lower bound
Figure BDA0002729527210000024
Wherein n is t ＝1，2，...，N t ，n r ＝1，2，...，N r ；
Step two, randomly generating an initial pilot frequency distribution scheme
Figure BDA0002729527210000025
Wherein the content of the first and second substances,
Figure BDA0002729527210000026
denotes the n-th t A set of pilots for each transmit antenna, and
Figure BDA0002729527210000027
according to pilot frequency set
Figure BDA0002729527210000028
Generating the n-th t OFDM symbol composed of N sub-carriers sent by transmitting antennas
Figure BDA0002729527210000029
Wherein n is t ＝1，2，...，N t
Figure BDA00027295272100000210
||·|| 2 Representing the euclidean norm of the vector; constructing a measurement matrix
Figure BDA00027295272100000211
And calculating the coherence of the corresponding measurement matrix
Figure BDA00027295272100000212
The measuring matrix
Figure BDA00027295272100000213
The k-th row and l-th column
Figure BDA00027295272100000214
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00027295272100000215
Figure BDA00027295272100000216
Figure BDA00027295272100000217
φ u representative measurement matrix
Figure BDA00027295272100000218
U th column of (d) v Representative measurement matrix
Figure BDA00027295272100000219
In the v-th column of (1),<·>a dot product operation representing a vector;
step three, setting the initial temperature T init End point temperature T stop Number of iterations T iter And an annealing rate T rate And an initial pilot frequency distribution scheme is adopted by adopting an extended simulated annealing algorithm
Figure BDA0002729527210000031
And optimizing to obtain an optimized final pilot frequency distribution scheme.
Welch lower bound of said step one
Figure BDA0002729527210000032
Wherein the function
Figure BDA0002729527210000033
In the third step, the initial temperature T init Is in the range of 1 to 10 -2 End point temperature T stop Is in the value range of 10 -6 ～10 -8 Number of iterations T iter Has a value range of 20 to 50 and an annealing rate T rate The value range of (A) is 0.95-0.99.
The simulated annealing algorithm expanded in the third step specifically comprises the following steps:
1) Initializing the current temperature T = T init ；
2) Setting an iteration counter t =1;
3) Computing a set of pilots
Figure BDA0002729527210000034
Potential energy of
Figure BDA0002729527210000035
Wherein n is t ＝1，2，…，N t ；
4) The set of pilots with the largest potential is selected,
Figure BDA0002729527210000036
for one of the sets that needs to be updated, randomSelecting
Figure BDA0002729527210000037
One element in (1)
Figure BDA0002729527210000038
As exchange elements, wherein
Figure BDA0002729527210000039
5) Computing the remaining set of pilots
Figure BDA00027295272100000310
Is selected probability of
Figure BDA00027295272100000311
And according to the calculated selection probability
Figure BDA00027295272100000312
Selecting another pilot set using roulette algorithm
Figure BDA00027295272100000313
Randomly picking as a set requiring updating
Figure BDA00027295272100000314
An element of
Figure BDA00027295272100000315
As exchange elements, wherein
Figure BDA00027295272100000316
6) Exchange elements
Figure BDA0002729527210000041
And
Figure BDA0002729527210000042
forming new pilot sets
Figure BDA0002729527210000043
And
Figure BDA0002729527210000044
calculating the corresponding MMMC
Figure BDA0002729527210000045
And
Figure BDA0002729527210000046
7) When it is satisfied with
Figure BDA0002729527210000047
And is
Figure BDA0002729527210000048
Or satisfy
Figure BDA0002729527210000049
And is
Figure BDA00027295272100000410
And is
Figure BDA00027295272100000411
Go to step 8), otherwise go to step 9);
8) Updating a pilot set
Figure BDA00027295272100000412
And
Figure BDA00027295272100000413
and updates the corresponding MMMC
Figure BDA00027295272100000414
And
Figure BDA00027295272100000415
9) Adding 1 to the value of T of the iteration counter, if T is less than or equal to T iter Go to Step 3);
10 Update the value of T to T.T rate If T < T stop Go to Step 2);
11 Output final pilot scheme
Figure BDA00027295272100000416
The invention has the beneficial effects that: aiming at the problems of overhigh computational complexity of the existing pilot frequency distribution technology and low algorithm convergence rate caused by adopting a random mode to update and optimize a pilot frequency distribution scheme, the pilot frequency distribution method of the multi-input multi-output orthogonal frequency division multiplexing system based on the extended simulated annealing algorithm is provided, and the computational complexity can be effectively reduced. According to the Welch lower bound of each measurement matrix corresponding to each pilot frequency set, the potential of each measurement matrix is fully explored, and an expanded simulated annealing algorithm is adopted to optimize a pilot frequency allocation scheme. In the extended simulated annealing algorithm, the invention provides an intelligent realization method for updating and optimizing the pilot frequency distribution scheme according to the acquired potential of each measurement matrix, so that the measurement matrix with higher potential has higher updating and optimizing probability, the convergence rate of the algorithm is effectively improved, and the optimization efficiency of the pilot frequency distribution scheme is improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram of a comparison of Mean Square Error (MSE) of channel estimates obtained with different pilot allocation schemes;
fig. 3 is a graph comparing BER of data transmission obtained by different pilot allocation schemes.
Detailed Description
The invention comprises the following steps:
step one, inputting the number N of subcarriers and the number N of transmitting antennas according to actual parameters of a system t The number N of receiving antennas r Number of pilot carriers
Figure BDA0002729527210000051
Sub-channels
Figure BDA0002729527210000052
Length of (2)
Figure BDA0002729527210000053
Calculating Welch lower bound
Figure BDA0002729527210000054
Wherein n is t ＝1，2，...，N t ，n r ＝1，2，...，N r ；
Step two, randomly generating an initial pilot frequency distribution scheme
Figure BDA0002729527210000055
Wherein the content of the first and second substances,
Figure BDA0002729527210000056
denotes the n-th t A set of pilots for each transmit antenna, and
Figure BDA0002729527210000057
according to pilot frequency set
Figure BDA0002729527210000058
Generating the n-th t OFDM symbol composed of N sub-carriers sent by transmitting antennas
Figure BDA0002729527210000059
Wherein n is t ＝1，2，...，N t ，
Figure BDA00027295272100000510
||·|| 2 Representing the euclidean norm of the vector; constructing a measurement matrix
Figure BDA00027295272100000511
And calculates the Measurement Matrix Mutual Coherence (MMMC) corresponding thereto
Figure BDA00027295272100000512
The measuring matrix
Figure BDA00027295272100000513
Elements of the k-th row and l-th column
Figure BDA00027295272100000514
The expression of (a) is:
Figure BDA00027295272100000515
wherein the content of the first and second substances,
Figure BDA00027295272100000516
according to the expression of the measurement matrix,
Figure BDA00027295272100000517
calculated using the following expression:
Figure BDA00027295272100000518
wherein phi is u Representative measurement matrix
Figure BDA0002729527210000061
U th column of (d) v Representative measurement matrix
Figure BDA00027295272100000612
In the v-th column of (1),<·>a dot product operation representing a vector; due to the measurement matrix
Figure BDA0002729527210000063
Figure BDA0002729527210000064
The expression of (c) is simplified as:
Figure BDA0002729527210000065
step three, setting the initial temperature T init End point temperature T stop Number of iterations T iter And an annealing rate T rate And an Extended Simulated Annealing (ESA) algorithm is adopted to allocate the initial pilot frequency scheme
Figure BDA0002729527210000066
And optimizing to obtain an optimized final pilot frequency distribution scheme.
Welch lower bound of said step one
Figure BDA0002729527210000067
The calculation was performed using the following formula:
Figure BDA0002729527210000068
wherein the function f (n) t ) The expression of (a) is:
Figure BDA0002729527210000069
in the third step, the initial temperature T init Is in the range of 1 to 10 -2 End point temperature T stop Is in the value range of 10 -6 ～10 -8 Number of iterations T iter Has a value range of 20 to 50 and an annealing rate T rate The value range of (A) is 0.95-0.99.
The ESA method in the third step specifically comprises the following steps:
step 1) initialization: current temperature T = T init ；
Step 2) setting an iteration counter t =1;
step 3) calculating a pilot set
Figure BDA00027295272100000610
Potential energy of
Figure BDA00027295272100000611
Wherein n is t ＝1，2，…，N t ；
Step 4) selects the set of pilots with the largest potential,
Figure BDA0002729527210000071
for one of the sets that needs to be updated, wherein
Figure BDA0002729527210000072
Figure BDA0002729527210000073
Representing sets of pilots
Figure BDA0002729527210000074
Potential energy of, i.e. corresponding measurement matrix
Figure BDA0002729527210000075
And randomly selecting
Figure BDA0002729527210000076
An element of
Figure BDA0002729527210000077
As exchange elements, wherein
Figure BDA0002729527210000078
Step 5) calculating the rest of the pilot frequency set
Figure BDA0002729527210000079
Is selected probability of
Figure BDA00027295272100000710
And according to the calculated selection probability
Figure BDA00027295272100000711
Selecting another pilot set using roulette algorithm
Figure BDA00027295272100000712
As a set requiring updating and randomly choosing
Figure BDA00027295272100000713
An element of
Figure BDA00027295272100000714
As exchange elements, wherein
Figure BDA00027295272100000715
Step 6) exchange of elements
Figure BDA00027295272100000716
And
Figure BDA00027295272100000717
forming new pilot sets
Figure BDA00027295272100000718
And
Figure BDA00027295272100000719
computing the corresponding MMMC
Figure BDA00027295272100000720
And
Figure BDA00027295272100000721
step 7) when satisfying
Figure BDA00027295272100000722
And is provided with
Figure BDA00027295272100000723
Or satisfy
Figure BDA00027295272100000724
And is
Figure BDA00027295272100000725
And is
Figure BDA00027295272100000726
Go to Step 8), otherwise go to Step 9);
step 8) updating the pilot set
Figure BDA00027295272100000727
And
Figure BDA00027295272100000728
and updates the corresponding MMMC
Figure BDA00027295272100000729
And
Figure BDA00027295272100000730
step 9) adding 1 to the T value of the iteration counter, and if T is less than or equal to T iter Go to Step 3);
step 10) update the T value to T.T rate If T < T stop Go to Step 2);
step 11) output final pilot scheme
Figure BDA0002729527210000081
The invention will be further described with reference to the drawings and examples of the invention.
The embodiment of the invention is realized by the following steps: as shown in fig. 1, firstly, system parameters including the number N of subcarriers and the number N of transmitting antennas are set according to actual requirements t Number of receiving antennas N r Initial temperature T init Annealing rate T rate End point temperature T stop Number of iterations T iter N th t Number of pilots for each transmit antenna
Figure BDA0002729527210000082
Sub-channels
Figure BDA0002729527210000083
Length of (2)
Figure BDA0002729527210000084
System parameters are equalized and a measurement matrix is calculated
Figure BDA0002729527210000085
Welch, and then generates a random pilot allocation scheme based on system parameters
Figure BDA0002729527210000086
Calculating a pilot allocation scheme
Figure BDA0002729527210000087
And finally, optimizing the pilot frequency allocation scheme by adopting an extended simulated annealing algorithm (ESA) to obtain a final allocation scheme. The concrete description is as follows:
the first step is as follows: the system parameter setting specifically comprises the following steps:
MIMO UWB OFDM system consisting of N t A transmitting antenna and N r And the receiving antenna is used for transmitting information in a packet communication mode. Each message consists of a preamble and a data load, wherein the preamble consists of an OFDM symbol and is used for channel estimation; payload consists of a number of OFDM symbols for data transmission. The number of subcarriers of each OFDM symbol is N, and the nth symbol t The OFDM symbols transmitted by the transmitting antennas are
Figure BDA0002729527210000088
Assuming that the Cyclic Prefix (CP) length of the system is larger than all sub-channels
Figure BDA0002729527210000089
Length of (2)
Figure BDA00027295272100000810
Wherein n is t ＝1，2，...，N t ，n r ＝1，2，...，N r Then at the n-th r OFDM symbol received by a receiving antenna
Figure BDA00027295272100000811
Can be represented by the following expression:
Figure BDA00027295272100000812
wherein the content of the first and second substances,
Figure BDA0002729527210000091
for additive white Gaussian noise, diag (-) means a diagonal matrix operation, the matrix
Figure BDA0002729527210000092
The ith row and the jth column of the element
Figure BDA0002729527210000093
Obtained by the following expression:
Figure BDA0002729527210000094
wherein the content of the first and second substances,
Figure BDA0002729527210000095
suppose that the n-th t The pilot frequency distribution of the transmitting antennas in the preamble is
Figure BDA0002729527210000096
And the intersection of the pilot frequency distribution in the preamble with other transmitting antennas is empty, then
Figure BDA0002729527210000097
In addition to
Figure BDA0002729527210000098
Formed by pilots, the remaining subcarriers are all 0, i.e.
Figure BDA0002729527210000099
Thus, OFDM symbols
Figure BDA00027295272100000910
The decomposition can be performed according to different transmitting antennas to obtain the following expression:
Figure BDA00027295272100000911
wherein the content of the first and second substances,
Figure BDA00027295272100000912
transmitted pilot signal
Figure BDA00027295272100000913
Received pilot noise
Figure BDA00027295272100000914
Matrix array
Figure BDA00027295272100000915
The expression of the ith row and jth column element of (1) is:
Figure BDA00027295272100000916
wherein the content of the first and second substances,
Figure BDA00027295272100000917
to reduce the number of pilots required, we assume
Figure BDA00027295272100000918
In this situation, the conventional channel estimation methods, such as Least Square (LS) method and Minimum Mean-square Error (MMSE), cannot obtain an accurate channel estimation result. However, due to ultra-wideband channels
Figure BDA0002729527210000101
Is generally sparse, so we can use the method of compressed sensing to realizeThe accurate channel estimation can be realized by the following expression:
Figure BDA0002729527210000102
wherein the measuring matrix
Figure BDA0002729527210000103
Is dependent on
Figure BDA0002729527210000104
Figure BDA0002729527210000105
And
Figure BDA0002729527210000106
in the present invention, we are working on
Figure BDA0002729527210000107
The design of (2). Therefore, we assume that each transmitted pilot signal has the same energy, i.e.
Figure BDA0002729527210000108
Wherein | · | purple 2 Representing the euclidean norm of the vector. Due to the fact that
Figure BDA0002729527210000109
Only with the n-th t Dependent on the transmitting antenna, independent of the receiving antenna, so we define the function f (n) t )：
Figure BDA00027295272100001010
Based on the function f (n) t )，N r An individual measurement matrix
Figure BDA00027295272100001011
Can be uniformly simplified into a measurement matrix
Figure BDA00027295272100001012
The k-th row and l-th column of the element
Figure BDA00027295272100001013
The expression of (a) is:
Figure BDA00027295272100001014
wherein the content of the first and second substances,
Figure BDA00027295272100001015
at this time, the measurement matrix
Figure BDA00027295272100001016
Welch lower bound of
Figure BDA00027295272100001017
Can be based on parameters
Figure BDA00027295272100001018
And
Figure BDA00027295272100001019
the calculation is performed by the following expression:
Figure BDA00027295272100001020
the second step is that: generation and measurement matrix for initial pilot allocation scheme
Figure BDA00027295272100001021
The coherence calculation is specifically as follows:
number of pilots set according to the first step
Figure BDA00027295272100001022
Randomly generating corresponding initial pilot allocation scheme
Figure BDA00027295272100001023
Wherein the content of the first and second substances,
Figure BDA00027295272100001024
denotes the n-th t A set of pilots for each transmit antenna, and
Figure BDA0002729527210000111
at this time, it can be generated according to the first step
Figure BDA0002729527210000112
And
Figure BDA0002729527210000113
constructing a measurement matrix
Figure BDA0002729527210000114
And calculates the corresponding MMMC
Figure BDA0002729527210000115
The specific expression is as follows:
Figure BDA0002729527210000116
wherein phi is u Representative measurement matrix
Figure BDA0002729527210000117
U column of (phi) v Representative measurement matrix
Figure BDA00027295272100001121
The (c) th column of (2),<·>representing a dot product operation of the vector. Due to the fact that
Figure BDA0002729527210000119
Figure BDA00027295272100001110
The expression of (c) can be simplified as:
Figure BDA00027295272100001111
the third step: the ESA optimization pilot frequency allocation scheme adopting the extended simulated annealing algorithm specifically comprises the following steps:
due to the measurement matrix
Figure BDA00027295272100001112
Coherency of
Figure BDA00027295272100001113
The smaller the channel estimation result, the better. For the MIMO system, we use the sum μ { Φ } of MMMC of all measurement matrices as a cost function to design the pilot allocation scheme, where the expression of μ { Φ } is:
Figure BDA00027295272100001114
at this step, we pass the design
Figure BDA00027295272100001115
Reducing mu { phi } as much as possible, thereby obtaining a better channel estimation result, wherein the specific expression is as follows:
Figure BDA00027295272100001116
parameter acquisition measurement matrix based on first-step setting
Figure BDA00027295272100001117
Welch lower bound of
Figure BDA00027295272100001118
And the second step of the initial pilot allocation scheme
Figure BDA00027295272100001119
Measuring matrix
Figure BDA00027295272100001120
And its corresponding MMMC
Figure BDA0002729527210000121
Excavation measurement matrix
Figure BDA0002729527210000122
The initial pilot frequency allocation scheme is optimized through an ESA algorithm, and the performance of the system is improved.
To improve system performance, the proposed ESA algorithm is as follows:
inputting: number of transmitting antennas N t Number of receiving antennas N r Initial temperature T init End point temperature T stop Number of iterations T iter Annealing rate T rate Initial pilot allocation scheme
Figure BDA0002729527210000123
Number of frequencies of leading
Figure BDA0002729527210000124
Measuring matrix
Figure BDA0002729527210000125
Welch lower bound of
Figure BDA0002729527210000126
MMMC
Figure BDA0002729527210000127
Sub-channels
Figure BDA0002729527210000128
Length of (2)
Figure BDA0002729527210000129
Wherein n is t ＝1，2，...，N t ，n r ＝1，2，...，N r ；
And (3) outputting: optimized pilot allocation scheme
Figure BDA00027295272100001210
Step 1) initialization: current temperature T = T init ；
Step 2) setting an iteration counter t =1;
step 3) calculating a pilot set
Figure BDA00027295272100001211
Potential energy of
Figure BDA00027295272100001212
Wherein n is t ＝1，2，...，N t ；
Step 4) selecting the set of pilots with the largest potential
Figure BDA00027295272100001213
As one of the sets that needs to be updated, wherein
Figure BDA00027295272100001214
And randomly selecting
Figure BDA00027295272100001215
An element of
Figure BDA00027295272100001216
As an exchange element, wherein
Figure BDA00027295272100001217
Step 5) calculating the rest of the pilot frequency set
Figure BDA00027295272100001218
Is selected probability of
Figure BDA00027295272100001219
And according to the calculated selection probability
Figure BDA00027295272100001220
Selecting another pilot set by roulette algorithm
Figure BDA0002729527210000131
As a set requiring updating and randomly choosing
Figure BDA0002729527210000132
An element of
Figure BDA0002729527210000133
As exchange elements, wherein
Figure BDA0002729527210000134
Step 6) exchange of elements
Figure BDA0002729527210000135
And
Figure BDA0002729527210000136
forming new pilot sets
Figure BDA0002729527210000137
And
Figure BDA0002729527210000138
and calculates the corresponding MMMC
Figure BDA0002729527210000139
And
Figure BDA00027295272100001310
step 7) when
Figure BDA00027295272100001311
Or
Figure BDA00027295272100001312
Figure BDA00027295272100001313
Go to Step 8), otherwise go to Step 9);
step 8) update guideFrequency aggregation
Figure BDA00027295272100001314
And
Figure BDA00027295272100001315
and updates the corresponding MMMC
Figure BDA00027295272100001316
And
Figure BDA00027295272100001317
step 9) adding 1 to the T value, and if T is less than or equal to T iter Go to Step 3);
Step 10)T＝T·T rate if T < T stop Go to Step 2);
step 11) output final pilot scheme
Figure BDA00027295272100001318
The proposed algorithm fully exploits the measurement matrix
Figure BDA00027295272100001319
The algorithm is more intelligent, the convergence rate is higher, the calculation complexity is greatly reduced, and the calculation efficiency is effectively improved.
The invention designs a simulation experiment by the pilot frequency distribution scheme, and in the simulation experiment, the MIMO system consists of N t =8 transmitting antennas and N r The number of subcarriers is N =1024, and the number of pilots allocated to each transmitting antenna is N 1 ＝N 2 ＝N 3 ＝90，N 4 ＝N 5 ＝N 6 ＝104，N 7 ＝176，N 8 =266. As shown in Table 1, an initial pilot allocation scheme is generated randomly
Figure BDA00027295272100001320
MMMC of each matrix (labeled P0) is μ { Φ } 1 }＝0.2182，μ{Φ 2 }＝0.2265，μ{Φ 3 }＝0.2465，μ{Φ 4 }＝0.2184，μ{Φ 5 }＝0.2578，μ{Φ 6 }＝0.2485，μ{Φ 7 }＝0.1676，μ{Φ 8 =0.1896, with a sum μ { Φ } =1.7731. To verify the validity of the method, we performed the following simulation experiment.
Simulation 1: to verify that ESA can effectively reduce μ { Φ }, we performed the following simulation experiment.
According to the set initial temperature T init ＝10 -2 End point temperature T stop ＝10 -8 Number of iterations T iter =50, annealing rate T rate =0.99. The initial pilot frequency allocation scheme P0 is optimized by adopting the ESA method, and the pilot frequency allocation scheme obtained after optimization is marked as ESA-P. As shown in Table 1, the MMMC of each matrix in the allocation scheme is μ { Φ } 1 }＝0.1368，μ{Φ 2 }＝0.1454，μ{Φ 3 }＝0.1427，μ{Φ 4 }＝0.1298，μ{Φ 5 }＝0.1324，μ{Φ 6 }＝0.1348，μ{Φ 7 }＝0.1177，μ{Φ 8 =0.1001, with a sum μ { Φ } =1.0396. In the optimization process, the total number of times of calculating mu { phi } is 68750. Compared with the scheme P0, the method can effectively reduce mu { phi }.
To visually demonstrate the superiority of the ESA method, we compare with the current most advanced Pilot allocation method, random Sequential Search (SSS), which is specified in the table Qi Chenhao, pilot design schemes for sparse channel estimation in OFDM systems, IEEE Transactions on Vehicular Technology 2015, fourth. The initial pilot allocation scheme P0 is also optimized by SSS, and the pilot allocation scheme obtained after optimization is marked as SSS-P. As shown in Table 1, the MMMC of each matrix in the allocation scheme is μ { Φ } 1 }＝0.1569，μ{Φ 2 }＝0.1480，μ{Φ 3 }＝0.1414，μ{Φ 4 }＝0.1390，μ{Φ 5 }＝0.1451，μ{Φ 6 }＝0.1479，μ{Φ 7 }＝0.1147，μ{Φ 8 =0.0963, with a sum μ { Φ } =1.0892. In the optimization process, the total calculation is carried outThe number of μ { Φ } is 8900960. By comparison, the proposed ESA has much lower computational complexity than SSS, and the scheme ESA-P has lower μ { Φ } than SSS-P.
Table 1: ESA and SSS Performance comparison
Figure BDA0002729527210000151
Simulation 2: to verify the performance of the optimized pilot allocation scheme, the following experiment is now performed.
Sending 500 messages on each transmitting antenna, wherein each message is composed of 1 OFDM symbol as a preamble and 500 OFDM symbols as a payload, the preamble is used for estimating a channel, and the payload is used for transmitting data. The channel is constant during the transmission of one message but varies from message to message. Based on this, we calculate the Mean-Squared Error (MSE) of the channel estimation and the Bit Error Rate (BER) of the data transmission under different signal-to-Noise ratios (SNR)
As shown in FIG. 2, because ESA-P has the smallest μ { Φ }, the pilot allocation scheme achieves the best channel estimation result, and therefore, in the SNR range of 0dB to 30dB, ESA-P achieves lower MSE than SSS-P and P0, and the method is proved to be capable of effectively improving the performance of channel estimation.
As shown in FIG. 3, since ESA-P achieves lower MSE than SSS-P and P0, the pilot allocation scheme achieves lower bit error rate in the SNR range of 0dB to 30dB, and proves that the method can effectively improve the performance of MIMO.

Claims (4)

1. A pilot frequency distribution method of a multiple-input multiple-output orthogonal frequency division multiplexing system is characterized by comprising the following steps:
step one, inputting the number N of subcarriers and the number N of transmitting antennas according to actual parameters of a system t The number N of receiving antennas r Number of pilot carriers
Figure FDA0003882022030000011
Sub-channels
Figure FDA0003882022030000012
Length of (2)
Figure FDA0003882022030000013
Calculating Welch lower bound
Figure FDA0003882022030000014
Wherein n is t ＝1，2，...，N t ，n r ＝1，2，...，N r ；
Step two, randomly generating an initial pilot frequency distribution scheme
Figure FDA0003882022030000015
Wherein the content of the first and second substances,
Figure FDA0003882022030000016
denotes the n-th t A set of pilots for each transmit antenna, and
Figure FDA0003882022030000017
according to pilot frequency set
Figure FDA0003882022030000018
Generating the n-th t OFDM symbol composed of N sub-carriers sent by transmitting antennas
Figure FDA0003882022030000019
Wherein n is t ＝1，2，...，N t ，
Figure FDA00038820220300000110
||·|| 2 Representing the euclidean norm of the vector; constructing a measurement matrix
Figure FDA00038820220300000111
And calculateThe corresponding measurement matrix mutual coherence MMMC
Figure FDA00038820220300000112
The measuring matrix
Figure FDA00038820220300000113
Elements of the k-th row and l-th column
Figure FDA00038820220300000114
Wherein the content of the first and second substances,
Figure FDA00038820220300000115
Figure FDA00038820220300000116
φ u representative measurement matrix
Figure FDA00038820220300000117
U th column of (d) v Representative measurement matrix
Figure FDA00038820220300000118
The (c) th column of (2),<·>a dot product operation representing a vector;
step three, setting the initial temperature T init End point temperature T stop Number of iterations T iter And an annealing rate T rate And an initial pilot frequency distribution scheme is adopted by adopting an extended simulated annealing algorithm
Figure FDA0003882022030000021
And optimizing to obtain an optimized final pilot frequency distribution scheme.
2. The pilot allocation method of mimo-ofdm according to claim 1, wherein: welch lower bound of said step one
Figure FDA0003882022030000022
Wherein the function
Figure FDA0003882022030000023
3. The pilot allocation method of mimo-ofdm according to claim 1, wherein: in the third step, the initial temperature T init Is in the range of 1 to 10 -2 End point temperature T stop Is in the value range of 10 -6 ～10 -8 Number of iterations T iter Has a value range of 20 to 50 and an annealing rate T rate The value range of (a) is 0.95 to 0.99.
4. The pilot allocation method of mimo-ofdm according to claim 1, wherein: the simulated annealing algorithm expanded in the third step specifically comprises the following steps:
1) Initializing the current temperature T = T init ；
2) Setting an iteration counter t =1;
3) Computing a set of pilots
Figure FDA0003882022030000024
Potential energy of
Figure FDA0003882022030000025
Wherein n is t ＝1，2，…，N t ；
4) A set of pilots with the largest potential is selected,
Figure FDA0003882022030000026
for one of the sets to be updated, randomly picking
Figure FDA0003882022030000027
An element of
Figure FDA0003882022030000028
As exchange elements, wherein
Figure FDA0003882022030000029
5) Computing the remaining set of pilots
Figure FDA00038820220300000210
Is selected probability of
Figure FDA00038820220300000211
And according to the calculated selection probability
Figure FDA00038820220300000212
Selecting another pilot set using roulette algorithm
Figure FDA0003882022030000031
Randomly picking as a set requiring updating
Figure FDA0003882022030000032
An element of
Figure FDA0003882022030000033
As exchange elements, wherein
Figure FDA0003882022030000034
6) Exchange elements
Figure FDA0003882022030000035
And
Figure FDA0003882022030000036
forming new pilot sets
Figure FDA0003882022030000037
And
Figure FDA0003882022030000038
calculating the corresponding MMMC
Figure FDA0003882022030000039
And
Figure FDA00038820220300000310
7) When it is satisfied with
Figure FDA00038820220300000311
And is provided with
Figure FDA00038820220300000312
Or satisfy
Figure FDA00038820220300000313
And is
Figure FDA00038820220300000314
And is
Figure FDA00038820220300000315
Go to step 8), otherwise go to step 9);
8) Updating a pilot set
Figure FDA00038820220300000316
And
Figure FDA00038820220300000317
and updates the corresponding MMMC
Figure FDA00038820220300000318
And
Figure FDA00038820220300000319
9) Adding 1 to the value of T of the iteration counter, if T is less than or equal to T iter Go to Step 3);
10 Update the value of T to T.T rate If T < T stop Go to Step 2);
11 Output final pilot scheme
Figure FDA00038820220300000320
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