CN100561999C - A Synchronization Method for Multiple Input Multiple Output - Orthogonal Frequency Division Multiplexing System - Google Patents

Abstract

The invention discloses a MIMO-OFDM synchronization method. By using the characteristics of IFFT transformation, the training sequence inserted by each antenna at the transmitting end can still obtain two identical half sequence. Coarse time synchronization is performed in the time domain of the receiving end, and fine time synchronization is performed in the frequency domain; after time synchronization at the receiving end is obtained, frequency synchronization can be easily obtained. Since the present invention inserts synchronous symbols whose even bits are all zero and odd bits are training sequences at the sending end, different time delays can be distinguished, and it is suitable for distributed MIMO systems. Therefore, it has the advantages of easy implementation, strong practicability, and wide application; at the same time, it has the advantages of less bandwidth occupation and high spectrum utilization.

Description

A Synchronization Method for Multiple Input Multiple Output - Orthogonal Frequency Division Multiplexing System

technical field

The invention belongs to the technical field of communication, and in particular relates to a multiple-input multiple-output-orthogonal frequency division multiplexing (MIMO-OFDM) synchronization technology.

Background technique

OFDM has attracted more and more attention due to its high data transmission rate, strong anti-multipath interference ability, and high spectrum efficiency. It has been successfully used in wired and wireless communications. Such as: DAB (Digital Audio Broadcasting), DVB, EEE802.11a and HyperLAN/2, in IEEE802.16 currently being formulated, OFDM technology is also involved in a large number. OFDM, a new modulation technique, can also be used in a new generation of mobile communication systems. The use of OFDM technology will greatly improve the transmission data rate and spectrum efficiency of the new generation of mobile communication systems, and has a good anti-multipath ability, see the literature: Bingham, J.A.C., "Multicarrier modulation for data transmission: an idea whose time has come, "IEEE Communications Magazine, Volume: 28 Issue: 5, May 1990, Page(s): 5-14 and Literature: Yun Hee Kim; Iickho Song; Hong Gil Kim; Taejoo Chang; Hyung Myung Kim," Performance analysis of a coded OFDM system in time-varying multipath Rayleigh fading channels," Vehicular Technology, IEEE Transactions on, Volume: 48 Issue: 5, Sept.1999, Page(s): 1610-1615.

One of the weaknesses of OFDM technology is the requirement for time and frequency synchronization, especially frequency synchronization, which is much higher than that of single-carrier systems. It is generally required that the frequency offset of the system using OFDM technology does not exceed 2% of its subcarrier spacing, see the literature van de Beek, J.J.; Sandell, M.; Borjesson, P.O., "ML estimation of time and frequency offset in OFDMsystems , "Signal Processing, IEEE Transactions on, Volume: 45 Issue: 7, July 1997, Page(s): 1800-1805.

In future broadband wireless communication systems, there are two most serious challenges: multipath fading channel and bandwidth efficiency. OFDM reduces the effects of multipath fading by converting frequency selective multipath fading channels into flat channels in the frequency domain. The MIMO technology can generate independent parallel channels in space to transmit multiple data streams at the same time, which can effectively increase the transmission rate of the system. In this way, combining the two technologies of OFDM and MIMO to form MIMO-OFDM can achieve two effects: one is that the system has a high transmission rate, and the other is that the system achieves strong reliability through diversity. See literature H. Sampath, S. Talwar, J. Tellado, et al. "A Fourth-Generation MIMO-OFDM: Broadband Wireless System: Design, Performance, and Field Trial Results". IEEE Communications Magazine, Vol.40, No.9 , Sept.2002, pp.143-149.

One of the weaknesses of OFDM technology is that it is very sensitive to synchronization errors, so the MIMO-OFDM system is also very sensitive to synchronization errors. Generally speaking, synchronization is divided into time synchronization and frequency synchronization. In a multipath environment, OFDM has high requirements for time synchronization, which is also the requirement of MIMO-OFDM system for time synchronization. In terms of frequency synchronization, since MIMO-OFDM system can be regarded as N parallel MIMO subsystems, the frequency offset The introduced ICI will deteriorate the signal-to-noise ratio of each subcarrier, thereby deteriorating the performance of the entire MIMO-OFDM communication system, see literature A. Stamoulis; S.N.Diggavi; N.Al-Dhahir, Intercarrier interference in MIMO OFDM, Signal Processing, IEEE Transactions on, Volume: 50, Issue: 10, Oct, 2002, pp.2451-2464. In the MIMO-OFDM system, the position of the synchronization module is shown in Figure 1. The purpose of time synchronization is to find the boundaries of each OFDM symbol in the received serial data stream; and the purpose of frequency synchronization is to find and correct the frequency offset at the receiving end.

In order to obtain fast and accurate synchronization, the synchronization in the MIMO-OFDM system is often accomplished by means of training sequences. Considering the characteristics of the MIMO-OFDM channel, some training sequences used in the OFDM system cannot be directly used as the training sequence of the MIMO-OFDM system, see the literature: Mody, A.N.Stuber, G.L.Synchronization for MIMO-OFDMsystems.Global Telecommunications Conference, 2001. GLOBECOM'01. IEEE, Volume: 1, 25-29 Nov.2001 Pages: 509-513 vol.1.

There are currently two customary training sequence insertion methods:

1) One method is to use time-orthogonal training sequences, that is, the times of inserting training sequences on different transmitting antennas are staggered from each other (as shown in FIG. 2 ). The training sequence on each antenna only needs to satisfy strong shift autocorrelation, and the training sequences of different antennas can be the same, so it is more convenient to design, and the time delay between antennas can be distinguished. The disadvantage is that as the number of antennas increases, the bandwidth occupied by the training sequence also increases correspondingly, so the spectrum utilization rate is low. See literature: T.C.W.Schenk and A.van Zelst. Frequency Synchronization for MIMO-OFDM Wireless LAN Systems. Proc. IEEE Vehicular Technology Conference Fall 2003 (VTC Fall 2003), Orlando (FL), 6-9 October 2003, paper 05D-03 stated.

2) Another method is that each transmit antenna inserts an orthogonal training sequence at the same position, and the ability of the training sequence to resist multipath fading can be enhanced by means of multi-segment repetition. On the premise of satisfying the orthogonality, these sequences must also satisfy the shifted autocorrelation of the training sequence (as shown in FIG. 3 ). The algorithm assumes that the time delays from all transmitting antennas to all receiving antennas are the same, and the frequency offsets are the same, that is, there is only one time offset and one frequency offset between sending and receiving. Obviously, this algorithm cannot solve the synchronization problem when the arrival delays of different antennas are different. See literature: Mody, A.N.Stuber, G.L.Synchronization for MIMO-OFDM systems.Global Telecommunications Conference, 2001.GLOBECOM'01.IEEE, Volume: 1, 25-29Nov.2001 Pages: 509-513 vol.1.

Contents of the invention

The object of the present invention is to provide a kind of multi-input multi-output-orthogonal frequency division multiplexing (MIMO-OFDM) synchronization method, which utilizes the training sequence to carry out MIMO-OFDM synchronization, has the advantages of easy implementation, strong practicability, wide application range, and Distinguishes the characteristics of multi-antenna delay and high spectrum utilization.

In order to describe the content of this article conveniently, let us first define the terms:

FFT/IFFT: Fast Fourier Transform/Inverse Fast Fourier Transform

Cyclic prefix (CP): In order to eliminate the ICI caused by multipath, the signal filled in the guard interval of the OFDM symbol is a copy of the signal of the latter part of the OFDM symbol itself.

Framing: The basic unit of data transmission, which arranges data and redundant information according to certain specifications, and then sends them out.

The present invention provides a method for performing MIMO-OFDM synchronization using a training sequence, which consists of two parts, a sending end and a receiving end, and the specific steps are as follows:

The sending end processes the transmitted signal as follows (as shown in Figure 4):

Step 1: Define the number of transmitting antennas as M, M is a positive integer, and the number of M is greater than 1; select M PN sequences b _m [k] whose length is N ₁ , and N ₁ is a positive integer; the PN A "1" is added at the end of the sequence b _m [k] to form a sequence c _m (k) of length Q, k∈[0, Q-1], m∈[1, M]; at this time, c _m (k ) takes a complex number form, that is, c _m (k)∈{1+j, -1-j};

Step 2: Perform zero-insertion processing on the sequence c _m (k) obtained in step 1 to generate a training sequence T _m (i) transmitted by each antenna, i∈[0, N-1], where N is the number of FFT points of the OFDM system , and take a positive integer; the specific method of zero insertion processing is: the first information _{c 1} (1) of the sequence c 1 (k) is inserted into the first bit of the training sequence T ₁ (i) of the first transmitting antenna ; The second information c ₁ (2) of the sequence c ₁ (k) is inserted into the 2M+1 bit of the training sequence T ₁ (i); the third information c ₁ (3) is inserted into T ₁ (i) 4M+1 bit of , and so on, until the kth information c ₁ (k) is inserted into the 2(Q-1)M+1 bit of T ₁ (i), the rest of the training sequence T ₁ (i) Bits are all zero-inserted; for the second transmitting antenna, the first information c ₂ (1) of the sequence c ₂ (k) is inserted into the third bit of the corresponding training sequence T ₂ (i); the sequence c ₂ ( The second information c ₂ (2) of k) is inserted into the 2M+3 bit of the training sequence T ₂ (i); the third information c ₂ (3) is inserted into the 4M of the training sequence T ₂ (i) +3 bits, and so on, until the kth information c ₂ (k) is inserted into the 2(Q-1)M+3 bits of T ₂ (i), and the remaining bits of the training sequence T ₂ (i) are inserted zero; and so on, the first information c _M (1) of the sequence c _M (k) is inserted into the 2M-1th bit of the training sequence T _M (i) of the first transmitting antenna; the sequence c _M (k ) of the second information c _M (2), inserted into the 2M+2M-1 bit of the training sequence _TM (i); the third information c _M (3) inserted into the 4M+ of _TM (i) 2M-1 bit, and so on, until the kth information c _M (k) is inserted into the 2(Q-1)M+2M-1 bit of _TM (i), the rest of the training sequence _TM (i) Bit interpolation, as shown in formula (1) and Figure 5; here, N and the number of transmitting antennas M must satisfy: N=2MQ;

Step 3: insert the training sequence T _m (i) obtained in step 2 into the data sequence 1 into the data sequence m; the specific insertion method is: insert the training sequence T ₁ (i) into the data sequence 1 on the first antenna , the training sequence T ₂ (i) is inserted into the data sequence 2 on the second antenna, and so on until the training sequence T _M (i) is inserted into the data sequence M on the Mth antenna; T _m (i ) are inserted into the same positions for each antenna data sequence, and then the inserted sequence is subjected to IFFT operation, and the obtained result is then subjected to cyclic prefix (CP) processing, and the result obtained in this way is subjected to framing processing, and is composed of each The radio frequency antenna transmits (as shown in Figure 4);

The receiving end processes the received signal as follows (as shown in Figure 6):

Step 4: On the p-th receiving antenna, pass the received sequence transmitted by the transmitter through a sliding window of size N, p ∈ [1, P], P is the number of receiving antennas, which takes a positive integer and is greater than 1 ; Divide the data r _i in the window into two halves, the first half is r _i , 0≤i≤N/2-1, the second half is r _i , N/2≤i≤N-1; The information on the length of τ in front of the two half-sequences is removed, and the following information is used to correlate to obtain the correlation value φ(d), where d represents the time offset and takes a positive integer:

$\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Step 5: Normalize the correlation value φ(d) obtained in Step 4 to obtain a correlation peak M(d) (as shown in Figure 7):

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Among them, R(d) is the sum of the information power for formula (2) operation

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

，L取正整数，且其取值大于1；Step 6: Then set a hard-judgment threshold and a sliding window with a length of N, starting from the sequence in the sliding window corresponding to the time offset point exceeding the threshold in the correlation peak M(d), consecutively L pieces of length N The sequence is selected, set this sequence as g _i (t), i=0, 1, ..., L-1, t = 0, 1, ..., N-1; record the time deviation exceeding the threshold Move point to

, L takes a positive integer, and its value is greater than 1;

Step 7: Perform FFT operation on the L sequences g _i (t) of length N obtained in step 6 to obtain G _i (k), i=0, 1, ..., L-1, k=0 ,1,...,N-1:

${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;jnk</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Step 8: The sequence G _i (k) obtained in step 7 is then inserted into the training sequence in step 2 of the transmitting end, and the information of the corresponding position is extracted. The specific extraction method is: detecting the information transmitted by the first transmitting antenna Arrive at the time fine synchronization point of the p-th receiving antenna, the first, 2M+1, 4M+1 in G _i (k), and so on to the 2(Q-1)M+1 Extract the information; detect that the information transmitted by the second transmit antenna reaches the time fine synchronization point of the p-th receive antenna, and use the third, 2M+3, and 4M+3 bits in G _i (k) as By analogy, the 2nd (Q-1)M+3 bit information is extracted; by analogy, the information transmitted by the M-th transmitting antenna reaches the time fine synchronization point of the p-th receiving antenna, and the G _i (k) 2M-1 bit, 2M+2M-1 bit, 4M+2M-1 bit, and so on until the 2(Q-1)M+2M-1 bit information is extracted; and the local sequence c _m (k) Correlation multiplication is carried out, and the time fine synchronization point of the mth transmitting antenna signal can be obtained

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; \{</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; jM</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Wherein, G _i ^* (2m-1+2jM) represents the result of calculating the conjugate of G _i (2m-1+2jM).

求和，得到第m路发射天线发射的信号到达第p路接收天线的时间同步点：Step 9: Offset the time obtained in step 6 Synchronize with the time obtained in step 8

The sum is obtained to obtain the time synchronization point when the signal transmitted by the m-th transmitting antenna reaches the p-th receiving antenna:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Step 10: After obtaining the time synchronization point from step 9, obtain the time-adjusted information; then perform frequency synchronization on the time-adjusted information to obtain the information after frequency synchronization processing; then de-cyclic prefix the information after frequency synchronization processing (CP) processing; performing FFT processing on the information after removing the cyclic prefix (CP) processing.

It should be noted that, considering that the relative delays of the M antennas are different, the information of the front τ length is removed from both the front and back halves of the data in the window. τ≥D _p in step 1 of the receiving end, let d _m represent the relative delay of the receiving antenna receiving the signals of each transmitting antenna, D _p =max{d ₁ , d ₂ ,..., d _m }. In addition, in the processing steps of the receiving end, from step 1 to step 3 is time coarse synchronization processing, and from step 4 to step 5 is time fine synchronization processing.

The present invention is a method for MIMO-OFDM synchronization using a training sequence, which is characterized in that: in the frequency domain of the transmitting end, the training sequences of each antenna are placed separately to distinguish different time delays, and can perform time fine synchronization; in the time domain of the receiving end , these separately placed training sequences undergo IFFT transformation and have the same two halves after superposition. Therefore, a search window is set, and the autocorrelation operation of the two half-sequences before and after is performed. Set a threshold value, record the time offset point exceeding this threshold value, and obtain the time coarse synchronization point. Then take a segment of the sequence that exceeds this threshold and perform a sliding FFT operation, and then obtain a multi-segment sequence in the frequency domain. Afterwards, the information of the corresponding position in the multi-segment sequence is taken out, and the correlation operation is performed with the local training sequence. When the maximum peak value is obtained, it is considered that the precise time synchronization point has been obtained. After the time synchronization point is found, perform frequency synchronization.

The innovation of the present invention lies in the use of the characteristics of IFFT transformation, so that the training sequence inserted by each antenna of the transmitting end can still obtain two identical half-sequences after superimposition when the signal delays of the transmitting antennas arriving at the receiving antenna are different. Therefore, rough time synchronization is performed in the time domain of the receiving end, and fine time synchronization is performed in the frequency domain; after time synchronization at the receiving end is obtained, frequency synchronization can be easily obtained. In terms of time synchronization, the present invention takes into account the fact that the arrival delays of each transmitting antenna are different, so it has wider significance and is applicable to distributed MIMO systems.

The basis of the present invention is:

1) Since the training sequence is known, when the selected training sequence b[k] has excellent autocorrelation properties, it is easy to realize the time and frequency synchronization of OFDM.

2) Since the even bits in the synchronization symbol are all zero, the odd bits are all inserted training sequences. In the frequency domain of the transmitter, if the odd bit of the training sequence is inserted into a pseudo-random sequence, and the even bit is inserted into a zero, then two identical half-sequences can be obtained after IFFT. Therefore, our training sequence insertion method can ensure that after the training sequences on the M transmit antennas undergo IFFT, two identical half-sequences can be obtained. Therefore, even when the time delays for each transmitting antenna to reach the receiving antenna are different, the receiving antenna can still obtain two identical half-segment sequences (as shown in FIG. 8 ). Here, let t _m (i) be the result of corresponding T _m (i) after IFFT operation, let a _i , b _i , and c _i be t ₁ (i), t ₂ (i), t ₃ (i) respectively the sequence of. d ₂ , d ₃ are delays of t ₂ (i), t ₃ (i) sequences relative to t ₁ (i), respectively. When d ₃ is the maximum delay, the two half-sequences 1 and 2 are exactly the same after being superimposed as shown in the figure.

3) According to the above principle, two identical half-segment sequences can be used to perform coarse time synchronization and frequency synchronization. The positions are separated due to the previous training sequence inserted by each antenna. Therefore, the sliding FFT operation is performed on the sequence exceeding the threshold, and then the correlation operation with the local training sequence is performed at the receiving end to obtain the maximum peak and perform time fine synchronization processing.

The present invention has the following characteristics:

1. The training sequence at the origin is composed of a PN sequence plus a "1" at the end;

2. The even bits in the synchronization symbol at the sending end are all zero, and the odd bits are all inserted training sequences, and the training sequences of each antenna are placed separately to distinguish different delays;

3. The synchronization symbols of each transmitting antenna at the transmitting end are in the frequency domain, and their positions are the same.

4. Time synchronization at the receiving end is divided into coarse time synchronization in the time domain and fine time synchronization in the frequency domain.

5. The receiving end first autocorrelates the received data in the first and second halves to obtain the time coarse synchronization point. Then, the sequence exceeding the threshold is subjected to sliding FFT operation, and then part of the information is extracted and cross-correlated with the local training sequence to obtain the precise time synchronization point.

6. The objective function of time coarse synchronization at the receiving end is the result of the square of the accumulated value of each correlation value calculated in the search window and then performing normalization processing.

7. The objective function of time fine synchronization at the receiving end is the square of the accumulated value of each correlation value calculated in the search window. The beneficial effects of the present invention are:

By inserting synchronization symbols in which even bits are zero and odd bits are training sequences at the sending end, different time delays can be distinguished, which is suitable for distributed MIMO systems. Therefore, it has the advantages of easy implementation, strong practicability, and wide application; at the same time, it has the advantages of less bandwidth occupation and high spectrum utilization.

Description of drawings

Figure 1 is a block diagram of a general MIMO-OFDM system

Among them, 1 is the serial-to-parallel conversion module, 2 is the modulation module, 3 is the space-time processing module, 4 is the IFFT transformation module, 5 is the cyclic prefix CP module, 6 is the framing module, 7 is the synchronization module, and 8 is the deframing module Module, 9 is the CP module for removing the cyclic prefix, 10 is the FFT transformation module, 11 is the channel estimation module, 12 is the space-time processing module, and 13 is the turbo receiver module;

Figure 2 is a schematic diagram of MIMO-OFDM synchronization using time-orthogonal training sequences

In the figure, the receiving end multiplies and accumulates the conjugates of the corresponding bits of the two sequences received on each antenna to obtain the objective function value; among them, TX1 represents the training sequence inserted on the first transmitting antenna, and TX2 represents the first transmitting The training sequence inserted on the antenna; they all have a space of 2N _train length, where the first half of TX1 inserts the training sequence, and the second half inserts zeros; the first half of TX2 inserts zeros, and the second half inserts is Training sequence; the training sequences inserted on the two transmitting antennas are the same, which are a protection prefix with a length of 2N _g , and then two repeated training sequences with a length of N _c ;

Figure 3 is a schematic diagram of inserting orthogonal training sequences at the same position for MIMO-OFDM synchronization

In the figure, there are Q repeated lengths of _N1 pilot sequences, and their prefix lengths are all G;

Figure 4 is a schematic diagram of synchronous symbol insertion at the sending end

In the figure, the position where the training sequence is inserted is before the IFFT transformation; among them, 1 is the serial-to-parallel conversion module, 4 is the IFFT transformation module, 5 is the cyclic prefix CP module, and 6 is the framing module;

Figure 5 is a schematic diagram of the insertion of the training sequence of each antenna at the transmitting end to form a synchronization symbol

Among them, T ₁ (i) is the training sequence inserted on the first transmitting antenna, T ₂ (i) is the training sequence inserted on the first transmitting antenna, T ₃ (i) is the training sequence inserted on the first transmitting antenna training sequence; in T ₁ (i), c ₁ (1) is the first information of sequence c ₁ (k), c ₁ (2) is the second information of sequence c ₁ (k), c ₁ (3 ) is the third information of the sequence c ₁ (k); in T ₂ (i), c ₂ (1) is the first information of the sequence c ₂ (k), and c ₂ (2) is the sequence c ₂ (k ), c ₂ (3) is the third information of sequence c ₂ (k); in T ₃ (i), c ₃ (1) is the first information of sequence c ₃ (k), c ₃ (2) is the second information of the sequence c ₃ (k); M is the number of transmitting antennas;

Figure 6 is a schematic diagram of the receiving end synchronization process

Wherein, 9 is the decyclic prefix CP module, and 10 is the FFT transformation module;

Figure 7 is a schematic diagram of the correlation peak obtained in the coarse synchronization of the receiving end time

Wherein, the curve represents the normalized correlation peak M(d) obtained by step 5, and the amplitude value 0.8 represents the hard judgment threshold;

Fig. 8 is a schematic diagram of two identical half-sequences obtained by the receiving end under the condition that the time delays of each transmitting antenna are different in the basis of the present invention

Among them, t ₁ (i) represents the sequence transmitted by the first transmitting antenna obtained by the receiving antenna, t ₂ (i) represents the sequence transmitted by the second transmitting antenna obtained by the receiving antenna, and t ₃ (i) represents the sequence obtained by the receiving antenna The sequence transmitted by the third transmitting antenna; a ₁ to a ₇ represent the information of the received sequence t ₁ (i); b ₁ to b ₇ represent the information of the received sequence t ₂ (i); c ₁ to c ₇ Represents the information of the received sequence t ₃ (i); d ₂ represents the sequence transmitted by the second transmitting antenna, compared with the sequence transmitted by the first transmitting antenna, the time delay of reaching the receiving antenna; d ₃ represents the delay of the third The sequence transmitted by the first transmitting antenna, compared with the sequence transmitted by the first transmitting antenna, arrives at the delay of the receiving antenna;

Detailed ways

The implementation method of this patent under a specific MIMO-OFDM configuration is given below. It should be noted that the parameters in the following examples do not affect the generality of this patent.

It is assumed that the OFDM useful symbol length is N=2048. The MIMO model is four transmissions and four receptions, that is, M and P are both 4. The relative delays from the four transmitting antennas to the receiving antennas are 0, 5, 10, and 15 sampling points respectively. Then define τ in Formula 2 as 20 sampling points.

1. Origin:

Select four PN sequences, the m sequence whose period is 255, recorded as b _m [k]k∈[1, 255], add a "1" at the end to get c _m (k)k∈[1, 256] m ∈ [1, 4], c _m (k) ∈ {1+j, -1-j}. Interpolate according to formula 1 to obtain the synchronization symbols T _m (i)i∈[0, N-1] of the four transmitting antennas.

Second, the receiving end

，然后得到250个长度为N的序列，设这段序列为g_i(t)，i＝0，1，...，L-1，t＝0，1，...，N-1。然后按照公式5，得到频域信息G_i(k)，再按照公式6进行与本地序列相关运算，得到时间精同步点，于是粗精同步点按照公式7，就可以得到总的时间同步点。The receiving end passes the received data through a sliding window with a size of 2048. In this window, the objective function is calculated according to formula 2. When the function value is greater than the preset threshold of 0.8, the time coarse synchronization point is obtained.

, and then get 250 sequences of length N, set this sequence as g _i (t), i=0, 1, ..., L-1, t = 0, 1, ..., N-1. Then according to Formula 5, the frequency domain information G _i (k) is obtained, and then the local sequence correlation operation is performed according to Formula 6 to obtain the time fine synchronization point, so the coarse and fine synchronization point is according to Formula 7, and the total time synchronization point can be obtained.

Claims (1)

1, a kind of multi-input multi-out-OFDM synchronous method, it is made up of sending end and receiving end two parts, and concrete steps are as follows: The sending end processes the transmitted signal as follows: Step 1: Define the number of transmitting antennas as M, M is a positive integer, and the number of M is greater than 1; select M PN sequences b _m [k] whose length is N ₁ , and N ₁ is a positive integer; the PN A "1" is added at the end of the sequence b _m [k] to form a sequence c _m (k) of length Q, k∈[0, Q-1], m∈[1, M]; at this time, c _m (k ) takes a complex number form, that is, c _m (k)∈{1+j, -1-j}; Step 2: Perform zero-insertion processing on the sequence c _m (k) obtained in step 1 to generate a training sequence T _m (i) transmitted by each antenna, i∈[0, N-1], where N is the number of FFT points of the OFDM system , and take a positive integer; the specific method of zero insertion processing is: the first information _{c 1} (1) of the sequence c 1 (k) is inserted into the first bit of the training sequence T ₁ (i) of the first transmitting antenna ; The second information c ₁ (2) of the sequence c ₁ (k) is inserted into the 2M+1 bit of the training sequence T ₁ (i); the third information c ₁ (3) is inserted into T ₁ (i) 4M+1 bit of , and so on, until the kth information c ₁ (k) is inserted into the 2(Q-1)M+1 bit of T ₁ (i), the rest of the training sequence T ₁ (i) Bits are all zero-inserted; for the second transmitting antenna, the first information c ₂ (1) of the sequence c ₂ (k) is inserted into the third bit of the corresponding training sequence T ₂ (i); the sequence c ₂ ( The second information c ₂ (2) of k) is inserted into the 2M+3 bit of the training sequence T ₂ (i); the third information c ₂ (3) is inserted into the 4M of the training sequence T ₂ (i) +3 bits, and so on, until the kth information c ₂ (k) is inserted into the 2(Q-1)M+3 bits of T ₂ (i), and the remaining bits of the training sequence T ₂ (i) are inserted zero; and so on, the first information c _M (1) of the sequence c _M (k) is inserted into the 2M-1th bit of the training sequence T _M (i) of the first transmitting antenna; the sequence c _M (k ) of the second information c _M (2), inserted into the 2M+2M-1 bit of the training sequence _TM (i); the third information c _M (3) inserted into the 4M+ of _TM (i) 2M-1 bit, and so on, until the kth information c _M (k) is inserted into the 2(Q-1)M+2M-1 bit of _TM (i), the rest of the training sequence _TM (i) Zero interpolation in all bits; here, the relationship between N and the number of transmitting antennas M must satisfy: N=2MQ;

Step 3: insert the training sequence T _m (i) obtained in step 2 into the data sequence 1 into the data sequence m; the specific insertion method is: insert the training sequence T ₁ (i) into the data sequence 1 on the first antenna , the training sequence T ₂ (i) is inserted into the data sequence 2 on the second antenna, and so on until the training sequence T _M (i) is inserted into the data sequence M on the Mth antenna; T _m (i ) to insert the data sequence of each antenna at the same position, and then perform IFFT operation on the inserted sequence, and then add cyclic prefix CP to the obtained result, and then perform framing processing on the result obtained in this way, and use it by each radio frequency antenna launch out; The receiving end processes the received signal as follows: Step 4: On the p-th receiving antenna, pass the received sequence transmitted by the transmitter through a sliding window of size N, p ∈ [1, P], P is the number of receiving antennas, which takes a positive integer and is greater than 1 ; Divide the data r _i in the window into two halves, the first half is r _i , 0≤i≤N/2-1, the second half is r _i , N/2≤i≤N-1; The information on the length of τ in front of the two half-sequences is removed, and the following information is used to correlate to obtain the correlation value φ(d), where d represents the time offset and takes a positive integer: $\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ Step 5: Normalize the correlation value φ(d) obtained in Step 4 to obtain a correlation peak M(d): $\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ Among them, R(d) is the sum of the information power for formula (2) operation $\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$ Step 6: Then set a hard-judgment threshold and a sliding window with a length of N, starting from the sequence in the sliding window corresponding to the time offset point exceeding the threshold in the correlation peak M(d), consecutively L pieces of length N The sequence is selected, set this sequence as g _i (t), i=0, 1, ..., L-1, t = 0, 1, ..., N-1; record the time deviation exceeding the threshold Move point to

, L takes a positive integer, and its value is greater than 1; Step 7: Perform FFT operation on the L sequences g _i (t) of length N obtained in step 6 to obtain G _i (k), i=0, 1, ..., L-1, k=0 ,1,...,N-1: ${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;jnk</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ Step 8: The sequence G _i (k) obtained in step 7 is then inserted into the training sequence in step 2 of the transmitting end, and the information of the corresponding position is extracted. The specific extraction method is: detecting the information transmitted by the first transmitting antenna Arrive at the time fine synchronization point of the p-th receiving antenna, the first, 2M+1, 4M+1 in G _i (k), and so on to the 2(Q-1)M+1 Extract the information; detect that the information transmitted by the second transmit antenna reaches the time fine synchronization point of the p-th receive antenna, and use the third, 2M+3, and 4M+3 bits in G _i (k) as By analogy, the 2nd (Q-1)M+3 bit information is extracted; by analogy, the information transmitted by the M-th transmitting antenna reaches the time fine synchronization point of the p-th receiving antenna, and the G _i (k) 2M-1 bit, 2M+2M-1 bit, 4M+2M-1 bit, and so on until the 2(Q-1)M+2M-1 bit information is extracted; and the local sequence c _m (k) Correlation multiplication is carried out, and the time fine synchronization point of the mth transmitting antenna signal can be obtained

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; \{</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; jM</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$ Among them, G _i ^* (2m-1+2jM) represents the result of conjugating G _i (2m-1+2jM); Step 9: Offset the time obtained in step 6

Synchronize with the time obtained in step 8

The sum is obtained to obtain the time synchronization point when the signal transmitted by the m-th transmitting antenna reaches the p-th receiving antenna: ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$ Step 10: After obtaining the time synchronization point from step 9, obtain the time-adjusted information; then perform frequency synchronization on the time-adjusted information to obtain the information after frequency synchronization processing; then de-cyclic prefix the information after frequency synchronization processing CP processing; FFT processing is performed on the information after the CP processing without the cyclic prefix.

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