Development of Blind Frame Synchronization for Transfer System with Differential Space-Time Block Coding

The object of this research is the methods and algorithms for frame synchronization used in multi-antenna radio systems (Multiple Input Multiple Output – MIMO). The implementation of radio communication systems and, in particular, MIMO, implies that the demodulator synchronizes the phase of the reference carrier and the time of signal processing processes. Time synchronization is divided into symbolic and frame synchronization. As for the synchronization of the reference carrier and symbol synchronization, these types of synchronization are provided by traditional methods and are not considered in this paper. The frame synchronization in the vast majority of cases is provided by the use of pilot signals (sync words). At their core, they are markers and are periodically embedded in the data stream to indicate the beginning of another new data block. The resources of the transmission system, spent on the transmission of pilot signals, are not used to transmit user information, as a result of which the efficiency of using the time-frequency resource of the system is degraded. To a lesser extent, there are so-called «blind» signal processing methods based on the redundancy properties of the transmitted signal. These methods have no drawbacks from the use of pilot signals and are divided into methods for assessing the state of the communication channel, signal identification, and synchronization. Based on this, such methods are of practical interest.<br><br>In this work, let’s propose a frame synchronization method for demodulating differential space-time block coding signals using MIMO technology. The synchronization algorithm does not require the use of preambles and sync words, which ensure efficient use of the time-frequency resource. An analysis of the structure of the algorithm and the simulation results show its performance at low signal-to-noise ratios in the transmission system. The algorithm does not require knowledge of the state of the communication channel, has low computational complexity compared to existing analogues, and allows implementation with a different number of transmitting and receiving antennas.


Introduction
This work is a continuation of research on the develop ment of a transmission method with differential spacetime block coding (DSTBC) implemented using the Multiple Input Multiple Output (MIMO) technology [1].
To implement the method of transmission from the DSTBC in the demodulator, it is necessary to provide phase synchronization of the reference carrier, as well as time synchronization of signal processing processes [2,3]. The time synchronization task is divided into two: sym bolic (clock) synchronization and frame (block) synchroni zation. These two types of time synchronization are com pletely different in purpose and implementation. The task of symbol synchronization is to synchronize the clocks of the demodulator with the input stream of demodulated channel symbols so that each input symbol is processed in an appropriate time interval. The task of synchroniz ing frames (blocks) is to split the sequence of characters arriving at the decoder into blocks corresponding to the blocks at the output of the encoder. If the breakdown is not carried out correctly, decoding operations will be incorrect and restoration of transmitted characters be comes impossible.
As for synchronization of the reference carrier and symbol synchronization, these types of synchronization in demodulators of digital modulation signals are solved by traditional methods [4,5] and are not considered in this paper.
From literature it follows that in the vast majority of cases, frame synchronization is ensured by the use of pilot signals (sync words) (Reference Signal) [6,7] signals a priori known in the demodulator that have cer tain characteristics and properties. At their core, they are markers and are periodically embedded in the data stream to indicate the beginning of another new data block. It is obvious that the resources of the transmission sys tem spent on the transmission of pilot signals are not used directly for transmitting user information, as a re sult of which the efficiency of using the timefrequency TECHNOLOGY AUDIT AND PRODUCTION RESERVES -№ 1/2(51), 2020 ISSN 2664-9969 resource of the transmission system is degraded. The li terature also presents, but to a lesser extent, the socalled «blind» signal processing methods that do not require the transmission of special pilot signals, but are based on the properties of the transmitted information signal, in particular, using its redundancy [6,8]. These methods do not have the disadvantages created by the use of pilot signals, and are divided into methods for assessing the state of the com munication channel, signal identification, and synchroniza tion. Based on this, such methods are of practical interest.
There are works [9,10] that describe the methods of «blind» frame synchronization for orthogonal spacetime block coding (STBC). It should be noted that these methods: -use the spacetime redundancy of the transmitted signal (frames); -applicable for STBC orthogonal systems with one and two receiving antennas; -do not require knowledge of the state of the com munication channel and the signaltonoise ratio in the channel; -provide a low ability to detect the boundaries of frame intervals in the communication channel with Rayleigh fading at high signaltonoise ratios, as the authors themselves declare. It should also be noted that only these two blind frame synchronization methods for STBC orthogonal systems are described in the literature, and synchronization methods for STBC differential orthogonal systems are not described.
Based on the foregoing, in order to ensure frame syn chronization during demodulation of the DSTBC signals, it is decided to develop an effective frame synchronization algorithm based on this coding method without using pilot signals, which is the goal of this work. Thus, the subject of this research is the methods and algorithms for frame synchronization used in multiantenna radio communica tion systems (MIMO).

Methods of research
Below is the synchronization algorithm for the demodu lator of the DSTBC signals [1] in the MIMO scheme and. Since each channel symbol is transmitted twice during the DSTBC, the signal matrix can serve as an example: where x i * -complex conjugation of the symbol x i , it fol lows that the demodulated signal has a spacetime redun dancy, and it is possible to find a way to synchronize the working signal. Table 1 shows four consecutive frames transmitted over a communication channel. Here x i -the channel symbols of the LPSK signal. Table 1 Symbol transmission table by differential space-time block coding If it is necessary to demodulate the information trans mitted by frame 3 - is required, which will be the reference. This happens when the frame synchronization is correct. Having analyzed the Table 1, two immediate cases can be assumed in which frame synchronization is not set correctly.
In the first case, let's have the following values of the reference and signal matrices: In the second case, respectively: Thus, let's obtain three possible states, in one of which the frame synchronization is set correctly, and in the other two it is not true. Hypotheses on these condi tions can be respectively arbitrarily called: «early», «right» and «late».
Let's consider the demodulation of characters in the case of a hypothesis -«right». The samples of the signals received by the receiving antennas (frame 2 and frame 3), at the corresponding time points, can be written as: where, for example, y t Let's believe that the condition T T s 0  is satisfied, where T 0 -the coherence time, and T s -the duration of the channel symbol -hence, the matrix of channel coefficients H during T 0 is relatively constant [1]. In this case, the restored values of the differential coefficients transmitted by frame 3 are determined as: TECHNOLOGY AUDIT AND PRODUCTION RESERVES -№ 1/2(51), 2020 If to consider the 2 4 × MIMO scheme, then formu las (1)-(3) respectively will take the following form: An analysis of the matrices X 2err and X 3err shows that each of them contains symbols x i once (for example, in: X 2err : −x 2 * , x 1 * , x 3 , x 4 ), and also these matrices are not complex orthogonal forms (condition (2) in [1]). Given this, as well as the statistical independence and equi probability of the transmitted symbols x i , it should be concluded that when demodulating (in the estimates of the differential coefficients  R 1 and  R 2 ) there is no cohe rent accumulation of the transmitted symbols and they can be considered as readings from the implementation of some random process.
Consequently, the frame synchronization system of the DSTBC demodulator will analyze the three hypotheses outlined -«early», «right» and «late». The signal for choosing a particular hypothesis will be the minimum value of the sum of the accumulated values of the minimum distances for each hypothesis: where K -the number of frames (blocks) of observation for deciding on the presence/absence of frame synchroniza tion. As can be seen from the algorithm, these values are filtered (accumulation is performed). At each step, in order to correctly set the boundaries of the frames, a comparison is made between each other B false1 , B true , B false2 , and a particular hypothesis is selected based on the minimum of these values.

Research results and discussion
The simulation was performed in the MATLAB soft ware package using the Rayleigh channel of fading in the communication channel and observing the conditions for constant values of the channel coefficients h m n , during the coherence time T 0 . The model consisted of two (M = 2) transmitting and several (N = 1; 2; 4) receiving antennas, using QPSK modulation and K = 10; 20; 30; 40; 50. The input stream consisted of independent equally probable 5⋅10 7 bits of information, which was encoded using the DSTBC method [1] depending on the number of posi tions of the LPSK signal and the number of transmit ting antennas M, forming signal matrices X v that were transmitted to the radio channel, as indicated in Table 1. On the receiving side, the values were calculated: , where D erorr -the number of received frame blocks with no frame synchronization, on the signaltonoise ratio in the system (SNR).
Based on the analysis of the algorithm and the simula tion results, the following should be noted: 1) developed synchronization algorithm for analysis and decision making requires a significantly smaller number of frames (10-40) than the methods presented in [9, 10] -513-4097 frames are required; 2) description of the developed algorithm can easily be expanded for the cases of 4 transmitting and 8 receiving antennas in accordance with the DSTBC method (this extension of the algorithm was not included in the paper); also, the algorithm, if necessary, can be expanded for cases of delay or advancing relative to the beginning of the frame for a time or more; 3) this synchronization algorithm is not a separate structural part (such as methods [9,10]) in the imple mentation of the DSTBC method. At its core, the algo rithm is based on the DSTBC method and supplements it, extracting some data for further calculation and ensuring the decision on synchronization (formulas (3), (6)-(7) are part of the DSTBC method). In this regard, this synchro nization algorithm is much less computationally complex than previously proposed; TECHNOLOGY AUDIT AND PRODUCTION RESERVES -№ 1/2(51), 2020 ISSN 2664-9969 ISSN 2664-9969 4) when analyzing the dependences of the probability of the exit from synchronism ( ) P er_sinch (Fig. 1, 2) and the probability of error of the received bits (BER) [1,Fig. 6] it is possible to conclude that the developed synchroniza tion algorithm is more noiseresistant than the DSTBC method. Example: at QPSK, MIMO 2×2, K = 10; 20; 30; 40, -P er_sinch less than BER by 5; 7; 8.3 and 8.5 dB, re spectively.

Conclusions
The blind frame synchronization algorithm proposed for this work for the DSTBC method [1] is the first con sideration of the blind frame synchronization for STBC differential orthogonal systems. This algorithm has ad vantages over similar algorithms in the required number of frames to ensure synchronization and computational complexity, as well as being flexible for extensions. The simulation results confirm its ability to establish frame synchronization under the condition of a low signalto noise ratio in the system and the absence of the need for knowledge about the state of the communication channel.