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The escape times analysis implies existence of lower dimensional dynamics around the perfect synchronization.
The formulae has a delta-type stationary solution which represents the perfect synchronization with probability 1.
Besides, we also assume the perfect synchronization between the transmitter and receiver has been achieved.
The perfect synchronization is assumed and the synchronization issue is not discussed in this paper.
Moreover, the perfect synchronization of multiple antenna systems leads to high implication complexity.
It appears that the perfect synchronization of academy, publishing, research resources, and practice is beginning to develop.
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We note that, differently from the aforementioned state-of-the-art contributions, herein, the necessary perfect synchronization of both primary and secondary signals at the primary receiver is achieved by means of a simplified strategy, based on a hybrid transceiver design.
Figure 5 Remaining CFO. Figure 6 depicts the MSE of the channel estimation algorithm (blue plots) when the system has perfect synchronization and the MSE of the joint CFO and channel estimation process (red plots), when using QPSK, 16-QAM, and 64-QAM modulations.
The main difference between the SER obtained assuming the synchronization approaches and the curve assuming perfect synchronization is that the high variance of the CFO in low SNR regime leads to a performance gap when the synchronization techniques are considered.
Then, in the second time slot, with the assumption of perfect synchronization, RNs broadcast the processed version of the received signal to the two users to complete information exchange.
In the case of perfect synchronization at the beginning of the OFDM symbol, ϕ(−1)=0and therefore, (6) can be expressed alternatively as ϕ ( n ) = ∑ m = 0 n v ( m ), n = 0, 1, …, N − 1. (7).
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