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The phase noise process typically has a low-pass spectrum [1].
where ϕ Tx t) denotes the phase noise process of the oscillator used by the transmitter.
Note from (13) that the estimation algorithm does not need specific knowledge about the phase noise process.
Thus, ϕ Tx t)=ϕ Rx t), and we denote the common phase noise process by ϕ(t).
(iv) Recently, iterative joint estimation and decoding/detection algorithms have been proposed that make use of the a priori statistics of the phase noise process.
zero-mean circularly symmetric complex-valued Gaussian random variables with, and is a time-varying phase noise process with correlation matrix.
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(1) ; (2).. Figure 6 compares the BER degradations at resulting from Wiener phase noise and first-order phase noise; the value of is the same for both phase noise processes, such that the Wiener phase noise spectrum and first-order phase noise spectrum are the same for large.
(iv) Figure 6 compares the BER degradations at resulting from Wiener phase noise and first-order phase noise; the value of is the same for both phase noise processes, such that the Wiener phase noise spectrum and first-order phase noise spectrum are the same for large.
However, unlike the constant CFO and IQ imbalance, phase noise is a stochastic process during an OFDM symbol period and therefore causes a greater challenging problem.
At the transmitter, phase noise is introduced during the upconversion process, so the transmitted RF signal is: begin{array}{*{20}l} {hat{x}} & = Releft{{tilde{x}} e^{j 2pi f_{c}t+phi_{text{Tx}}(t))}right}, end{array} (1).
At the receiver, phase noise is introduced during the downconversion process: begin{array}{*{20}l} {hat{r}} & = text{LPF}left{{hat{x}} e^{-j 2pi f_{c}t+phi_{te^{-j 2pit-Delta t))}right} end{array} (2).
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