Why is the parabolic disc antenna and how is it connected with Fermat's law?

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Why is the parabolic disc antenna and how is it connected with Fermat's law?

According to Fermat's theorem, a ray follows the direction that takes the least amount of time, and occurs only when the angle of incidence is identical to the angle of reflection or propagation. The rays of light (EM-waves) travel the direction of stationary optical length, according to Fermat's theory (principle of least time).

Dish antennas are typically parabolic so that they can combine all incoming signals to increase their strength. Incoming signals are particularly weak for dish TV antennas. So we use parabolic antennas to add up many identical signals at the focus point. The above structure of a parabolic antenna suggests that all rays have nearly the same length (or take the least amount of time as per fermat's principle) to reach the focus point.

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Theoretical BER vs SNR for BPSK

Let's simplify the explanation for the theoretical Bit Error Rate (BER) versus Signal-to-Noise Ratio (SNR) for Binary Phase Shift Keying (BPSK) in an Additive White Gaussian Noise (AWGN) channel. Key Points Fig 1: Constellation Diagrams of BASK, BFSK, and BPSK [↗] BPSK Modulation: Transmits one of two signals: +√Eb or -√Eb , where Eb is the energy per bit. These signals represent binary 0 and 1 . AWGN Channel: The channel adds Gaussian noise with zero mean and variance N0/2 (where N0 is the noise power spectral density). Receiver Decision: The receiver decides if the received signal is closer to +√Eb (for bit 0) or -√Eb (for bit 1) . Bit Error Rate (BER) The probability of error (BER) for BPSK is given by a function called the Q-function. The Q-function Q(x) measures the tail probability of the normal distribution, i.e., the probability that a Gaussian random variable exceeds a certain value x. Formula for BER: BER=Q(...

MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ...

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Constellation Diagrams of ASK, PSK, and FSK

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Constellation Diagram of PSK in Detail

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