Why is the BER the same for BPSK and QPSK? 

Outstanding! 👌👌👍👍

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Nice video but why are you assigning a symbol vector magnitude of A to the BPSK symbols and a different symbol vector magnitude (A*sqrt(2)) to the QPSK symbols? This would mean that the QPSK system uses more power than the BPSK system. This is not a necessary assumption afaik for the QPSK system to have the same BER performance as the BPSK system

I understand symbol energy. But what is the notion of bit energy. The notion of bits comes only after demapping the received symbols. For eg for OPSK/QAM(2 bits/symbol), how can we divide the symbol energy /2 to get bit energy as there is no notion of bits until demapper output.. Please help here in my understanding

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In this case does Eb/N0 misleading or SNR misleading ?

The instantaneous power is the squared signal x(t), that is clear. But what is the unit of that signal? Is it always the voltage or can it be different (e.g. electr. field E, magn. field H, power density S = E × H in W/m^2)? Thanks a lot.

I had 3 ads during that 11 minutes 😂😂

Could you kindly provide us with a reference book in this field that offers an explanation similar to yours?

*BPSK and QPSK: Understanding Bit Error Rate* *Abstract* This video delves into the comparison of Bit Error Rate (BER) between BPSK (Binary Phase Shift Keying) and QPSK (Quadrature Phase Shift Keying) modulation schemes. The analysis reveals that while both methods can exhibit the same BER, this is contingent upon maintaining equal energy per bit rather than equal signal-to-noise ratio (SNR). The video elucidates the underlying reasons for this phenomenon, emphasizing the role of orthogonal basis functions (cosine and sine) and the impact of bit mapping on error probabilities. Furthermore, it clarifies that the observed BER equivalence between BPSK and QPSK under equal energy per bit is a unique case, not generalizable to higher-order modulation schemes like 16-QAM due to limitations in available degrees of freedom. *BPSK Modulation and Energy per Bit* * 0:00: The video aims to explain why BPSK (Binary Phase Shift Keying) and QPSK (Quadrature Phase Shift Keying) can have the same bit error rate (BER) under certain conditions. * 0:15: BPSK uses two constellation points on a constellation diagram, each representing a digital 0 or 1. * 0:39: The x-axis represents the cosine axis, modulating a cosine wave format at the carrier frequency. * 0:49: The y-axis represents the sine axis, with power determined by the square of the amplitude (a²). * 1:07: The energy devoted to sending one bit (energy per bit) is calculated as power multiplied by the time period (a² * T). * 1:26: Errors occur when noise pushes the received value beyond the decision boundary (amplitude "a") on the constellation diagram. *QPSK Modulation and Energy per Bit* * 2:01: QPSK employs four constellation points, each representing two bits. * 2:12: The video compares scenarios where the power in QPSK is double that of BPSK (2 * a²). * 2:36: Since QPSK transmits two bits per symbol, the energy per bit is calculated as (2 * a² * T) / 2, resulting in the same energy per bit as BPSK (a² * T). * 3:33: The video emphasizes that comparing BER between modulation schemes requires considering whether the comparison is based on the same signal-to-noise ratio (SNR) or the same energy per bit. *BER Comparison and Degrees of Freedom* * 3:56: When comparing BER with the same energy per bit, BPSK and QPSK exhibit the same BER due to the utilization of two orthogonal basis functions (cosine and sine). * 4:24: In QPSK, the decision boundaries are at 45 degrees, aligned with these basis functions. * 5:30: Noise is independent in orthogonal basis functions, leading to similar error probabilities in both BPSK and QPSK. * 7:30: The video highlights that symbol errors in QPSK may only result in a single bit error due to the bit mapping, hence the factor of 1/2 in the BER calculation. * 9:59: The property of achieving the same BER with doubled power and data rate is specific to the BPSK-QPSK comparison and does not extend to higher-order modulation schemes like 16-QAM due to the limited degrees of freedom (two: sine and cosine). i used gemini 1.5 pro Token count 3,910 / 1,048,576