Question

Given an AWGN channel, if the same BER is achieved using three schemes (BPSK, QPSK, and 16-QAM), compare the necessary energy per bit among the three.

We compare using BPSK, QPSK, and 16-QAM as the modulating schemes for communications in an AWGN channel.

If the same BER is achieved using all the three schemes, compare the necessary energy per bit among t three.

Answer 1

In an AWGN channel, the necessary energy per bit depends on the modulation scheme being used. BPSK requires the highest energy per bit, followed by QPSK, and 16-QAM requires the lowest energy per bit to achieve the same Bit Error Rate (BER).

Step-by-step explanation:

In communications over an Additive White Gaussian Noise (AWGN) channel, the necessary energy per bit depends on the modulation scheme being used. BPSK (Binary Phase Shift Keying), QPSK (Quadrature Phase Shift Keying), and 16-QAM (16-Quadrature Amplitude Modulation) are three commonly used modulation schemes. If the same Bit Error Rate (BER) is achieved using all three schemes, the necessary energy per bit can be compared.

BPSK, QPSK, and 16-QAM differ in their spectral efficiency, which is the number of bits that can be transmitted within a given bandwidth. BPSK is the least efficient among the three, followed by QPSK, and 16-QAM is the most efficient. Therefore, to achieve the same BER, BPSK requires the highest energy per bit, followed by QPSK, and 16-QAM requires the lowest energy per bit.

For example, BPSK can transmit 1 bit per symbol, QPSK can transmit 2 bits per symbol, and 16-QAM can transmit 4 bits per symbol. This means that when the same BER is achieved, fewer symbols need to be transmitted with 16-QAM compared to QPSK and BPSK, resulting in lower energy per bit for 16-QAM.