Question

If the same bit rate is achieved with all three schemes (BPSK,QPSK, 16-QAM), compare the necessary bandwidth between the three schemes.

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

If the same bit rate is achieved using all the three schemes, compare the necessary bandwidth among the three.

Answer 1

In a comparison of BPSK, QPSK, and 16-QAM as modulating schemes for communications in an AWGN channel:

1. If the same BER is achieved using all three schemes, the necessary energy per bit differs. BPSK requires the least energy per bit, followed by QPSK, and then 16-QAM.
2. If the same bit rate is achieved, the necessary bandwidth differs among the three schemes. BPSK requires the least bandwidth, followed by QPSK, and then 16-QAM.
3. If the communication consumes the same power and achieves the same BER, the bit rate and bandwidth also differ among the three schemes. BPSK offers the highest bit rate and highest bandwidth, followed by QPSK, and then 16-QAM.

Step-by-step explanation:

Comparing BPSK, QPSK, and 16-QAM as modulating schemes in an AWGN channel, we can analyze the necessary energy per bit, bandwidth, and bit rate under different conditions.

1. If the same Bit Error Rate (BER) is achieved using all three schemes:

• - BPSK: BPSK uses two distinct phase angles to represent binary 0 and 1. The necessary energy per bit would be the lowest among the three schemes.
• - QPSK: QPSK represents two bits per symbol, using four phase angles. The necessary energy per bit would be higher compared to BPSK, as more bits are represented per symbol.
• - 16-QAM: 16-QAM represents four bits per symbol, using a combination of amplitude and phase. The necessary energy per bit would be higher than both BPSK and QPSK, as more bits are represented per symbol.

2. If the same bit rate is achieved using all three schemes:

• - BPSK: BPSK represents one bit per symbol. Therefore, it would require the widest bandwidth among the three schemes to achieve the same bit rate.
• - QPSK: QPSK represents two bits per symbol. It would require a narrower bandwidth compared to BPSK to achieve the same bit rate.
• - 16-QAM: 16-QAM represents four bits per symbol. It would require the narrowest bandwidth among the three schemes to achieve the same bit rate.

3. If the communication consumes the same power and achieves the same BER using all three schemes:

• - In this case, the necessary energy per bit would be the same for all three schemes.
• - The bit rate would depend on the modulation scheme and the bandwidth available. BPSK would have the lowest bit rate, followed by QPSK, and then 16-QAM.
• - The necessary bandwidth would depend on the modulation scheme and the required bit rate. BPSK would require the widest bandwidth, followed by QPSK, and then 16-QAM.

Your question is incomplete, but most probably the full question was:

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

• 1. If the same BER is achieved using all the three schemes, compare the necessary energy per bit among the three.
• 2. If the same bit rate is achieved using all the three schemes, compare the necessary bandwidth among the three.
• 3. If the communication consumes the same power (note: power is energy per unit time) using all the three schemes, and the same BER is achieved as well, compare the bit rate and bandwidth among the three.