Why QPSK and 4-QAM Should Have Same BER? (with Simulator)

M-PSK vs M-QAM BER Calculator

Understand Bit Error Rate (BER), Eb/N0, QPSK, 4-QAM, M-PSK and M-QAM through theory, mathematics and interactive simulation.

What is BER?

Bit Error Rate (BER) represents the probability that a transmitted bit is received incorrectly after passing through a communication channel.

BER = Number of Error Bits / Total Transmitted Bits

What is Eb/N0?

Eb/N0 measures signal energy per bit relative to noise spectral density. Higher Eb/N0 means cleaner communication and lower BER.

Eb/N0 (Linear) = 10^(Eb/N0(dB)/10)

M-PSK BER Formula

For coherent M-PSK systems:

BER ≈ (2/log₂(M)) Q(√(2log₂(M)Eb/N0) sin(π/M))

Special Cases:

BPSK: BER = Q(√(2Eb/N0))

QPSK: BER = Q(√(2Eb/N0))

M-QAM BER Formula

BER ≈ [4(1−1/√M)/(log₂M)] Q(√(3log₂(M)Eb/N0/(M−1)))

Why QPSK and 4-QAM Should Have Same BER

QPSK and 4-QAM have identical constellation spacing. Both effectively transmit 2 bits/symbol. Therefore:

BER(QPSK) = BER(4-QAM)

At Eb/N0 = 10.53 dB: BER ≈ 1 × 10⁻⁶ for both modulation schemes.

Interactive BER Calculator

Eb/N0 (dB) Modulation Type MPSK MQAM Modulation Order (M)

Waiting for calculation...

Common Student Mistakes

Mistake	Effect
Using Degrees instead of Radians	Incorrect BER
Confusing Es/N0 with Eb/N0	Wrong Results
Using QPSK approximation incorrectly	BER mismatch
Ignoring Gray Coding	Higher BER

Simulation Workflow

1. Generate random bits
2. Map bits into symbols
3. Apply M-PSK or M-QAM modulation
4. Add AWGN noise
5. Demodulate received symbols
6. Compare received bits with transmitted bits
7. Compute BER

Frequently Asked Questions

Why does BER decrease with Eb/N0?

Higher signal energy improves symbol detection.

Why are QPSK and 4-QAM equivalent?

They have identical Euclidean distance between constellation points.

Which performs better, PSK or QAM?

At higher modulation orders, QAM is usually more power efficient.