Modulation Efficiency Calculator

Calculate spectral efficiency and SNR requirements for digital modulation schemes.

Modulation Selection

Modulation Scheme

Channel Parameters

Symbol Rate (Msym/s)

Channel Bandwidth (MHz)

Error Correction

Coding Rate

Target BER

OFDM Parameters (Optional)

Subcarriers

Cyclic Prefix (%)

Modulation Comparison

Modulation	bits/sym	Eb/N0 (BER 10^-6)
BPSK/QPSK	1/2	10.5 dB
8-PSK	3	14 dB
16-QAM	4	14.5 dB
64-QAM	6	18.5 dB
256-QAM	8	24 dB
1024-QAM	10	28 dB

Uncoded AWGN channel, practical systems need 1-3 dB margin

Modulation Formulas

Spectral Efficiency

eta = R * log2(M) * (1 - CP)
R = code rate, M = constellation size, CP = cyclic prefix

Spectral efficiency measures how many bits per second can be transmitted per Hz of bandwidth. Higher-order modulation increases efficiency but requires better SNR.

SNR and Eb/N0

SNR = Eb/N0 * (Rb/B)
SNR(dB) = Eb/N0(dB) + 10*log10(bits/symbol)

Eb/N0 is energy per bit over noise density
Higher modulation needs higher SNR
Coding gain reduces Eb/N0 requirement