DCO-OFDM vs Regular OFDM

Difference between DCO-OFDM and Regular OFDM

1. Regular OFDM (Orthogonal Frequency Division Multiplexing)

• In standard OFDM (used in RF communication):
  • The signal is complex-valued (has real and imaginary parts).
  • Subcarriers carry data in QAM/PSK modulation.
  • Signal can take both positive and negative values.
  • Usually transmitted over RF channels.
• No need for DC bias or clipping because the channel can handle bipolar signals.

2. DCO-OFDM (Direct Current-biased Optical OFDM)

• DCO-OFDM is a variant of OFDM designed for optical communication, e.g., VLC or optical fiber.
• Key differences from regular OFDM:

1. Unipolar requirement
   • Optical transmitters (LEDs, lasers) can only emit positive light intensity.
   • OFDM signals are naturally bipolar, so negative values need to be removed or shifted.
2. DC Bias Addition
   • A DC bias is added to make the signal strictly positive.
   • Formula: xDCO(t) = xOFDM(t) + BDC
   • If bias is too small → negative values get clipped → clipping noise.
3. Hermitian symmetry
   • Ensures the IFFT output is real-valued.
   • Enforced as: X[k] = X*[N-k]
4. Clipping
   • Any remaining negative values after DC bias are clipped to zero.
   • This introduces non-linear distortion, unlike regular OFDM.

3. Hermitian Symmetry and Real-Time Domain Signal

Time-domain signal in OFDM

The IFFT gives the time-domain samples:

x[n] = (1/N) * Σ X[k] * e^(j 2π k n / N), k=0..N-1
    

• X[k] are the frequency-domain subcarrier symbols.
• x[n] is the transmitted time-domain signal.

Hermitian symmetry in DCO-OFDM

To make x[n] real-valued, DCO-OFDM enforces:

X[N-k] = X*[k],  k = 1,2,...,N/2-1
    

Each subcarrier X[k] has a mirror subcarrier X[N-k] which is its complex conjugate.

Why the time-domain signal becomes real

X[k] * e^(j 2π k n / N) + X[N-k] * e^(j 2π (N-k) n / N)

    

X[k] * e^(j 2π k n / N) + X*[k] * e^(-j 2π k n / N)
= 2 * Re{ X[k] * e^(j 2π k n / N) }

    

The imaginary parts cancel out exactly.

Frequency-domain layout (Hermitian symmetry)

Suppose N = 8 subcarriers for simplicity:

k	0	1	2	3	4	5	6	7
X[k]	DC	X1	X2	X3	Nyquist	X3*	X2*	X1*

4. Summary

1. Input signal x[n] must be real-valued.
2. Complex conjugates exist in the frequency domain.
3. After IFFT, transmitted signal is completely real.
4. DC bias makes it positive for optical transmission.

Further Reading

1. MATLAB Code for DCO-OFDM