Rules for Selecting DC Bias in DCO-OFDM

Key characteristics of DCO-OFDM include:

• Intensity Modulation and Direct Detection (IM/DD)
• Hermitian symmetry to generate real-valued signals
• DC bias addition to ensure signal non-negativity
• Bottom clipping of residual negative samples

Therefore, this is standard baseband IM/DD DCO-OFDM used in VLC systems.

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1. Mathematical Signal Model

Unbiased OFDM Signal

After applying Hermitian symmetry and IFFT, the time-domain OFDM signal is approximately Gaussian:

x₀(t) ~ N(0, σₓ²)

where σₓ² is the variance of the unclipped OFDM signal.

DC Bias Definition

The DC bias is defined as:

B_DC = μ √E{x(t)²} = μ σₓ

In decibels:

B_DC(dB) = 10 log₁₀(μ²)

where:

• μ is the DC bias scaling factor
• σₓ is the standard deviation of the OFDM signal

Clipping Operation

After adding DC bias, the signal is clipped to enforce non-negativity:

x(t) =
{
  x₀(t) + B_DC ,  if x₀(t) + B_DC > 0
  0             ,  otherwise
}

This asymmetric clipping is a defining feature of DCO-OFDM.

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2. Classification of the DCO-OFDM Scheme

Aspect	Type
Detection	IM/DD
Carrier	Baseband
Optical Source	LED
Biasing	Fixed DC Bias
Clipping	Bottom Clipping
OFDM Variant	Electrical OFDM → Optical OFDM
Application	Visible Light Communication

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3. Rules for Selecting DC Bias

The selection of DC bias is critical due to the trade-off between clipping distortion and optical power efficiency.

Rule 1: Bias Relative to Signal Variance

The DC bias is typically chosen as a multiple of the signal standard deviation:

B_DC = μ σₓ

Common values used in literature:

μ Value	Bias Level
2.0	High clipping distortion
2.5	Balanced (commonly used)
3.0	Low clipping, low power efficiency

Rule 2: Clipping Probability Constraint

Bias is selected to keep the clipping probability small:

P_clip = P(x₀(t) + B_DC < 0) = Q(μ)

• μ = 2.5 → P_clip ≈ 0.6%
• μ = 3.0 → P_clip ≈ 0.13%

Rule 3: LED Dynamic Range Constraint

The biased signal must remain within the LED operating range:

I_min ≤ x₀(t) + B_DC ≤ I_max

Excessive bias causes upper clipping, while insufficient bias increases lower clipping distortion.

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4. Power Efficiency Limitation of DCO-OFDM

As the modulation order increases:

• Signal variance σₓ² increases
• Required DC bias increases
• Optical power efficiency decreases
• LED nonlinearity becomes more significant

This makes DCO-OFDM less suitable for power-limited VLC applications.

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5. Comparison with ACO-OFDM

Feature	DCO-OFDM	ACO-OFDM
DC Bias	Required	Not required
Power Efficiency	Low	High
Spectral Efficiency	High	Low
Clipping Noise	Both sides	Even subcarriers only
VLC Suitability	Moderate	High

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Summary

The described scheme is standard IM/DD baseband DCO-OFDM for VLC, where DC bias selection is governed by a trade-off between clipping distortion, power efficiency, and LED dynamic range.

Further Reading