SSB vs VSB: Single Sideband vs Vestigial Sideband Modulation

This article delves into the differences between Single Sideband (SSB) and Vestigial Sideband (VSB) modulation techniques. Before we begin, it’s helpful to understand the basics of Double Sideband Suppressed Carrier (DSB-SC) versus SSB-SC modulation. This will provide context for the advantages and disadvantages of each method.

The Basics of SSB Modulation

In DSB-SC, the band structure exhibits symmetry. This means that even if only half of the signal is transmitted, the other half can be recovered at the receiver. By transmitting only half, we effectively reduce both the bandwidth and the power required for transmission by half.

Depending on which half of the DSB-SC signal is transmitted, we have two types of SSB modulation:

• LSB (Lower Side Band) modulation
• USB (Upper Side Band) modulation

Figure 1: SSB Signal Generation

As illustrated in Figure 1, an SSB signal can be generated using a DSB-SC modulator. The mathematical representation is as follows:

$\phi_{SSB}(t) = m(t) * \cos(\omega_c t) \pm \hat{m}(t) * \sin(\omega_c t)$

Where:

• $m(t)$ represents the message signal
• $\omega_c$ is the carrier frequency
• $\hat{m}(t)$ is the Hilbert transform of the message signal

The original signal is retrieved using coherent demodulation of SSB signals. $\phi_{SSB} (t)$ is multiplied by $\cos(\omega_c t)$ and then passed through a low-pass filter (LPF) to recover the original signal.

$\phi_{SSB} (t) * \cos(\omega_c t) = \frac{1}{2} m(t) + \frac{1}{2} \cos(2\omega_c t) \pm \frac{1}{2} \hat{m}(t) * \sin(2\omega_c t)$

The demodulated signal is passed through an LPF to remove unwanted high-frequency components.

Drawbacks of SSB Modulation

Despite its advantages in bandwidth and power efficiency, SSB modulation has some significant drawbacks:

• Difficult Signal Generation: Generating SSB signals can be complex and challenging.
• Selective Filtering: Recovering the original signal requires precise and selective filtering.
• Phase Shifter Requirements: The phase shifter needs to maintain a 90-degree phase shift with high accuracy.

Introducing VSB Modulation: A Compromise

To address the drawbacks of SSB modulation, Vestigial Sideband (VSB) modulation is often employed. VSB can be considered a compromise between SSB and DSB-SC.

In VSB modulation:

• One sideband is not completely rejected.
• One sideband is transmitted fully, along with a small portion (the vestige) of the other sideband.

This leads to a bandwidth requirement of $BW_v = B + v$, where $v$ represents the vestigial frequency band and $B$ represents the bandwidth of the message signal.

Figure 2: SSB Modulation vs VSB Modulation

Figure 3: VSB Signal Generation

Figure 3 illustrates VSB signal generation. $H_i(\omega)$ represents a filter that shapes the suppressed sideband. Mathematically:

$\phi_{VSB}(\omega) = [M(\omega - \omega_c) + M(\omega + \omega_c)] . H_i(\omega)$

To recover the original baseband signal from the VSB signal, the VSB signal is multiplied by $\cos(\omega_c t)$ and then passed through a Low Pass Filter (LPF). This process allows for the recovery of the original signal.