Understanding 8-PSK Modulation: Principles, Truth Table, and Bandwidth Efficiency

Phase Shift Keying (PSK) is a widely used digital modulation technique in which the phase of a carrier signal is varied to represent digital data. 8-PSK (8-Phase Shift Keying) is an advanced form of PSK that increases spectral efficiency by encoding three bits per symbol. It is commonly used in wireless communication standards such as satellite communications and cellular networks.

What is 8-PSK?

8-PSK is a type of phase modulation where the carrier signal can take one of eight possible phase shifts, each separated by 45° (π/4 radians). Since there are 8 different phase states, each symbol carries 3 bits of information (log₂8 = 3 bits), increasing data transmission rates without expanding bandwidth significantly.

Mathematically, the modulated signal for 8-PSK is represented as:

The constellation diagram for 8-PSK consists of 8 equally spaced points on a circle, each corresponding to a unique phase shift.

8-PSK Truth Table and Symbol Mapping

In an 8-PSK modulator, every 3-bit group from the digital data stream is mapped to one of eight phase shifts. Below is the truth table for 8-PSK modulation:

This mapping ensures that the symbols are distributed evenly in phase space, reducing the probability of bit errors.

8-PSK QIC Equation

The Quadrature In-Phase Component (QIC) equation describes how the modulated signal is formed using I (In-phase) and Q (Quadrature) components. These components are mathematically expressed as:

where θ_n is the phase shift from the truth table. The final 8-PSK modulated signal can be written as:

By using a reference oscillator and phase-shifting mechanism, we generate the desired 8-PSK signal, as shown in the block diagram.

Bandwidth Efficiency of 8-PSK

Bandwidth efficiency (η) is the number of bits transmitted per second per unit bandwidth. It is given by the formula:

Bit Error Rate (BER) of 8-PSK

The Bit Error Rate (BER) for 8-PSK is higher than BPSK and QPSK because of the closer spacing of phase states, making it more sensitive to noise and interference. The theoretical BER for 8-PSK in an AWGN (Additive White Gaussian Noise) channel is approximated as:

Compared to BPSK and QPSK, 8-PSK achieves a higher data rate but at the cost of higher error probability.

Bandwidth Efficiency Calculation for Different Modulation Schemes

Given a transmission rate of 10 Mbps, we calculate the bandwidth efficiency for different modulation schemes. The symbol rate for each modulation scheme is given by:

Conclusion:

• BPSK has the highest robustness but lowest efficiency.
• QPSK provides a good balance between bandwidth and error rate.
• 8-PSK increases spectral efficiency but is more sensitive to noise.
• 16-PSK further increases efficiency but suffers from high BER.

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Conclusion

8-PSK is a crucial modulation scheme used in wireless and satellite communications. It achieves higher bandwidth efficiency than BPSK and QPSK but comes at the cost of increased noise sensitivity. When selecting a modulation scheme, trade-offs between data rate, bandwidth, and BER must be considered to optimize performance for specific applications.

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