Transmission Speed Dependence on Modulation

Relationship Between Bits, Symbols, and Bit Rate

The description of the relationship between transmission speed and modulation uses two levels. A bit is an information unit, and a symbol is a signal state transmitted during one symbol interval.

• Bit: The most basic unit of digital information, representing a state of either 0 or 1.
• Symbol: A physical signal state (e.g., a specific amplitude or voltage level, frequency, or phase) transmitted over the channel during a fixed time interval and representing one or more information bits.

The connection between them is determined by the modulation scheme, which defines how many bits ($k$) occupy each symbol. For an alphabet with $M$ equally used states, the average number of bits per symbol is $k=\log_2(M)$.

$R_b = R_s \times k$

This formula describes one symbol stream and the gross rate. If the FEC code rate is $R_c$, the approximate user-data rate is $R_{payload} \approx R_b \times R_c$. Independent polarizations or additional constellation dimensions must be included separately.

Higher-Order Modulation and More Bits per Symbol

To increase the bit rate at the same symbol rate, we use higher-order modulation schemes. With the same pulse shaping, increasing $R_s$ usually widens the occupied bandwidth, while a larger alphabet $M$ increases the number of bits per symbol. This is visualized using constellation diagrams.

• BPSK (Binary Phase-Shift Keying): Has 2 symbol states. Each symbol carries $k=1$ bit. The points on the diagram are far apart.
• QPSK (Quadrature Phase-Shift Keying): Has 4 symbol states ($2^2$). Each symbol carries $k=2$ bits, doubling the bit rate compared to BPSK for the same symbol rate.
• 16-QAM (Quadrature Amplitude Modulation): Has 16 symbol states ($2^4$). Each symbol carries $k=4$ bits. The points are closer together.
• 64-QAM: Has 64 symbol states ($2^6$), carrying $k=6$ bits per symbol. The points form a denser arrangement.

For the same average power and comparable constellation geometry, a larger alphabet usually reduces the distance between neighboring points. The receiver then has a smaller decision margin and needs a higher SNR or OSNR.

Noise, SNR, and Receiver Requirements

A transmission channel introduces noise and distortion, and the receiver must assign each received point to the correct symbol. The relevant metric is the Signal-to-Noise Ratio (SNR).

At the same average signal power, increasing the number of constellation points reduces the distance between them. Noise and distortion can then move a received point across a decision boundary more easily.

The comparison assumes the same average power, symbol rate, target bit error rate (BER), and comparable coding. A particular receiver also depends on pulse shape, constellation geometry, and implementation.

• Lower-order modulation, such as BPSK: requires a lower SNR to reach a given error rate but carries fewer bits per symbol.
• Higher-order modulation, such as 64-QAM: carries more bits per symbol but requires a higher SNR to reach the same error rate.

Forward error correction (FEC) adds redundant bits and can lower the signal-quality requirement for a fixed post-decoding error rate. The code rate $R_c$ reduces the user-data rate relative to the gross rate, while the decoder threshold depends on the selected code. The required SNR or OSNR therefore depends on the code and implementation.

Relationship Between Modulation Order and Reach

Increasing the modulation order increases the number of bits per symbol but usually raises the SNR or OSNR required for a target error rate with comparable coding. Reach follows the link-margin budget together with modulation, coding, and power parameters. The effect of an additional bit per symbol depends on those parameters, so it has no fixed conversion factor such as a one-half reduction in reach.

Data rate and reach depend on symbol rate, polarization count, occupied spectrum, FEC and its code rate, target error rate, launch power, fiber and amplifier parameters, and DSP algorithms. The table compares the formats qualitatively. Actual reach values follow the link parameters.

Adaptive Modulation in Flexible Networks

Modern optical networks, such as Elastic Optical Networks (EON), can select a modulation format from the path parameters. The decision considers available bandwidth, symbol rate, SNR or OSNR margin, dispersion, nonlinearities, amplifier count, FEC, and the target error rate.

• For short-haul links (e.g., an intra-city connection between data centers), where the measured OSNR margin is large, the system may select a high-order modulation like 16-QAM or 64-QAM to increase the rate within the available bandwidth.
• For long-haul or ultra-long-haul links (e.g., a trans-Atlantic submarine cable), where the signal must traverse thousands of kilometers and many amplifiers, the system may select a lower-order modulation like BPSK or QPSK when the target BER and OSNR budget require it.

Selecting a format for each path allows network operators to use available fibers and transponders while meeting the required user-data rate, target error rate, and OSNR margin.