Modulation & Demodulation

Modulation

In electronics and telecommunications, modulation is the process of varying one or more properties of a high-frequency periodic waveform, called the carrier signal, with a modulating signal which typically contains information to be transmitted. This is done in a similar fashion to a musician modulating a tone (a periodic waveform) from a musical instrument by varying its volume, timing and pitch. The three key parameters of a periodic waveform are its amplitude (“volume”), its phase (“timing”) and its frequency (“pitch”). Any of these properties can be modified in accordance with a low frequency signal to obtain the modulated signal. Typically a high-frequency sinusoid waveform is used as carrier signal, but a square wave pulse train may also be used.

In telecommunications, modulation is the process of conveying a message signal, for example a digital bit stream or an analog audio signal, inside another signal that can be physically transmitted. Modulation of a sine waveform is used to transform a baseband message signal into a passband signal, for example low-frequency audio signal into a radio-frequency signal (RF signal). In radio communications, cable TV systems or the public switched telephone network for instance, electrical signals can only be transferred over a limited passband frequency spectrum, with specific (non-zero) lower and upper cutoff frequencies. Modulating a sine-wave carrier makes it possible to keep the frequency content of the transferred signal as close as possible to the centre frequency (typically the carrier frequency) of the passband.

A device that performs modulation is known as a modulator and a device that performs the inverse operation of modulation is known as a demodulator (sometimes detector or demod). A device that can do both operations is a modem (from “modulator–demodulator”).

Demodulation

Demodulation is the act of extracting the original information-bearing signal from a modulated carrier wave. A demodulator
is an electronic circuit (or computer program in a software defined radio) that is used to recover the information content from the modulated carrier wave.

These terms are traditionally used in connection with radio receivers, but many other systems use many kinds of demodulators. Another common one is in a modem, which is a contraction of the terms modulator/demodulator.

Eb/No

E_b/N₀ (the energy per bit to noise power spectral density ratio) is an important parameter in digital communication or data transmission. It is a normalized signal-to-noise ratio (SNR) measure, also known as the “SNR per bit”. It is especially useful when comparing the bit error rate (BER) performance of different digital modulation schemes without taking bandwidth into account.

E_b/N₀ is equal to the SNR divided by the “gross” link spectral efficiency in (bit/s)/Hz, where the bits in this context are transmitted data bits, inclusive of error correction information and other protocol overhead. When forward error correction (FEC) is being discussed, E_b/N₀ is routinely used to refer to the energy per information bit (i.e. the energy per bit net of FEC overhead bits); in this context, E_s/N₀ is generally used to relate actual transmitted power to noise.

The noise spectral density N₀, usually expressed in units of watts per hertz, can also be seen as having dimensions of energy, or units of joules, or joules per cycle. E_b/N₀ is therefore a non-dimensional ratio.

E_b/N₀ is commonly used with modulation and coding designed for noise-limited rather than interference-limited communication, and for power-limited rather than bandwidth-limited communications Examples of power-limited communications include deep-space and spread spectrum, and is optimized by using large bandwidths relative to the bit rate.

Shannon limit

The Shannon–Hartley theorem says that the limit of reliable data rate of a channel depends on bandwidth and signal-to-noise ratio according to:

I < B log2 ( 1 + S/N )

where

• I is the information rate in bits per second excluding error-correcting codes;
• B is the bandwidth of the channel in hertz;
• S is the total signal power (equivalent to the carrier power C); and
• N is the total noise power in the bandwidth.

Cutoff Rate

For any given system of coding and decoding, there exists what is known as a cutoff rate R₀, typically corresponding to an E_b/N₀
about 2 dB above the Shannon capacity limit.The cutoff rate used to be thought of as the limit on practical error correction codes without an unbounded increase in processing complexity, but has been rendered largely obsolete by the more recent discovery of turbo codes.

Signal-to-Noise Ratio

Signal-to-noise ratio (often abbreviated SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise. While SNR is commonly quoted for electrical signals, it can be applied to any form of signal (such as isotope levels in an ice core or biochemical signaling between cells).

Signal-to-noise ratio is sometimes used informally to refer to the ratio of useful information to false or irrelevant data in a conversation or exchange. For example, in online discussion forums and other online communities, off-topic posts and spam are regarded as “noise” that interferes with the “signal” of appropriate discussion.

Improving SNR in practice

Recording of the noise of a thermo gravimetric analysis device that is poorly isolated from a mechanical point of view; the middle of the curve shows a lower noise, due to a lesser surrounding human activity at night.

All real measurements are disturbed by noise. This includes electronic noise, but can also include external events that affect the measured phenomenon — wind, vibrations, gravitational attraction of the moon, variations of temperature, variations of humidity, etc., depending on what is measured and of the sensitivity of the device. It is often possible to reduce the noise by controlling the environment. Otherwise, when the characteristics of the noise are known and are different from the signals, it is possible to filter it or to process the signal. When the signal is constant or periodic and the noise is random, it is possible to enhance the SNR by averaging the measurement.

Digital Signals

When a measurement is digitised, the number of bits used to represent the measurement determines the maximum possible signal-to-noise ratio. This is because the minimum possible noise level is the error caused by the quantization of the signal, sometimes called Quantization noise. This noise level is non-linear and signal-dependent; different calculations exist for different signal models. Quantization noise is modeled as an analog error signal summed with the signal before quantization (“additive noise”).

This theoretical maximum SNR assumes a perfect input signal. If the input signal is already noisy (as is usually the case), the signal’s noise may be larger than the quantization noise. Real analog-to-digital converters also have other sources of noise that further decrease the SNR compared to the theoretical maximum from the idealized quantization noise, including the intentional addition of dither.

Although noise levels in a digital system can be expressed using SNR, it is more common to use Eb/No, the energy per bit per noise power spectral density.

The modulation error ratio (MER) is a measure of the SNR in a digitally modulated signal.

Optical SNR

Optical signals have a carrier frequency, which is much higher than the modulation frequency (about 200 THz and more). This way the noise bandwidth covers a bandwidth which is much wider than the signal itself. The resulting signal influence relies mainly on the filtering of the noise. To describe the signal quality without taking the receiver into account the optical SNR (OSNR) is used. The OSNR is the ratio between the signal power and the noise power in a given bandwidth. Most commonly a reference bandwidth of 0.1 nm is used. This bandwidth is independent from the modulation format, the frequency and the receiver. For instance a OSNR of 20dB/0.1 nm could be given, even the signal of 40 GBit DPSK would not fit in this bandwidth. OSNR is measured with a Optical Spectrum Analyzer