1.5  Concepts and Elements of Communication Systems

Some concepts of communication systems are discussed in the sequel, with emphasis to analog communications while Section 2.3 concentrates in digital communications.

1.5.1  Tx and Rx are designed according to the channel

A communication system designer builds the transmitter (Tx) and receiver (Rx) taking advantage of the many degrees of freedom available and techniques developed over the last decades. The real-world channels are analog and the better the designer understands the channel, the more efficient can be the design of the Tx and Rx blocks. To some extent, the designer even has control over specific channel parameters. For example, the operating frequency of a wireless digital communication can be chosen or the diameter of the copper wire used in a DSL deployment. Or an optical fiber can be built according to desired properties for signal transmission. However, in many telecommunication studies, the designer is assumed to have no control over the channel and the task is to use it in the best way.

1.5.2  Modulation

The role of modulation is to create waveforms that can withstand the channel and be properly interpreted by the receiver. For example, when using the atmosphere in wireless systems, antennas may become large when the system operates at low frequencies.⁷ Ideally, an antenna requires a radiating element that is at least one-quarter of the wavelength $\lambda$ given by

with $c\approx 3\times 10^8$ m/s being approximately the speed of radio waves (and light) and $f$ the wave frequency. If $s(t)$ has a spectrum concentrated in $f=1$ kHz, for example, $\lambda =300$ km and the ideal antenna would have 75 km. Hence, a common task of the modulator is frequency translation, also called frequency upconversion or simply upconversion.

For example, assume that the source information $m(t)$ is an analog voice signal obtained with a microphone that has its power concentrated at frequencies from DC to 4 kHz. The multiplication of $m(t)$ by a sinusoid $c(t)=\text{cos}<!--\; FUNCTION\; APPLICATION\; -->(2\pi f_{c}t+{\varphi }_c)$ translates the spectrum $M(f)$ of $m(t)$, originally centered at DC, to the carrier frequency $f_c$. The multiplication $m(t)\times c(t)$ by a carrier is the most common method of frequency upconversion, which is used by many modulators.

Some people consider that “modulation” corresponds only to this process of frequency upconversion via a carrier. However, in this text, following the modern jargon, the term modulation denotes the flexible process of incorporating information into a waveform $s(t)$. And it should be noted that this modulation process may even not include frequency upconversion.⁸ These two definitions are highlighted in Table 1.2.

When the communication system does not use upconversion and most of the power is concentrated in the vicinities of 0 Hz, it is said to operate in baseband. The systems that use frequency upconversion are called bandpass.

1.5.3  Duplexing: Sharing the channel in full-duplex systems

Most communication systems are full-duplex, meaning that the information can simultaneously flow in both directions.⁹

In some full-duplex systems, the transmit and receive channels can be clearly distinguished because, for example, there is an individual circuit for each channel. In other cases, full-duplex operation is emulated by duplexing. Duplexing is often performed by creating channels via time-division duplex (TDD) or frequency-division duplex (FDD). TDD divides the time into slots that are allocated to the transmitter and receiver, while FDD adopts distinct frequency bands to Tx and Rx.

Besides TDD and FDD, another enabling technique for achieving full-duplex is echo cancellation. The principle is that the transmitter knows its signal $s(t)$ and can subtract it from the observed signal $s(t)+r(t)$ to recover $r(t)$. In practice, special circuits or digital signal processing are used to try separate the Tx and Rx signals. For example, in the telephony copper plant, a hybrid circuit is used to split the Tx and Rx paths. In radar and other wireless communication systems, another three-port network called duplexer allows the transmitter and receiver to use the same antenna [ url5dup].

1.5.4  TDD/FDD versus TDM/FDM versus TDMA/FDMA

Very close to TDD and FDD are the concepts of TDM (time-division multiplex) and FDM (frequency-division multiplex). While the term duplex (TDD and FDD) is used when emulating a full-duplex operation between a pair of communication agents, multiplexing (TDM or FDM) is adopted when several signals, eventually from different users, are organized to share the same channel, which is typically point-to-point.

Yet another close pair of concepts is TDMA and FDMA, which are techniques for multiple access that are based on time and frequency-division as in TDM and FDM, but also include the required protocols for a user to get access to a time-slot (in case of TDMA) or a frequency (in case of FDMA). TDMA, FDMA, CDMA (code division multiple access) or combinations of them are often used in point-to-multipoint connections. For example, the Long-Term Evolution (LTE) wireless communication standard uses both TDMA and FDMA, simultaneously.

Beware of the fact that the jargon with respect the these terms is not always consistent.

1.5.5  Thermal noise and receiver noise floor

The thermal noise (or Johnson–Nyquist noise) is created by the agitation of charged particles such as electrons and increases with the temperature.¹⁰ It is often modeled as having a flat PSD with (unilateral) level given by

where $T_k$ is the absolute temperature in Kelvin and $K_b\approx 1.38\times 10^{-23}$ J/K is the Boltzmann’s constant in Joules per Kelvin.

The room temperature is often assumed to be a value between 290 and $300$ K (17 to 27 degrees Celsius, respectively) and, assuming $T_k=300$, then $N_0=4.14\times 10^{-21}$ W/Hz or, alternatively, $-174$ dBm/Hz.

Because the PSD is white, the noise power $P$ that it imposes to the receiver depends on the bandwidth (BW) of the receiver analog front end according to $P=N_0\mathrm{\text{BW}}$. Due to Eq. (1.9), the thermal noise PSD is often specified through the temperature $T_k$, in Kelvin. Hence, even if the actual temperature is 290 K, for example, it is possible to state that the “equivalent noise temperature” is $T_k=50$ K or any other value that reflects the correct PSD $N_0$.

The so-called noise floor is the noise power experienced by a receiver and is typically modeled as thermal noise (note that the receiver may be impacted by other noise sources and even human-made interference signals).¹¹ It is often important to have a good estimate of the noise floor because any other impairment (such as the ADC quantization noise) with power significantly lower than the noise floor will seldom deteriorate the receiver performance. For example, given a noise floor with PSD $N_0=-174$ dBm/Hz, it is sensible to allow a quantization noise with flat PSD of $-194$ dBm/Hz given that it is 20 dB below the noise floor.