eitf45 -L2- physical layer.pdf

# Introduction to data and signals This section differentiates between static data representations for storage and dynamic signals for transmission, covering analog and digital signal characteristics [3](#page=3). ### 1.1 Data vs. signal Data and signals represent information differently, catering to distinct purposes in computer communications [4](#page=4). * **Data:** Data is a static representation of information primarily used for storage. It is a fixed representation of a message or value [4](#page=4). * **Signal:** A signal is a dynamic representation of information employed for transmission. Signals are time-varying physical quantities that carry information through a medium [4](#page=4). ### 1.2 Analog vs. digital signals The fundamental distinction between analog and digital signals lies in their continuity and representation of amplitude [5](#page=5). * **Analog signals:** * Are continuous in both time and amplitude [5](#page=5). * Vary smoothly over time and can take on any value within a given range. * Are often represented in the electrical or optical domain [5](#page=5). * An example of an analog signal is a continuous waveform, often depicted as a smooth curve over time [5](#page=5). * **Digital signals:** * Are discrete in both time and amplitude [5](#page=5). * Exist at specific points in time and can only take on a limited set of predefined values, typically binary (0s and 1s) [5](#page=5). * Are characterized by their binary representation [5](#page=5). * An example of a digital signal is a series of distinct pulses or levels representing binary data [5](#page=5). > **Tip:** Understanding the difference between analog and digital signals is crucial for comprehending how information is stored and transmitted in computer networks. Analog signals are often the raw form of information, which then needs to be digitized for efficient and reliable transmission over digital communication systems [3](#page=3) [4](#page=4) [5](#page=5). --- # Digitalization of analog signals The digitalization of analog signals is a fundamental process in computer communications, transforming continuous analog signals into a discrete digital format through three primary steps: sampling, quantization, and encoding [6](#page=6). ### 2.1 The three key steps of digitalization The conversion of an analog signal into a digital representation involves a sequence of distinct operations [6](#page=6). #### 2.1.1 Sampling Sampling is the process of discretizing a continuous signal in time. An analog signal, denoted as $s(t)$, is converted into a sequence of samples, $s_n$, at regular intervals. The time between consecutive samples is called the sampling time, $T_s$, and the reciprocal of this, $F_s = 1/T_s$, is the sampling frequency. It is crucial to retain information about the sampling time to accurately reconstruct the original signal [6](#page=6) [7](#page=7). The **Shannon-Nyquist Sampling Theorem** provides the theoretical basis for sampling. It states that if a continuous signal $s(t)$ is band-limited, meaning its highest frequency component is $F_{max}$, then the signal can be uniquely determined and perfectly reconstructed from its samples $s_n = s(nT_s)$ if and only if the sampling frequency $F_s$ is greater than or equal to twice the highest frequency component ($F_s \geq 2F_{max}$). The term $F_s/2$ is known as the Nyquist frequency, and $2F_{max}$ is the Nyquist rate [8](#page=8). > **Example:** Telephony voice signals typically occupy frequencies from 0 to 4 kHz. According to the Nyquist theorem, the sampling frequency must be at least $2 \times 4 \text{ kHz} = 8 \text{ kHz}$. If an 8-bit encoding is used for each sample, the data rate for telephony would be $8000 \text{ samples/second} \times 8 \text{ bits/sample} = 64,000 \text{ bits/second}$, or 64 kbps [9](#page=9). #### 2.1.2 Aliasing A critical issue that arises if the sampling frequency is too low is **aliasing**. Aliasing occurs when a signal's frequency components higher than $F_s/2$ are misinterpreted as lower frequencies, leading to distortion and an inability to reconstruct the original signal accurately. This happens because the sampling process effectively folds the higher frequency components into the baseband range. To avoid aliasing, it is essential to ensure the sampling rate is at least twice the highest frequency present in the signal [11](#page=11) [8](#page=8). > **Tip:** To prevent aliasing in practice, anti-aliasing filters (low-pass filters) are often used before sampling to remove frequencies above $F_s/2$. #### 2.1.3 Quantization Quantization is the process of discretizing the amplitude of the sampled signal. Each sample, which is a continuous amplitude value, is mapped to one of a finite number of discrete levels. For $k$ bits, there are $M = 2^k$ equidistant quantization levels. Each sample is then represented by a $k$-bit binary word corresponding to its assigned amplitude level [12](#page=12) [6](#page=6). The difference between the original sample's amplitude and its quantized level is the **quantization error** or distortion. This error is an inherent part of the quantization process and contributes to noise in the digitized signal [13](#page=13). For a uniform quantizer and assuming a uniformly distributed input signal, the average distortion is given by $D^2/12$, where $D$ is the range of the input signal divided by the number of quantization levels. A common metric to assess the quality of quantization is the **Signal-to-Quantization Noise Ratio (SQNR)**. For a uniform quantizer, it can be expressed as: $$SQNR = \frac{E[X^2]}{E[(X - X_Q)^2]} = \frac{(M\Delta)^2/12}{\Delta^2/12} = M^2$$ where $M$ is the number of quantization levels and $\Delta$ is the step size between levels [13](#page=13). In decibels, this becomes: $$SQNR_{dB} = 10 \log_{10}(M^2) = 20 \log_{10}(M)$$ Since $M=2^k$, where $k$ is the number of bits, the SQNR can also be expressed as: $$SQNR_{dB} = 20 \log_{10}(2^k) = k \cdot 20 \log_{10} \approx k \cdot 6 \text{ dB}$$ [2](#page=2). This formula indicates that for every additional bit used in quantization, the SQNR increases by approximately 6 dB [13](#page=13). #### 2.1.4 Encoding Encoding is the final step, where the quantized amplitude levels are represented using binary codes. Each discrete amplitude level is assigned a unique binary code word of a specific length, typically determined by the number of quantization levels ($k$ bits for $M=2^k$ levels). This binary representation is the digital signal that can be transmitted or stored [14](#page=14) [6](#page=6). > **Example:** For CD audio, music signals have frequencies up to 20 kHz. Thus, the sampling frequency is $2 \times 20 \text{ kHz} = 40 \text{ kHz}$. With 16-bit encoding, each sample is represented by 16 bits. The data rate for CD audio is $44,100 \text{ Hz} \times 16 \text{ bits} = 705,600 \text{ bits/second}$. For stereo audio (2 channels), this rate doubles to approximately 1.4 Mbps [15](#page=15). --- # Transmission media and digital transmission techniques This topic explores the physical pathways for data transmission and the methods used to represent digital information as signals [3](#page=3). ### 3.1 Transmission media Transmission media are the physical conduits through which data travels, categorized into guided and unguided types [17](#page=17). #### 3.1.1 Guided media Guided media physically confine the signal and include: * **Twisted pair copper cables**: Consist of two copper wires twisted around each other to reduce electrical disturbances. They are commonly used for telephony loops (e.g., CAT3) and Ethernet (e.g., CAT5, CAT6) [18](#page=18). * **Coaxial cable**: While mentioned as a category, specific details are not provided in the provided text. * **Optical fibre**: Transmits data using light pulses through a glass core, relying on total internal reflection. It offers very high capacity, low attenuation and noise, and is not susceptible to radio interference. There are two main types [19](#page=19): * **Multi-mode**: Typically 50-100 µm in diameter [19](#page=19). * **Single-mode**: Typically 5-10 µm in diameter [19](#page=19). #### 3.1.2 Unguided media Unguided media, also known as wireless media, broadcast signals through the air and include: * **Radio**: Used in cellular (mobile) networks with ranges of 2-3 km Wi-Fi (around 50 m) Bluetooth (around 10 m) NFC (around 5 cm) and LoRa (IoT) networks (5-15 km) [20](#page=20). * **Light**: This includes infrared or visible light, though specific applications are not detailed in the provided text. ### 3.2 Digital transmission techniques Digital transmission involves converting binary data into analog signals to transmit it through a continuous medium. This can be achieved through baseband transmission or by modulating a carrier signal [21](#page=21). #### 3.2.1 Baseband transmission Baseband transmission sends digital signals directly without modulating them onto a higher frequency carrier. The signal's spectrum is concentrated at low frequencies, ideally starting from DC. Different line coding schemes are used to represent bits as voltage levels [21](#page=21): * **On-off keying (OOK)**: Represents a '1' with an "on" signal (amplitude A) and a '0' with an "off" signal (amplitude 0) for the duration of a bit interval ($T_b$). The signal can be represented as $s(t) = A \cdot x$ for $0 \leq t \leq T_b$ where $x$ is the bit value [22](#page=22). > **Example**: A bit sequence `10010010101111100` would be transmitted as alternating pulses of amplitude A and no pulse (amplitude 0) [22](#page=22). * **Bipolar signalling**: Uses two signal amplitude levels, +A and -A, to represent bits. For instance, +A could represent a '1' and -A a '0'. The signal can be represented as $a(t) = A \cdot (-1)^x$ for $0 \leq t \leq T_b$ where $x$ is the bit value [23](#page=23). > **Tip**: Bipolar signalling is often preferred over unipolar signalling (like OOK) as it has a DC component of zero on average, which is beneficial for transmission over some media [23](#page=23). * **Non-Return to Zero (NRZ)**: In NRZ encoding, a pulse maintains its level throughout the entire bit interval ($T_b$) [24](#page=24). > **Tip**: NRZ is a common and simple encoding scheme. However, it can lead to long strings of identical bits, which can cause clocking issues at the receiver if not handled properly. * **Return to Zero (RZ)**: In RZ encoding, the pulse returns to zero for a portion of the bit interval. This ensures a transition within each bit period, which aids in clock synchronization. RZ can be implemented using electrical or optical signals [24](#page=24) [25](#page=25). > **Example**: An RZ pulse might be high for the first half of the bit interval and then drop to zero for the second half. * **Manchester coding**: This scheme encodes bits by splitting each bit interval ($T_b$) into two halves. A transition occurs in the middle of each bit period. A transition from low to high (or high to low) in the first half, followed by the opposite transition in the second half, can represent a '1', while the opposite pattern represents a '0'. Alternatively, a mid-bit transition can represent the bit value, e.g., a transition from negative to positive for a '1' and positive to negative for a '0' [26](#page=26). > **Exam Question Insight**: Manchester encoding can be thought of as two combined signals, often related to the clock and data signals [28](#page=28). * **Differential Manchester coding**: This method uses a zero transition at the start of each signal time slot to indicate the data. For a transmitted '0', the same pulse pattern as the previous slot is used. For a transmitted '1', the inverted pulse pattern is used, meaning $a_t \neq a_{t-1}$ [27](#page=27). > **Exam Question Insight**: This scheme uses a transition at the start of each bit period to signal, and the presence or absence of a mid-bit transition determines the bit value [27](#page=27). #### 3.2.2 Carrier transmission (Modulation) Carrier transmission, also known as analog transmission, involves modulating a carrier signal with the digital data. This is useful for transmitting digital data over channels that are designed for analog signals, such as radio waves or telephone lines. Common modulation techniques include [21](#page=21) [29](#page=29): * **ASK (Amplitude Shift Keying)**: A form of OOK applied to a carrier frequency ($f_0$). The amplitude of the carrier signal is varied to represent digital data. For example, a '1' could be represented by a carrier wave with amplitude A, and a '0' by no carrier wave (amplitude 0) [30](#page=30). > **Formula**: $s(t) = A \cdot x \cdot \cos(2\pi f_0 t)$ for $0 \leq t \leq T_b$, where $x$ is the bit value [30](#page=30). * **BPSK (Binary Phase Shift Keying)**: Uses an NRZ signal at a carrier frequency ($f_0$) and encodes information in the phase of the carrier wave. For example, a '1' might be represented by a cosine wave, and a '0' by a cosine wave shifted by 180 degrees (i.e., a negative cosine wave) [31](#page=31). > **Formula**: $s(t) = A \cdot \cos(2\pi f_0 t + \phi)$ where $\phi$ changes based on the bit value [31](#page=31). * **PAM (Pulse Amplitude Modulation)**: This technique uses discrete amplitude levels to represent data. Bipolar signalling is a binary form of PAM where data is stored in the amplitude transmitted with a pulse shape $g(t)$. The signal can be represented as $a(t) = a_n \cdot g(t)$, where $a_n$ represents the amplitude level for the $n$-th symbol [32](#page=32). * **M-PAM**: An extension of PAM where $M$ different amplitude levels are used to represent $k = \log_2(M)$ bits per symbol. This allows for more efficient data transmission by encoding multiple bits within a single symbol [33](#page=33). > **Example**: In 4-PAM, there are $M=4$ amplitude levels, meaning $k = \log_2 = 2$ bits can be represented by each symbol. For instance, levels might represent `00`, `01`, `10`, and `11` [33](#page=33) [34](#page=34) [4](#page=4). > **Example**: 8-PAM uses $M=8$ amplitude levels, allowing for $k = \log_2 = 3$ bits per symbol to be transmitted [34](#page=34) [8](#page=8). --- # Channel impairments and lecture summary This section details common physical impairments that affect communication channels and provides a summary of the lecture's key topics concerning the physical layer. ### 4.1 Channel impairments Communication channels are subject to several impairments that can degrade the quality of transmitted signals. These impairments can lead to errors in the received data and necessitate robust error detection and correction mechanisms. The primary impairments discussed are attenuation, distortion, noise, and multipath propagation [35](#page=35). The received signal $y(t)$ can be generally modeled as the transmitted signal $x(t)$ convolved with the channel's impulse response $h(t)$, plus additive noise $n(t)$. This can be represented as [35](#page=35): $$y(t) = x(t) \ast h(t) + n(t)$$ #### 4.1.1 Attenuation Attenuation refers to the gradual loss of signal strength as it travels through a communication medium. This loss occurs due to energy dissipation in the medium, such as resistance in wires or absorption in the air. As signals attenuate, their amplitude decreases, making them more susceptible to being corrupted by noise. Amplifiers are often used to compensate for attenuation, but they can also amplify noise [35](#page=35). #### 4.1.2 Distortion Distortion occurs when the shape of the transmitted signal is altered as it passes through the channel. This can happen if different frequency components of a signal are delayed by different amounts (delay distortion) or if the amplitude-frequency response of the channel is not uniform. Distortion can cause intersymbol interference (ISI), where the tail of one symbol encroaches upon the next, leading to errors in decoding [35](#page=35). #### 4.1.3 Noise Noise is any unwanted signal that interferes with the transmitted signal. Noise can originate from various sources, including thermal noise (random motion of electrons), crosstalk (interference from adjacent channels), and external interference (e.g., from electrical equipment). Noise is often random and can be additive, meaning it is simply added to the signal [35](#page=35). #### 4.1.4 Multipath propagation (fading) Multipath propagation occurs when a signal travels through multiple paths from the transmitter to the receiver. This is common in wireless communication due to reflections, diffractions, and scattering of the signal off objects. The different paths can cause the signal components to arrive at the receiver at different times and with different amplitudes and phases. This can lead to constructive or destructive interference, resulting in signal strength fluctuations known as fading [35](#page=35). ### 4.2 Lecture summary: Physical layer The lecture's summary of the physical layer covers fundamental concepts related to data representation, transmission media, and signal transmission methods [36](#page=36). #### 4.2.1 Data and signal A key distinction is made between data (the information itself) and the signal (the physical representation of that data for transmission). The lecture discusses the difference between analog signals (continuous in time and amplitude) and digital signals (discrete in time and amplitude) [36](#page=36). #### 4.2.2 Digitalisation of analog signals The process of converting analog signals into digital signals involves several steps [36](#page=36): * **Sampling:** Measuring the analog signal's amplitude at regular intervals in time. The sampling rate must be at least twice the highest frequency component of the signal (Nyquist theorem). * **Quantisation:** Assigning a discrete amplitude level to each sampled value. This process introduces quantisation error. * **Encoding:** Representing the quantised amplitude levels using binary codes. #### 4.2.3 Transmission media Various physical media are used for signal transmission, including guided media (e.g., twisted-pair cable, coaxial cable, fiber optic cable) and unguided media (e.g., radio waves, microwaves). The choice of medium affects signal characteristics, data rates, and susceptibility to impairments [36](#page=36). #### 4.2.4 Transmission The lecture outlines two primary methods of signal transmission [36](#page=36): * **Digital transmission:** This can be either baseband transmission (where the digital signal is sent directly over the medium without modulation) or involve the use of a carrier signal. * **Analog transmission:** This involves modulation, where digital data is used to modify the characteristics (amplitude, frequency, or phase) of an analog carrier signal. --- ## Common mistakes to avoid - Review all topics thoroughly before exams - Pay attention to formulas and key definitions - Practice with examples provided in each section - Don't memorize without understanding the underlying concepts

| Term | Definition | |------|------------| | Data | A static representation of information, typically used for storage. | | Signal | A dynamic representation of information, used for transmission. | | Analog Signal | A signal characterized by continuous time and continuous amplitude. | | Digital Signal | A signal characterized by discrete time and discrete amplitude, often represented in a binary format. | | Sampling | The process of discretizing a continuous signal in time to obtain discrete time samples. | | Sampling Frequency | The rate at which a continuous signal is sampled, denoted as $F_s$, where $F_s = 1/T_s$ and $T_s$ is the sampling time. | | Shannon-Nyquist Sampling Theorem | States that a band-limited signal with a highest frequency component $F_{max}$ can be uniquely determined by its samples if the sampling frequency $F_s$ is at least twice the highest frequency component ($F_s \geq 2F_{max}$). | | Nyquist Frequency | Half of the sampling frequency ($F_s/2$), representing the maximum frequency component that can be accurately captured by sampling. | | Nyquist Rate | The minimum sampling frequency required to avoid aliasing, which is twice the maximum frequency of the signal ($2F_{max}$). | | Aliasing | An effect that occurs when a signal is sampled at a rate lower than the Nyquist rate, causing higher frequencies to appear as lower frequencies in the sampled data, distorting the original signal. | | Quantization | The process of discretizing the amplitude of a sampled signal, mapping continuous amplitude values to a finite set of discrete levels. | | Encoding | The process of representing the quantized amplitude levels of a signal using a binary representation (bits). | | ADC (Analog to Digital Converter) | A device that converts an analog signal into a digital signal. | | DAC (Digital to Analog Converter) | A device that converts a digital signal into an analog signal. | | Distortion | An alteration of the original signal's shape or characteristics during transmission, which can be caused by various factors in the communication channel. | | Noise | Unwanted disturbances or signals that interfere with the intended signal during transmission, degrading its quality. | | Attenuation | The loss of signal strength over distance as it travels through a transmission medium. | | Multipath Propagation (Fading) | A phenomenon where a transmitted signal reaches the receiver via multiple paths, causing constructive or destructive interference and signal strength fluctuations. | | Baseband Transmission | A method of transmitting digital data directly as a sequence of pulses without using a carrier signal. | | Carrier Transmission | A method of transmitting digital data by modulating a high-frequency carrier signal with the digital information. | | Modulation | The process of varying one or more properties (amplitude, phase, or frequency) of a carrier wave in accordance with the information to be transmitted. | | Amplitude Shift Keying (ASK) | A modulation technique where the amplitude of a carrier signal is varied to represent digital data. On-Off Keying (OOK) is a form of ASK. | | Phase Shift Keying (PSK) | A modulation technique where the phase of a carrier signal is varied to represent digital data. | | Binary Phase Shift Keying (BPSK) | A type of PSK that uses two distinct phases of the carrier signal to represent binary data (0 and 1). | | Pulse Amplitude Modulation (PAM) | A technique where the amplitude of a pulse is varied to represent data. Binary PAM uses two amplitude levels. | | M-PAM | A form of Pulse Amplitude Modulation that uses M distinct amplitude levels to represent $k = \log_2(M)$ bits of data per symbol. | | Twisted Pair Cable | A type of cable consisting of two insulated copper wires twisted around each other to reduce electromagnetic interference. | | Coaxial Cable | A type of electrical cable with an inner conductor surrounded by an insulating layer, a braided metal shield, and an outer insulating layer. | | Optical Fiber | A thin strand of glass or plastic that transmits data using light signals. | | Radio | Electromagnetic waves used for wireless communication. | | Manchester Coding | A line code that encodes clock and data into transitions in the signal. A transition occurs in the middle of each bit period, and a zero crossing at the start of the bit period indicates the data bit. | | Differential Manchester Coding | A line code that uses a transition at the beginning of each bit period to indicate the data. The absence or presence of an additional transition indicates the data bit value. |