Chapter 2

2.1 SIGNALS

• Definition: Data (information) is exchanged between two parties, but what actually travels through the network are signals.

• Types of Signals:

  • Analog Signals: Can take many values.

  • Digital Signals: Take a limited number of values.

2.1.1 Analog Signals

• Forms:

  • Periodic (commonly used in data communication)

  • Aperiodic (nonperiodic)

• Types:

  • Simple (Sine wave, cannot be decomposed)

  • Composite (Combination of multiple sine waves)

Characteristics of a Sine Wave

1. Peak Amplitude: Maximum signal intensity (measured in volts).

2. Period (T) & Frequency (f):

   • Period (T): Time taken for one complete cycle.

   • Frequency (f): Number of cycles per second (Hz).

   • Relationship: f = 1 / T

3. Phase: Position of the wave relative to time 0 (measured in degrees or radians).

4. Wavelength (λ):

   • Distance a signal travels in one period.

   • Formula: λ = c / f (c = propagation speed of medium, f = frequency).

5. Time vs. Frequency Domains:

   • Time-domain plot: Shows signal amplitude over time.

   • Frequency-domain plot: Represents signal as spikes based on frequency and amplitude.

Composite Signals

• Definition: Combination of multiple sine waves.

• Why? Single sine waves do not carry meaningful data.

• Bandwidth: Difference between highest and lowest frequencies in a composite signal.

  • Example: A signal with frequencies from 1000 Hz to 5000 Hz has a bandwidth of 4000 Hz.

2.1.2 Digital Signals

• Definition: Information can also be represented by digital signals (e.g., 1 as a positive voltage, 0 as zero voltage).

• Levels:

  • Binary: 2 levels (0 and 1)

  • Multilevel: More than 2 levels, allowing more bits per level.

  • Formula: Bits per level = log₂(L) (where L = number of levels).

Bit Rate

• Definition: Number of bits transmitted per second (bps).

• Units:

  • Kbps (kilobits per second) = 1,000 bps

  • Mbps (megabits per second) = 1,000,000 bps

• Example: Downloading 100 pages/min (24 lines per page, 80 characters per line, 8 bits per character) results in a bit rate of 1.536 Mbps.

Bit Length

• Definition: Distance occupied by one bit on the transmission medium.

• Formula: Bit length = 1 / bit rate

• Example: For a bit rate of 1.536 Mbps, bit length = 0.651 µs.

Transmission of Digital Signals

• Baseband Transmission: Sending digital signals without converting to analog.

• Broadband Transmission (Modulation): Converting digital signals to analog for transmission.

2.2: Signal Impairment

Signal Impairment Overview

Transmission media are not perfect, causing signal impairment, meaning the signal at the receiving end differs from the transmitted one. Three main causes of impairment are attenuation, distortion, and noise.

2.2.1 Attenuation and Amplification

• Attenuation: A loss of signal energy as it travels through a medium due to resistance.

• Amplification: Used to restore signal strength.

• Decibels (dB) measure signal strength; negative dB means loss (attenuation), while positive dB means gain (amplification).

  • Formula: dB = 10 log₁₀ (P₂ / P₁)

  • Example: If signal power is reduced to half, attenuation = -3 dB.

2.2.2 Distortion

• Occurs when the signal changes shape during transmission.

• Common in composite signals (with multiple frequencies) because different frequencies travel at different speeds, causing phase shifts.

2.2.3 Noise

• Unwanted interference that alters the signal.

• Types of noise:

  • Thermal noise: Random electron movement in a wire.

  • Induced noise: From external devices like motors.

  • Crosstalk: Signal leakage between wires.

  • Impulse noise: Sudden bursts from lightning or power lines.

• Signal-to-Noise Ratio (SNR): Measures signal strength compared to noise.

  • Formula: SNR = Signal Power / Noise Power

  • SNR (dB) = 10 log₁₀ (SNR)

2.2.4 Data Rate Limits

How fast data can be transmitted depends on bandwidth, signal levels, and noise.

Nyquist Bit Rate (Noiseless Channel)

• Formula: BitRate = 2 × B × log₂(L)

  • B = Bandwidth (Hz), L = Signal levels, BitRate = Bits per second.

• Increasing signal levels increases bit rate but makes reception harder.

Shannon Capacity (Noisy Channel)

• Formula: C = B × log₂(1 + SNR)

  • C = Max bit rate (bps), B = Bandwidth, SNR = Signal-to-noise ratio.

• Determines the upper limit of data rate in real-world conditions.

• Example: A phone line with 3,000 Hz bandwidth and SNR of 3,162 has a max bit rate of 34.88 kbps.

2.2.5 Performance Metrics

1. Bandwidth

• Measured in two ways:

  • Hertz (Hz): Frequency range of a channel.

  • Bits per second (bps): Data transmission capacity.

• Example: A telephone line’s bandwidth is 4 kHz, but with advanced technology, data transmission can reach 56 kbps.

• It is the potential measurement of a link

2. Throughput

• Actual data transfer rate, which is always lower than bandwidth due to network limitations.

• Example: A highway designed for 1,000 cars/min but only allows 100 due to congestion.

• It is how realistically we can send data/measurement of a link.

3. Latency (Delay)

• Total time for data to travel from sender to receiver, from the first bit.

• Types of delays:

  1. Propagation delay (time to travel through the medium)

  2. Transmission delay (time to push bits into the channel)

  3. Queuing delay (waiting time in buffers)

  4. Processing delay (time for devices to handle the signal)

• Formula: Latency = Propagation + Transmission + Queuing + Processing Delay

4. Bandwidth-Delay Product

• Defines the amount of data(bits) that can fill a link at any moment.

• Formula: Bandwidth × Delay

• Example: A 5 bps bandwidth with 5s delay means 25 bits can exist in the link at once.

5. Jitter

• Variation in delay between received packets, causing issues in real-time applications like video and audio streaming.

2.3: Digital Transmission

Overview of Digital Transmission

To send information over a network, it must be converted into either a digital signal or an analog signal. This section focuses on digital transmission, which requires:

1. Digital-to-digital conversion (if data is already digital)

2. Analog-to-digital conversion (if data is originally analog)

2.3.1 Digital-to-Digital Conversion

When transmitting digital data over a digital medium, digital-to-digital conversion is used. This involves:

• Line Coding (always needed)

• Block Coding (optional)

• Scrambling (optional)

Line Coding

• Converts digital data (bits) into a digital signal.

• At the sender: Data is encoded into a signal.

• At the receiver: The signal is decoded back into data.

Block Coding

• Introduces redundancy to improve synchronization and error detection.

• Converts m-bit blocks into n-bit blocks (mB/nB encoding, where n > m).

• Example: 4B/5B encoding converts 4-bit groups into 5-bit groups.

• Steps involved:

  1. Division (split data into m-bit groups)

  2. Substitution (replace with n-bit groups)

  3. Combination (merge back into a data stream)

2.3.2 Analog-to-Digital Conversion

When transmitting analog data (e.g., from a microphone or camera), it must be digitized for transmission. Two main techniques are used:

Pulse Code Modulation (PCM)

• The most common digitization method.

• Consists of three steps:

  1. Sampling – The analog signal is measured at regular intervals.

  2. Quantization – Each sample is assigned a discrete value.

  3. Encoding – The quantized values are converted into a stream of bits.

• PCM Bandwidth: The minimum required bandwidth for PCM is Bmin = nb × Banalog (nb = number of bits per sample).

Delta Modulation (DM)

• A simpler alternative to PCM.

• Instead of encoding the absolute signal amplitude, DM only records changes from the previous sample.

• More efficient than PCM but less accurate.

2.4 Analog Transmission

Analog transmission is used when a bandpass channel is available, and digital transmission is not feasible. There are two types of conversions:

1. Digital-to-Analog Conversion: Converts digital data into an analog signal by modifying its characteristics.

2. Analog-to-Analog Conversion: Converts a low-pass analog signal into a bandpass analog signal.

Digital-to-Analog Conversion

A sine wave can be modified in three ways to carry digital data:

• Amplitude Shift Keying (ASK): Changes the amplitude of the signal while keeping frequency and phase constant.

  • Binary ASK (BASK): Uses two amplitude levels to represent binary data.

  • Multilevel ASK: Uses more amplitude levels to encode multiple bits at a time.

• Frequency Shift Keying (FSK): Changes the frequency of the carrier signal to represent different binary values.

  • Binary FSK (BFSK): Uses two different carrier frequencies to represent 0 and 1.

• Phase Shift Keying (PSK): Modifies the phase of the signal while keeping amplitude and frequency constant.

  • Binary PSK (BPSK): Uses two phase values (0° and 180°) for binary data.

• Quadrature Amplitude Modulation (QAM): Combines ASK and PSK for more efficient transmission.

Analog-to-Analog Conversion

Analog modulation is needed when using a bandpass channel. The three primary methods are:

• Amplitude Modulation (AM): The carrier wave's amplitude changes to match the signal's amplitude. The bandwidth is twice the signal's bandwidth.

• Frequency Modulation (FM): The frequency of the carrier wave varies with the signal amplitude while phase and amplitude remain constant. The bandwidth is determined by the modulation index.

• Phase Modulation (PM): The phase of the carrier wave varies based on the signal amplitude. It is similar to FM but depends on the signal’s derivative.

Both FM and PM require greater bandwidth than AM but provide better noise resistance.

Multiplexing (Section 2.5 Summary)

Multiplexing is a technique that enables multiple signals to be transmitted simultaneously over a single data link. This maximizes bandwidth efficiency and prevents resource wastage. Instead of adding individual links for increasing traffic, higher-bandwidth links can be used to accommodate multiple signals.

Multiplexed System Structure

A multiplexed system consists of:

• Multiplexer: Combines multiple input signals into one output stream (many-to-one).

• Demultiplexer: Separates the received composite signal back into its original components (one-to-many).

• Link: The physical path used for data transmission.

• Channel: A portion of the link designated for a specific transmission.

Types of Multiplexing

1. Frequency-Division Multiplexing (FDM)

   • An analog technique used when the link’s bandwidth is greater than the combined bandwidths of transmitted signals.

   • Each signal modulates a unique carrier frequency, forming a composite signal for transmission.

   • Guard bands prevent signal overlap.

   • Digital signals can be converted to analog before applying FDM.

2. Time-Division Multiplexing (TDM)

   • A digital technique that allocates time slots to different connections, allowing them to share the link sequentially.

   • Unlike FDM, TDM divides the link based on time rather than frequency.

   • Analog data can be digitized before being multiplexed using TDM.

Multiplexing enhances communication efficiency by utilizing available bandwidth effectively, making it a fundamental concept in data and telecommunications.

2.6 Transmission Media

Transmission media are the physical pathways that carry signals from a source to a destination, operating below the physical layer. They can be categorized into guided media (wired) and unguided media (wireless).

1. Guided Media

Guided media direct signals through a physical medium, including:

• Twisted-Pair Cable: Two copper wires twisted together to reduce interference. Used in telephone lines and DSL connections.

• Coaxial Cable: A central conductor with insulation, shielding, and an outer cover. It supports higher frequencies but requires frequent repeaters. Used in early telephone networks and cable TV.

• Fiber-Optic Cable: Uses light signals through a glass/plastic core with reflective cladding. It offers low attenuation and high bandwidth, making it ideal for backbone networks and hybrid cable TV systems.

2. Unguided Media (Wireless)

Unguided media transmit electromagnetic waves without physical conductors:

• Radio Waves: Omnidirectional, suitable for long-range broadcasts (e.g., AM radio), but prone to interference.

• Microwaves: Unidirectional, requiring line-of-sight communication. Used in cellular networks and satellites.

• Infrared: Short-range communication that cannot penetrate walls, reducing interference. Used in remote controls and indoor wireless systems.

Each medium has distinct advantages and applications based on bandwidth, range, and interference resistance.