Communication Systems

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This section covers the block diagrams of analog and digital communication systems, baseband vs bandpass transmission, noise types and statistics, and the key performance figures — SNR, BER, and noise figure — used to characterize a communication link.

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Block Diagram of a Communication System General chain:

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Information source → Transmitter (source coding, channel coding, modulation) → Channel (adds noise/distortion) → Receiver (demodulation, decoding) → Destination.

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Analog communication system: message signal is continuous-valued and modulates a carrier directly (e.g.

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Digital communication system: message is first converted to a bit stream (sampling, quantizing, coding) before modulation; more robust to noise, supports encryption/multiplexing/error correction.

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Baseband system: signal transmitted directly at its original frequency range, without shifting to a carrier (e.g. within a LAN cable).

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Bandpass (passband) system: signal is modulated onto a high-frequency carrier for transmission (e.g. radio broadcast).

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Noise in Communication Systems Noise Type Description Thermal (Johnson) noise Caused by random electron motion due to temperature; modeled as white Gaussian noise, power = kTB Shot noise Due to discrete/random arrival of charge carriers (e.g. in diodes, photodetectors) Flicker (1/f) noise Dominant at low frequencies; inversely proportional to frequency White Gaussian noise Constant power spectral density across all frequencies; amplitude follows a Gaussian distribution Impulse noise Sudden, short-duration high-amplitude spikes (e.g. from switching, lightning) Equivalent noise bandwidth: the bandwidth of an ideal rectangular filter that would pass the same total noise power as the actual system.

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Additive White Gaussian Noise (AWGN) channel: standard channel model where noise is added to the signal, is statistically independent of it, has flat (white) power spectral density, and Gaussian amplitude distribution.

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Performance Measures Measure Meaning Signal-to-Noise Ratio (SNR) Ratio of average signal power to average noise power, usually expressed in dB:

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SNR(dB) = 10log₁₀(P_signal/P_noise) Bit Error Rate/Ratio (BER) Fraction of received bits that are in error = (number of bit errors)/(total bits transmitted) Figure of Merit Ratio of output SNR to input SNR for a demodulator; measures how well a modulation scheme fights noise Noise degrades SNR, increases BER, and can mask the desired signal; a receiver must maintain SNR above a threshold for acceptable performance.

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This section covers amplitude modulation and its variants (DSB-SC, SSB-SC, VSB), their demodulation methods, and angle modulation (FM/PM) including narrowband/wideband FM, spectra of angle-modulated signals, and pre-emphasis/de-emphasis.

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Amplitude Modulation Family Scheme Key Feature Amplitude Modulation (AM) Carrier amplitude varies with message; transmits carrier + both sidebands; simple envelope detection DSB-SC Double sideband, suppressed carrier; both sidebands sent but carrier removed — saves power, needs synchronous detection SSB-SC Only one sideband transmitted; saves bandwidth (half of DSB) and power; used in voice/HF radio VSB Vestigial sideband: one sideband plus a small vestige of the other; compromise between SSB complexity and DSB bandwidth; used in analog TV video Demodulation of AM Signals Square-law demodulator: uses a nonlinear (square-law) device followed by a low-pass filter to recover the message from its square-law distortion products.

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Synchronous (coherent) demodulation: multiplies the received signal by a locally generated carrier in phase with the transmitted carrier, then low-pass filters; required for DSB-SC and SSB-SC.

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Carrier recovery techniques:

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Costas loop and squaring loop are used to regenerate a phase-coherent carrier at the receiver when no carrier is transmitted (as in DSB-SC/SSB-SC).

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Angle Modulation — FM & PM Type Description Frequency Modulation (FM) Instantaneous carrier frequency varies proportionally with the message amplitude Phase Modulation (PM) Instantaneous carrier phase varies proportionally with the message amplitude Narrowband FM (NBFM) Modulation index β « 1; bandwidth ≈ 2fₘ (similar to AM bandwidth) Wideband FM (WBFM) β > 1; larger bandwidth, given by Carson's rule:

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BW ≈ 2(Δf + fₘ) = 2fₘ(β+1) The spectrum of an angle-modulated signal contains an infinite number of sidebands spaced at multiples of fₘ, with amplitudes given by Bessel functions of the first kind Jₙ(β).

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Pre-emphasis: boosts high-frequency components of the message before FM modulation (transmitter) to improve their SNR, since noise power in FM demodulation rises with frequency.

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De-emphasis: a complementary low-pass filter at the receiver that restores the original spectral balance and reduces high-frequency noise introduced by the channel.

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This section covers binary and M-ary digital modulation schemes, error probability, matched filtering, source coding, the Shannon–Hartley channel capacity theorem, and multiplexing.

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Binary Digital Modulation Scheme Description BASK (Binary Amplitude Shift Keying) Carrier amplitude switched between two levels (often on/off) to represent bits 0/1 BFSK (Binary Frequency Shift Keying) Carrier frequency switched between two values representing bits 0/1; more noise- resistant than BASK BPSK (Binary Phase Shift Keying) Carrier phase switched between 0° and 180° representing bits 0/1; best noise performance among the three M-ary Techniques M-ary modulation encodes log₂M bits per symbol by using M distinct signal states, increasing bandwidth efficiency at the cost of higher required SNR.

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QPSK (Quadrature PSK):

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4 phase states (90° apart), carrying 2 bits/symbol; same bandwidth as BPSK but twice the bit rate.

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QAM (Quadrature Amplitude Modulation): varies both amplitude and phase, combining ASK and PSK to pack more bits/symbol (e.g.

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16-QAM = 4 bits/symbol); very bandwidth-efficient but more sensitive to noise.

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Detection, Capacity & Multiplexing Error probability in PSK systems decreases as the distance between constellation points (and hence transmitted energy per bit, E_b/N₀) increases;

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BPSK has the lowest error probability among common binary schemes for a given SNR.

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Matched filter: the optimum linear filter that maximizes output SNR for detecting a known pulse shape in additive white noise; its impulse response is a time-reversed, delayed version of the transmitted pulse.

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Source coding removes redundancy from the source data to reduce the number of bits needed (e.g.

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Huffman coding), improving transmission efficiency.

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Pulse Code Modulation (PCM): converts an analog signal to a digital bit stream via sampling, quantization, and binary encoding.

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Concept Statement Shannon–Hartley theorem C = B log₂(1 + S/N), the maximum error-free channel capacity C (bits/s) for bandwidth B (Hz) and SNR S/N Multiplexing Combining multiple signals to share one transmission medium; achieved in frequency (FDM), time (TDM), code (CDM), or wavelength (WDM)

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This section covers pulse amplitude modulation, pulse code modulation (encoding, quantization, companding), delta modulation and its variants, and the noise performance of these pulse systems.

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Pulse Amplitude Modulation (PAM) PAM: amplitude of a train of regularly spaced pulses is varied in proportion to the message signal's instantaneous amplitude.

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Bandwidth requirement:

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PAM bandwidth is proportional to the pulse rate; narrower pulses require greater transmission bandwidth (BW ∝ 1/τ, where τ is pulse width).

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Pulse Code Modulation (PCM) Stage Function Sampling Signal sampled at ≥ Nyquist rate (fₛ ≥ 2fₘₐₓ) to allow perfect reconstruction Quantization Each sample rounded to the nearest of a finite set of levels; introduces quantization error/noise Encoding Each quantized level represented as a binary codeword Decoding Receiver maps codewords back to quantized amplitude levels Quantization error: the difference between the actual sample value and its quantized level; for uniform quantization, max error = ±(step size)/2.

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Companding: compressing the signal's dynamic range before quantization (at transmitter) and expanding it after (at receiver) to give better SNR for low-amplitude signals; common laws are μ-law (North America/Japan) and A-law (Europe).

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Differential PCM (DPCM): encodes the difference between consecutive samples (which is smaller) rather than the sample itself, reducing the number of bits needed.

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Multiplexing of several PCM streams (typically via TDM) allows many channels to share one digital transmission link.

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Delta Modulation (DM) Concept Description Delta Modulation (DM) Encodes only the sign of the difference between consecutive samples as a single bit (1-bit quantizer); step size is fixed Slope overload distortion Occurs when the signal changes faster than the fixed step size can track Granular noise Occurs when a nearly constant signal causes the step to hunt above/below it Adaptive DM (ADM) Step size adapts to the signal's rate of change, reducing both slope overload and granular noise Continuously Variable Slope DM (CVSDM) A form of adaptive DM where the step size varies continuously based on recent bit patterns Sigma-delta modulation Uses oversampling and noise shaping (integrator + 1-bit quantizer + feedback) to push quantization noise out of the signal band

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This section covers channel coding fundamentals, Hamming distance, parity checking, linear and cyclic block codes, and an introduction to convolutional coding including code trees, trellis diagrams and decoding.

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Channel Coding Fundamentals Channel coding adds controlled redundancy to transmitted data so the receiver can detect and/or correct errors introduced by the noisy channel.

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Hamming distance between two codewords: the number of bit positions in which they differ.

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A code with minimum distance d_min can detect up to (d_min−1) errors and correct up to ⌊(d_min−1)/2⌋ errors.

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Parity checking: a single parity bit appended so the total number of 1s is even (even parity) or odd (odd parity); detects single-bit errors but cannot correct them or detect all multi-bit errors.

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Block Codes Code Type Description Block code (n,k) k message bits encoded into n > k coded bits; code rate = k/n Linear block code Any linear combination (sum) of two valid codewords is also a valid codeword Systematic linear block code Codeword = original message bits followed by (or alongside) parity/check bits, so the message is directly visible in the codeword Cyclic code A linear block code where every cyclic shift of a valid codeword is also a valid codeword; efficiently encoded/decoded using shift registers and generator polynomials Encoding (systematic linear block code): generator matrix G maps k message bits to n codeword bits, c = mG.

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Decoding (syndrome decoding): receiver computes the syndrome using the parity-check matrix H; a nonzero syndrome indicates an error, and its pattern can identify the error location (for correctable errors).

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Cyclic redundancy check (CRC): a common cyclic code application for error detection, dividing the message by a generator polynomial and appending the remainder.

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Convolutional Coding Unlike block codes, a convolutional coder generates output bits continuously from a sliding window of input bits using shift registers, so each output depends on the current and several previous input bits (constraint length).

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Code tree: shows all possible output sequences as branches from a root, growing with each input bit.

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Trellis diagram: a compact, repeating structure representing the coder's states and transitions over time (used for decoding).

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State diagram: shows the coder's finite states and the transitions between them for each possible input.

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Decoding method: the Viterbi algorithm finds the maximum-likelihood path through the trellis, offering efficient decoding of convolutional codes.

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This section covers data communication fundamentals — parallel vs serial transmission, bandwidth utilization via multiplexing (FDM/TDM/WDM), network topologies, and the layered OSI and TCP/IP architectures.

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Parallel vs Serial Communication Mode Description Parallel communication Multiple bits sent simultaneously over separate wires; fast over short distances but costly/susceptible to skew over long distances Serial communication Bits sent one at a time over a single line; slower per wire but scales well over long distances (used in most modern networks) Multiplexing Techniques Technique Principle Frequency Division Multiplexing (FDM) Each signal is assigned a distinct frequency band within the shared channel; used in analog systems (e.g. cable TV, radio) Time Division Multiplexing (TDM) Each signal is assigned a distinct time slot in a repeating frame; used in digital systems (e.g.

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PCM telephony) Wavelength Division Multiplexing (WDM) Each signal is assigned a distinct wavelength (color) of light in a shared optical fiber; used in high-capacity fiber-optic links Network Topologies & Layered Architecture Common network topologies: bus, star, ring, mesh, and tree — each with different tradeoffs in cost, reliability, and ease of expansion.

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Layered architecture divides network communication into independent layers, each providing services to the layer above and using services from the layer below, simplifying design and interoperability.

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OSI Layer Function 7.

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Application Provides network services directly to end-user applications (e.g.

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HTTP, FTP, email) 6.

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Presentation Data translation, encryption/decryption, compression 5.

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Session Establishes, manages, and terminates sessions between applications 4.

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Transport End-to-end reliable delivery, segmentation, flow control (e.g.

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Network Logical addressing and routing of packets between networks (e.g.

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Data Link Framing, physical addressing (MAC), error detection on a single link 1.

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Physical Transmission of raw bits over the physical medium (cables, radio) The TCP/IP model is a simpler, practically-implemented 4-layer stack (Application, Transport, Internet, Network Access) that roughly maps onto the 7-layer OSI model and is the basis of the modern Internet.