Digital Communications

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  • Digital Communications System

    • Digital communication systems convert analogue signals into digital signals using Pulse Code Modulation (PCM).

    • PCM involves sampling, quantization, and coding.

    • Sampling reads amplitude values of a continuous signal at regular intervals.

    • The signal after sampling is a discrete time signal, also referred to as a PAM signal.

    Sampling Methods

    Impulse sampling is also known as ideal sampling.

    Pulse sampling uses a train of pulses and can be natural or flat-top.

    Natural pulse sampling uses a FET as a switch.

    Flat-top pulse sampling uses a sample-and-hold circuit.

    Sample and hold circuits charge a capacitor during the sampling interval and hold the voltage for quantization.

    Shannon's sampling theorem states that an analogue signal with a max frequency of fmax can be reconstructed if the sampling frequency, fs, is greater than or equal to 2fmax.

    fmax is the Nyquist frequency.

    2fmax is the Nyquist rate.

    Aliasing occurs when a signal is sampled below the Nyquist rate, causing a loss of information.

  • Quantization

    • Quantization converts the amplitude of a PAM signal into a discrete value.

    • Quantization width/resolution is the spacing between quantization levels.

    • Uniform quantization has a consistent resolution.

    • Quantization error is the difference between the sample value and the quantized value.

    • Non-uniform quantization uses variable step sizes, achieved through compression and expansion (companding).

    • Mu-law and A-law are companding standards.

  • Pulse Code Modulation (PCM)

    • Encoding converts a quantised PAM signal into a code, usually binary.

    • The number of bits, n, required for a PCM code word is determined by n = log2(M), where M is the number of quantization levels.

  • Variants of PCM

    • Differential PCM (DPCM) encodes the first sample and the differences between successive samples.

    • Delta modulation compares consecutive quantized samples and outputs a 1 if the current is greater and a 0 if it is less than the previous one.

    • Slope overload occurs if the input signal changes faster than the step generator in delta modulation.

    • Granular noise/hunting is another error that can occur in delta modulation.

    • Line coding converts digital data to digital signals.

    • Desirable properties of a line code include no baseline wander, no DC components, self-synchronisation, built-in error detection, noise immunity, low complexity and transparency.

    • HDB3 is a line code similar to AMI.

  • Information Theory

    • Information theory provides a quantitative measure of information in message signals.

    • A discrete information source has a set of symbols as possible outcomes.

    • A memoryless source produces symbols independent of previous symbols.

    • The information content of a symbol is measured in bits.

    • The Hartley equation defines the information content of a symbol.

    • Entropy is the average information content of a source.

    • The source coding theorem states that the minimum average length of a code word is related to the entropy.

    • Efficiency of a code is the ratio of entropy to average length.

    • A Binary Symmetric Source (BSS) has two outputs with probabilities z and (1-z).

    • Shannon-Hartley theorem defines the maximum data rate for a channel.

    • Source coding reduces the number of bits in a codeword.

    • Shannon-Fano and Huffman coding are types of entropy coding.

  • Channel Coding

    • Channel coding detects and corrects errors in received data.

    • Random errors are single bit errors due to white noise.

    • Burst errors involve two or more bits in error due to a burst of noise.

    • Forward error correction (FEC) adds redundant bits for error correction.

    • Block codes add (n-k) redundant bits to k information bits.

    • Code rate = k/n.

    • Redundant bits = (n-k).

    • Redundancy = [(n-k)/n] x 100%.

    • Hamming distance is the number of differing bits between two code words.

    • Minimum Hamming distance is the lowest Hamming distance in a code set.

    • Hamming weight is the number of ones in a codeword.

    • Systematic codes have separate data and redundant bits.

    • Linear block codes have a modulo-2 sum of two codewords that is also a codeword.

    • Even parity adds a bit to make the total number of 1s even.

    • Odd parity adds a bit to make the total number of 1s odd.

    • Cyclic codes are a subset of linear block codes where a cyclic shift of a codeword results in another valid codeword.

    • CRC encoding involves polynomial division to create a transmitted codeword.

  • Hamming Codes

    • Hamming codes are used for single-error correction.

    • Parity bits are placed at bit positions that are powers of 2 (e.g., 1, 2, 4, 8).

    • Parity bits are calculated based on the data bits.

    • Check bits at the receiver determine the location of an error.

  • Digital Modulation

    • Digital modulation uses digital messages to modulate a high-frequency carrier wave.

    • Amplitude Shift Keying (ASK) changes the amplitude of the carrier.

      • On-Off Keying (OOK) is a variant of ASK.

    • Frequency Shift Keying (FSK) changes the frequency of the carrier.

      • Continuous Phase FSK (CPFSK) has smooth transitions.

    • Phase Shift Keying (PSK) changes the phase of the carrier.

      • Binary PSK (BPSK) uses two phases.

      • Quadrature PSK (QPSK) uses four phases.

    • Differential PSK (DPSK) encodes data based on phase changes relative to the previous bit.

  • Noise in Communication Systems

    • Noise is unwanted voltages and currents that corrupt the signal.

    • External noise includes man-made, atmospheric, and space noise.

    • Internal noise includes thermal, shot, and flicker noise.

    • Thermal noise is due to the thermal agitation of electrons.

    • Noise power is the power available to the load.

    • Spectral noise power density is the power per unit frequency.

    • Additive White Gaussian Noise (AWGN) is thermal noise with a white spectrum and Gaussian distribution.

    • Signal-to-noise ratio (SNR) compares signal power to noise power.

    • Noise ratio (NR) is the ratio of input to output SNRs.

    • Noise figure (NF) is 10log(NR).

    • Intermodulation noise occurs due to non-linearities in the communication channel.

  • Optical Communication Systems

    • Optical communication systems use light to transmit information.

    • Transmitters use LEDs or lasers.

    • Excitation is when an electron moves to a higher energy level.

    • Emission occurs when an electron returns to a lower energy level.

    • Spontaneous emission occurs naturally.

    • Stimulated emission is induced by a passing photon.

    • LEDs are pn-junction semiconductor devices that emit light when forward biased.

      • They can have a homojunction or heterojunction structure.

      • They can be surface or edge emitters.

    • LASERs use stimulated emission of radiation for light amplification.

      • They require population inversion for lasing action.

      • Laser light is monochromatic, coherent, has a narrow beam, and high irradiance.

    • Output power is the optical power emitted.

    • Output pattern is the area and angle of emitted light.

    • Spectral width is the range of wavelengths emitted.

    • Modulation can be direct or indirect.

    • Direct modulation varies the electrical supply to the light source.

    • Indirect modulation uses an external modulator.

  • Photodetectors

    • Responsivity is the ratio of electrical power output to optical power input.

    • Quantum efficiency is the ratio of electrons generated to incident photons.

    • Dark current is the current generated with no light.

    • Noise floor is the minimum detectable power.

    • Response time is the time to respond to an optical input.

    • Noise equivalent power (NEP) is the power for a signal-to-noise ratio of one.

  • Optical Fibres

    • Optical fibres consist of a core, cladding, and jacket.

    • Refractive index determines the velocity of light in a material.

    • Reflection occurs at the boundary of two media.

    • Refraction is the bending of light at a boundary.

    • Snell's law relates the angles and refractive indices of two media.

    • Critical angle is the angle of incidence where the angle of refraction is 90 degrees.

    • The cone of acceptance defines the rays that can propagate through a fibre.

    • Numerical aperture (NA) is the sine of the acceptance angle.

    • Fresnel reflection occurs when light moves between media with different refractive indices.

    • Fibres are classified by material, refractive index profile and propagation modes.

      • Single-mode step-index fibres have a small core and allow a single mode of light.

      • Multimode step-index fibres have a larger core and allow multiple modes of light.

      • Multimode graded-index fibres have a variable refractive index and reduce modal dispersion.

    • The normalised frequency (V-number) determines the number of modes that can propagate in a fiber.

    • Attenuation is the loss of optical power as light travels through the fibre.

      • It is caused by absorption, scattering and radiation.

      • Absorption is due to impurities.

      • Scattering is caused by imperfections.

        • Rayleigh scattering occurs due to small particles.

      • Waveguide scattering occurs at the core-cladding interface.

      • Radiation occurs due to macrobends and microbends.

    • Dispersion is the spreading out of light pulses.

      • It limits the maximum rate at which pulses can be transmitted.

      • Types of dispersion include modal, chromatic and polarization.

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