Glossary – Simulation of telesystems

You are expected to be understand all terms in bold typeface.

Matlab and Simulink

MATLAB – Matrix Laboratory.

Simulink – A graphically programmed data-flow oriented tool within Matlab for modeling and analysis of dynamic systems.

Matlab function - .m-file that starts with the reserved word “function”. May also be an internal function or a compiled function. A Matlab function has its own workspace for local arrays (variables).

Matlab script – .m-file that does not include a function header. Affects arrays (variables) in the base workspace.

Toolbox – a set of Matlab-functions and scripts,

Blockset – a library of Simulink models.

Array – A variable in Matlab. An array may be

- a scalar (singel element),

- a row vector (1 by N elements),

- a column vector (N by 1 elements),

- a matrix (M by N elements, i.e. a 2D array),

- a multidimensional array (for example 3D array, concisting of K pages, where each page is an M by N matrix),

- a struct (consisting of named fields, where each field is an array. For example, the struct a may consist of the fields a.b and a.c.)

The elements in an array can be real valued or complex valued.

Base workspace – The arrays (variables) that are seen from the command line, or from a Matlab script, but not from a Matlab function.

Signals and signal processing

Signal: A varying physical quantity, for example a voltage or a current, that can carry information.

Digital signal: A signal with a finite number of levels and a certain symbol rate or sample rate. This may be a bit stream transmitted as a pulse train over a baseband channel. A digital signal may be a digitized analog signal.

Quantization: Analog-to-digital conversion.

Sampel Rate – The number of samples per second taken from an analogue continous signal to make a time-discrete signal.

Periodic waveform: A signal that repeats it self at regular intervals, the so called period time. Some named examples are since wave, sawtooth wave, square wave and triangle wave.

Fundamental frequency: Number of periods per second of a periodic wave form. One divided by the period time.

Amplitude: Peak voltage or peak current. A nonnegative scalar measure of a wave's magnitude of oscillation, that is, the magnitude of the maximum disturbance in the medium during one wave cycle.

Complex representation of a sinewave: A sinewave of constant amplitude and phase can be divided into an Inphase signal with amplitude I, and a Quadrature phase signal, with amplitude Q. The phase difference between the I and Q signals is 90°. The sinewave can be represented by a constant complex number C = I + jQ, where j is the imaginary unit. This number can be represented graphically by a two-dimensional vector. The amplitude of the sinewave is the absolute value of C (the distance between the point C and origin in the graphical representation), which can be found using Pythagoras’ theorem. The phase of the sinewave is the argument of C (the angle of the graphical vector representation). The real component of C is I, and the imaginary component of C is jQ.

RMS voltage: Root mean square (in Volt). The quadratic mean of a voltage signal. The power or energy of a signal depends on its RMS value rather than its amplitude. A DC signal (constant current and voltage) of a certain voltage gives raise to the same power as an AC signal (alternating current and voltage) with the same RMS voltage. In case of a sine wave, the RMS voltage is 71% of the amplitude (the peak voltage). In case of a square wave, the RMS voltage is equal to the amplitude. In case of a stochastic (random) signal with mean value 0, the RMS value corresponds to the standard deviation of the signal.

Power: Energy per time unit, for example radiated as heat from a resistor, or radio waves from an antenna. Measured in Watt and defined as, where is the RMS voltage, and R is the resistance. The power is sometimes normalized and measured in Volt² (V²), defined as .

Signal processing: The analysis, interpretation and manipulation of signals, for example filtering, equalization, noise cancellation, source coding, measuring, etc.

Analog signal processing: Processing of a signal by means of analog components, for example passive components such as capacitors, inductors and resistors, but also active components such as transistors and operational amplifiers.

Digital signal processing: Processing of a digitized and sampled analog signal, by means of digital electronic components and perhaps also software.

Harmonics: Frequency components of a periodic signal. A periodic signal can be described as a sum of sine waves, each with different amplitudes and phases. This is called Fourier series development. If the fundamental frequency (the first harmonic) is f, the second harmonic has the frequency 2f, the third harmonic the frequency 3f, etc.

DC (direct current) component: Mean value of a voltage or a current.

Spectrum: The frequency domain description of a signal. The spectrum is typically illustrated as a plot where the horizontal axis is the frequency, and the vertical axis may be the amplitude (in Volt), the power (in Watt), the power density (in Watt/Hz) and/or the (in radians or degrees). The spectrum may correspond to the fourier series development of a periodic (cyclic) waveform, or the fourier transform of a non-periodic signal, expressed as a mathematical function of the frequency.

Fourier transform: Calculation of a frequency domain representation of a signal, i.e. the spectrum, from a time domain representation of a signal. Similar to the fourier series development, but may be calculated for a non-periodic signal. The fourier transform of a non-periodic signal, for example noise or an instantaneous (non-repeated) shot, is a continous function.

Discrete fourier transform: Fourier transform of a sampled signal, calculated for a limited window of the signal, i.e. a limited number of samples. The window size, i.e. the number of samples, is typically a power of two, for example 2^N. The calculation results in a limited number of fourier transform values, called Fourier coefficients. The number of calculated Fourier coefficients is equal to the window size, i.e. 2^N in our example.

Fast fourier transform (FFT): An efficient algorithm for calculation of the discrete fourier transform.

Inverse fast fourier transform (IFFT): An algorithm for calculation of the inverse discrete fourier transform, i.e. for calculation of a time domain signal based on a frequency domain signal. Based on a limited number of fourier coefficients, the algorithm calculates the sample values.

Components and algorithms of a digital communication systems

Source coding: Sampling, digitalization and/or compression. The aim is to minimize the number of bit/s but achieve sufficient signal quality.

Channel coding: Addition of forward error correction (FEC) codes and bit interleaving. See below. Sometimes modulation is also included in the term, but not always.

Multiplex method: A scheme for combining many analog signals or digital bit streams into a single signal. Examples are:

- Time Division Multiplexing (TDM), using a frame consisting of a fixed number of timeslots.

- Frequency Division Multiplexing (FDM), using modulation and one frequency channel per signal.

- Statistical Multiplexing, for example packet mode communication.

- Code Division Multiplexing, also known as spread spectrum communication, for example frequency hopping or direct sequence code division multiplexing.

Multiple access method, or channel access method: a scheme that allows several terminals connected to the same physical medium to transmit over it, and to share its capacity. Examples of multiple access methods are time division multiple access (TDMA) and carrier sense multiple access with collision detection (CSMA/CD). A multiple access protocol is synonym to media access control (MAC).

Examples of circuit mode channel access methods, providing fixed bit rate and delay:

- Frequency division multiple access (FDMA)

- Time-division multiple access (TDMA)

- Code division multiple access (CDMA) or spread spectrum multiple access (SSMA), for example

- Direct-sequence CDMA (DS-CDMA)

- Frequency-hopping

Examples of packet mode channel access methods, providing varying bit rate and delay: (You are not expected to know all these methods.)

- Contention based random access methods:

- Aloha

- Slotted Aloha

- Multiple Access with Collision Avoidance (MACA)

- Multiple Access with Collision Avoidance for Wireless (MACAW)

- Carrier Sense Multiple Access (CSMA)

- Carrier sense multiple access with collision detection (CSMA/CD)

- Carrier sense multiple access with collision avoidance (CSMA/CA)

- Token passing:

- Token ring

- Token bus

- Polling

- Resource reservation (scheduled) packet-mode protocols:

- Dynamic Time Division Multiple Access (Dynamic TDMA)

- Reservation ALOHA (R-ALOHA)

Where these methods are used for dividing forward and reverse communication channels, they are known as duplexing methods, such as:

- Time division duplex (TDD)

- Frequency division duplex (FDD)

Modulation: The process of varying a carrier signal, typically a sinusoidal signal, in order to use that signal to convey a message signal and transfer it over an analog bandpass channel. Analog and digital modulation facilitate frequency division multiplex (FDM), where several low pass information signals are transferred simultaneously over the same shared physical medium, using separate bandpass channels.

Analog modulation: The aim of analog modulation is to transfer an analog lowpass message signal, for example an audio signal or TV signal, over an analog bandpass channel, for example a limited radio frequency band or a cable TV network channel. Example of analog modulation methods are:

- Amplitude modulation (AM)

- Frequency modulation (FM)

- Phase modulation (PM)

- Qaudrature modulation (AM), where a cosine and a sine carrier wave of the same frequency are modulated by two channels, the inphase message signal (I) and the Quadrature phase message signal (Q) and sumarized. This results in a combination of AM and PM.

Digital modulation: The aim of digital modulation is to transfer a digital bit stream over an analog bandpass channel, for example over the public switched telephone network (where a filter limits the frequency range to between 300 and 3400 Hz) or a limited radio frequency band. An analog carrier signal is modulated by a digital bit stream. This can be described as a form of analog-to-digital conversion. The changes in the carrier signal are chosen from a finite number of alternative symbols (the modulation alphabet).

Example of digital modulation methods are:

- Frequency Shift Keying (FSK), where a finite number of frequencies are used, typically two frequencies.

- Amplitude Shift Keying (ASK), where a finite number of frequencies are used, typically two amplitudes.

- Phase shift Keying (PSK), where a finite number of phases are used for example two (2PSK = BPSK = Binary PSK), 4 (4PSK = QPSK = Quadruple PSK), 8 (8PSK), 16 (16PSK), etc.

- Differential PSK (DPSK) and Differential QPSK (DQPSK). Not sensitive to constant phase shift.

- Continuous phase modulation (CPM), for example Minimum-shift keying (MSK) and Gaussian minimum-shift keying (GMSK). These can be seen as a mix of PSK and FSK.

- Quadrature Amplitude Modulation (QAM), for example 8QAM, 16QAM, etc. These can be seen as a mix of PSK and ASK.

- Orthogonal Frequency Division Multiplexing (OFDM), also known as Discrete Multitone modulation (DMT).

If the symbol alphabet consists of M = 2^N alternative symbols, each symbol represents a message consisting of N bits. If the symbol rate (also known as the baud rate) is f_S symbols/second (or baud), the data rate is Nf_S bit/second.

In the case of QAM, an inphase signal (the I signal, for example a cosine waveform) and a quadrature phase signal (the Q signal, for example a sine wave) are amplitude modulated with a finite number of amplitudes. It can be seen as a two channel system. The resulting signal is a combination of PSK and ASK, with a finite number of at least two phases, and a finite number of at least two amplitudes.

In the case of PSK, ASK and QAM, the modulation alphabet is often conveniently represented on a constellation diagram, showing the amplitude of the I signal at the x-axis, and the amplitude of the Q signal at the y-axis, for each symbol.

PSK and ASK, and sometimes also FSK, can be generated and detected using the principle of QAM. The I and Q message signals can be combined into a complex valued signal called the equivalent lowpass signal or equivalent baseband signal. This is a representation of the real valued modulated physical signal (the so called passband signal or RF signal).

These are the general steps used by the modulator to transmit data:

1. Group the incoming data into codewords;
2. Map the codewords to attributes, for example amplitudes of the I and Q signals (the equivalent low pass signal), or frequency or phase values.
3. Apply pulse shaping and/or other filtering to limit the bandwidth and form the spectrum, typically using digital signal processing.
4. Digital-to-analog conversion (DAC) of the I and Q signals. Sometimes the next step is also achieved using DSP, and then the DAC should be done after that.
5. Pulse-amplitude modulate (multiply) the high-frequency sine and cosine carrier waveform by the I and Q signals, resulting in that the equivalent low pas signal is frequency shifted into a modulated passband signal or RF signal.
6. Amplification and analog bandpass filtering to avoid harmonic distortion and periodic spectrum.

At the receiver, the demodulator typically performs:

1. Bandpass filtering
2. Automatic gain control, AGC (to compensate for varying attenuation)
3. Frequency shifting of the RF signal to baseband I and Q signals, or to an intermediate frequency (IF) signal.
4. Sampling and analog-to-digital conversion (ADC). (Sometimes before the above point.)
5. Filtering, for example equalization (channel-adaptive filtering).
6. Detection of the amplitudes of the I and Q signals, or the frequency or phase of the IF signal;
7. Quantization of the amplitudes, frequencies or phases to the nearest allowed values, using mapping.
8. Map the quantized amplitudes, frequencies or phases to codewords (bit groups);
9. Parallel-to-serial conversion of the codewords into a bit stream
10. Pass the resultant bit stream on for further processing such as removal of any error-correcting codes.

Orthogonal Frequency Division Multiplex (OFDM), essentially the same thing as Coded OFDM (COFDM) and Discrete multi-tone modulation (DMT), is based on the idea of Frequency Division Multiplex (FDM), but is utilized as a digital modulation scheme. The bit stream is split into several parallel data streams, each transferred over its own sub-carrier using some conventional digital modulation scheme. The sub-carriers are summarized into an OFDM symbol. The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe channel conditions — for example, multipath and narrowband interference — without complex equalization filters. Channel equalization is simplified because OFDM may be viewed as using many slowly-modulated narrowband signals rather than one rapidly-modulated wideband signal. Since the symbols are so long, it is affordable to include a guard interval between each symbol, and thus avoid inter-symbol interference (ISI).

Example: Instead of using one fast modulator with bandwidth B, symbol length T and data rate R, we utilize N parallel modulators. The bit stream is split into N data streams, each of data rate R/N, modulating its own sub-carrier and transferred over a sub-channel width bandwidth B/N. The sub-carriers are sumarized into a symbol of length TN. Due to the long symbol length, we can afford to introduce a quite long guard interval between the symbols, in view to eliminate inter-symbol interference. Frequency selective fading can be combated without complex equalization, since the fading can be considered as flat within each sub-channel, and an error correcting code can handle that some of the sub-carriers are faded.

Capacity and performance of a communication system

Bandwidth: May denote one of the following:

- Analog bandwidth in Hertz (Hz) of a signal or communication channel. Measured in Hertz (Hz). In case of a baseband channel or baseband signal, the bandwidth is equivalent to the upper cut-off frequency of the signal spectrum or the lowpass filter. In case of a passband signal, it is the upper cut-off frequency minus the lower cut-off frequency of the signal spectrum or the bandpass filter.

- Digital bandwidth consumption in bit/s. Proportional to the analog bandwidth of the signal. This may be equivalent to the raw bitrate (inclusive of forward error correction codes, synchronization and other physical layer protocol overhead), net bit rate (exclusive of forward error correction codes), throughput, or goodput.

- Channel capacity in bit/s. Maximum possible net bit rate. Can be calculated by the Shannon-Hartley formula for a certain analog channel bandwidth and signal-to-noise ratio.

Latency – Delay from transferring a message. It may include:

- Transmission delay – time from the first until the last bit of a message or packet has left the transmitter. (Message or packet length in bits divided by the bit rate.)

- Propagation delay – time from the message haft left the transmitter until it has reached the receiver.(Distance divided by the propagation speed).

- Packet queuing delay in store-and-forward packet mode nodes.

- Protocol overhead, caused by flow control, congestion avoidance, automatic repeat request retransmissions, etc.

- Processing delay, due to slow electronic circuits, etc.

Bit Error Rate (BER) or error rate is the percentage of bits with errors divided by the total number of bits that have been transmitted, received or processed over a given time period. Also known as bit error probability.

Symbol Error Rate (SER) is the percentage of the modulated symbols with errors divided by the total number of symbols that have been transmitted, received or processed over a given time period.

Packet Error Rate (PER) is the percentage of the data packets that are affected by at least one bit error.

Channel impairments

Noise - Fluctuations in and the addition of external factors to the stream of target information (signal) being received at a detector.

White Noise - Statistically random radio noise characterized by a wide frequency spectrum with a constant spectral density N₀ (expressed as W/Hz) over a specified frequency band. If the noise signal is sampled (time discrete), consequtive samples are independent, i.e. non-correlated.

Noise power spectral density N₀(f). Expressed as W/Hz, watts per hertz of bandwidth. If the noise is white, N₀ is constant over the studied band, and the noise power is N = N₀B, where the B is the bandwidth.

Additive Gaussion White Noise (AWGN) channel – A communication channel model where the only impairment is linear addition of white noise. The noise is generated by a random process, and the voltage values are Gaussian distributed (also known as Normal distributed). Wideband Gaussian noise comes from many natural sources, such as the thermal vibrations of atoms in antennas (referred to as thermal noise or Johnson-Nyquist noise), black body radiation from the earth and other warm objects, cross-talk from and from celestial sources such as the sun. Sometimes interference (crosstalk) from wideband signal sources, for example radio transmitters, is included in the noise concept.

Signal-to-noise ratio (SNR) - the power ratio between a signal (useful information) and the background noise:

S/N = Signal power / Noise power

= (Signal RMS voltage/ Noise RMS voltage)²

SNR in dB = 10 log₁₀ (S/N)

= 20 log₁₀ (Signal RMS voltage/ Noise RMS voltage)

Carrier-to-noise ratio (CNR). Often the equivalent to the SNR. Used to analyze a modulated signal. C/N = carrier power / Noise power. CNR in dB = 10 log₁₀ (C/N)

Co-channel interference – cross-talk between transmitters sending at the same channel.

Carrier-to-interference and noise ratio (CINR): Includes co-channel interference. C/(I+N) or in dB 10 log₁₀ (C/(I+N)). Often equivalent to SNR.

Energy per bit per noise power spectral density (E_b/N_o): A normalized CNR measure, often used when comparing the bit error rate (BER) of different modulation methods without taking the bit rate or bandwidth into consideration. See the example below.

The CNR can be calculcated as follows:

where R is the bitrate in bit/s and B is the channel bandwidth in Hertz.

Energy per symbol per noise power spectral density (E_s/N_o). A normalized measure of the CNR. Similar usage as E_b/N_o.

BERTool – a graphical user interface (GUI) in Matlab that enables you to analyze BER vs E_s/N_o performance of a communications links. via simulation-based, semianalytic, or theoretical approach.

Phase Noise – variation of the channel phase shift. May be caused by variating multi-path propagation, Doppler shift and synchronization problems between the sender and receiver local oscillators.

Multipath propagation implies that several echoes of a signal reaches the receiver, following different paths, with different delays and amplitudes. Multipath may cause time-spreading and inter-symbol interference. The echoes may be sumarized constructively, or cancellation may occur. This is called fading. For a narrow-band signal, the fading can be considered as flat, i.e. as an attenuation that is constant for all frequencies.For a wideband signal, the fading may be frequency-selective, i.e. some freuquencies are attenuated, resulting in symbol distorsion.

Rayleigh fading occurs when there is no dominant path, for example in a non line of sight situation. The amplitudes are considered as random, with a Rayleigh distribution.

Rician fading occurs when there is a dominant path. The amplitudes are random, with a Rician distribution.

Error management

Error detection code: An encoder adds redundant data, making it possible for the receiver to detect errors. This may be utilized for ARQ (Automatic Repeat reQuest), or the data may just be cancelled. There are several cathegories for error detection codes:

- Parity check bits.

- Checksum.

- Cyclic Redundancy Check (CRC). This is based on discrete mathematics. The CRC code is the reminder of a modulo-2 division with a known denominator.

Forward error correction (FEC). An encoder adds redundant data, making it possible for the decoder on the receiver side to correct erroneous bits. There are two cathegories of FEC codes:

- Block codes. The encoder and decoder require a complete block of data, usually of fixed length, before the coding or decoding can be carried out. Common examples are Reed Salomon codes and Turbo Codes.

- Convolutional codes. Is the process of encoding intersperses parity bits into the data sequence in symbol streams of arbitrary length.

Code Rate = Message length(K)/Code word length(N) = Net bit rate/Raw (or gross) bit rate.

Bit interleaving – A process to change the order of the bits on the sender side, and reorder them on the receiver side, in view to spread burst errors in time and make it easier for the FEC to correct the errors.

Simulink samples, Frames and events

Multirate model = A Simulink model that contains signals with different sample times, for example different bit rates.

Sample time = Updating a signal integer multiples of a fixed time interval called the sample time

Samples per frame = How many samples each frame contains.

Sample time = Frame period / Samples per frame

A Frame is a block of values, representing for example a sequence or samples, combined into a vector. Frame-based simulation may result in faster simulation time than sample-based simulation.

In sample-based processing a system of blocks is simulated for one sample at a time.

In frame-based processing, all of the samples in a frame are processed before next block is simulated.

A triggered sub-system may sample a signal at asynchronous instants or events rather than at a fixed sample rate.