Digital Modulation 2

Multiple copies of a transmitted signal arrive at the receiver via different paths; some add constructively and others destructively, causing amplitude and phase variations including near 180-degree phase changes in deep fades

Fading where all delayed copies of the signal arrive within one symbol duration; the channel response is approximately flat across the signal bandwidth

Fading where delayed copies span more than one symbol period; different frequencies experience different attenuation and phase shifts, causing ISI

Distortion caused by delayed copies of different symbols arriving at the receiver at the same time; a consequence of frequency-selective fading

A statistical model for multi-path fading with no line-of-sight component; the received amplitude follows a Rayleigh distribution

The time difference between the earliest and latest arriving multi-path copies; determines whether fading is flat or frequency-selective for a given symbol rate

The relationship between delay spread and symbol duration; if all copies arrive within one symbol period it is flat fading, if they span more than one symbol period it is frequency-selective

A technique that splits a wide bandwidth into N narrowband sub-channels each experiencing approximately flat fading; used to combat frequency-selective fading and enable high throughput

Orthogonal Frequency Division Multiplexing; a multi-carrier scheme that divides total bandwidth into N orthogonal sub-carriers each independently modulated (e.g. with QAM) and transmitted simultaneously in parallel

Data -> Error Control Encoder -> QAM Modulator -> Serial-to-Parallel -> IFFT -> Add Cyclic Prefix and Pulse Shaping and Parallel-to-Serial ->D/A -> passband modulator -> Tx

Receive ->multiply by modulator -> LPF -> A/D -> Matched Filter, remove cyclic prefix and serial to parallel converter -> FFT -> Parallel-to-Serial -> QAM Demodulator -> Error Control Decoder -> Data

It converts N frequency-domain QAM symbols X[i] into N time-domain samples x[n]; this is equivalent to simultaneously modulating N sub-carriers without needing N separate front-ends

It converts the N received time-domain samples back into the frequency domain, recovering the QAM symbol on each sub-carrier

B_N = B/N, where B is the total OFDM bandwidth and N is the number of sub-carriers

T_N = N/B = 1/B_N; it is N times longer than a single-carrier symbol period at the same total bandwidth

The last mu samples of an OFDM symbol copied and appended to the beginning of that symbol before transmission

(1) It absorbs ISI from the previous OFDM symbol - the corrupted prefix samples are discarded at the receiver; (2) It converts linear convolution with the channel into circular convolution, enabling simple one-tap frequency-domain equalisation

At least as long as the maximum delay spread tau_max, i.e. mu >= tau_max in samples

The uncoded data rate is reduced by a factor of N/(N+mu); this overhead becomes smaller as N increases

Eliminates ISI with cyclic prefix over wide bandwidth; frequency diversity via coded interleaving across sub-carriers; adaptive modulation and power per sub-carrier possible

Cyclic prefix overhead reduces data rate; requires highly linear power amplifier due to high PAPR; poor adjacent band rejection of 20-30 dB; sensitive to frequency offsets and Doppler shift causing ICI

Peak-to-Average Power Ratio; in OFDM many sub-carriers sum coherently causing large amplitude peaks, requiring a highly linear power amplifier which is costly and power-inefficient

Inter-Carrier Interference; caused by frequency offset or Doppler shift which destroys sub-carrier orthogonality, causing each sub-carrier to interfere with its neighbours

Orthogonal Frequency Division Multiple Access; the multi-user version of OFDM where both time slots and sub-carriers are distributed among multiple users simultaneously

In OFDM-TDMA each time slot is dedicated entirely to one user across all sub-carriers; in OFDMA both time and frequency resources are shared, so different users can occupy different sub-carriers within the same time slot

Ignore

Single Carrier Frequency Division Multiple Access; similar to OFDMA but uses a pre-FFT spreading stage so each user transmits on a single carrier with lower PAPR than OFDMA

(1) Transmitted signal bandwidth is much larger than the data bandwidth; (2) A spreading code independent of the data is used for modulation; (3) The receiver de-spreads by correlating the received signal with a synchronised copy of the spreading code

An information-bearing signal is spread over a much larger bandwidth than required; this allows signals to hide below the noise floor, mitigates ISI and narrowband interference, and supports multiple users in the same band

Anti-jam communications and low probability of intercept, since the signal is hidden below the noise floor and appears noise-like to an unintended receiver

2nd and 3rd generation cellular systems (CDMA), 2nd generation wireless LAN (IEEE 802.11b), GPS, Bluetooth (FHSS), and LoRa (chirp spread spectrum)

Direct Sequence Spread Spectrum; the transmitted QAM signal is multiplied by a high-rate PN chip sequence c(t), spreading its bandwidth from B_QAM to B_DS = B_QAM + B_C

Data -> QAM Modulator [s_QAM(t)] -> Multiply by c(t) [s_DS(t)] -> RF Channel -> Multiply by c(t) [y(t)] -> QAM Demodulator -> Output; PN Code Generator -> Chip-Pulse Generator -> c(t) at both multipliers

Modulated signal S(f): narrow band around carrier; after spreading: S_DS(f) = S(f)S_c(f), wide band; at receiver input R(f): wide signal plus wide interference I(f); after despreading: signal restored to narrow band, interference spread wide and filtered out

A pseudo-noise sequence; a binary or +/-1 periodic sequence with autocorrelation resembling white noise (high at tau=0, low elsewhere), used as the spreading code in spread spectrum systems

A maximal-length sequence generated by an m-stage feedback shift register; has period L = 2^m - 1 chips and good autocorrelation properties

PG = L (the spreading factor, equal to the number of chips per data symbol); in dB: PG = 10log10(L); represents the improvement in signal-to-interference ratio after despreading

T_s = L * T_c, where T_s is the symbol period, T_c is the chip period and L is the spreading factor; the chip rate is L times the symbol rate

At the receiver the signal is multiplied by c(t) again; this despreads the wanted signal (restoring it to narrow band) while spreading the narrowband interference across the wide DSSS bandwidth; a bandpass filter then removes most of the interference power

Code Division Multiple Access; multiple users share the same bandwidth simultaneously, each assigned a unique PN spreading code; a receiver despreads only the intended user's signal while other users' signals appear as low-level interference

The carrier frequency is changed pseudo-randomly at a rate of hops per second according to a PN sequence; Bluetooth uses FHSS at 1600 hops/s across the 2.4 GHz band

An enhancement to basic FHSS that identifies and avoids frequency channels suffering interference (e.g. from WLAN) and excludes them from the hopping sequence to minimise collisions

A spread spectrum technique using wideband linear frequency-modulated chirp pulses to encode information; used in LoRa; robust to frequency-selective channels as the symbol can be recovered even if some frequencies are totally attenuated

OFDMA: divides bandwidth into easy-to-equalise sub-channels, sensitive to Doppler shift, easy spectrum aggregation, may need extra security; CDMA: wideband requires equalisation, robust to Doppler, PN codes add inherent security, harder to aggregate spectrum

Multiple Input Multiple Output; using multiple antennas at both transmitter and receiver to improve capacity or reliability by exploiting independent sub-channels between antenna pairs

Space-time coding (send different versions of the same data for diversity gain, improving BER slope) and spatial multiplexing (send completely different data streams simultaneously for throughput gain)

A 2x2 matrix: row 1 = [s0, s1], row 2 = [-s1*, s0*]; rows are time slots, columns are transmit antennas; two symbols are sent over two time slots from two antennas

r_k = h0s0 + h1s1 + n_k and r_{k+1} = -h0s1 + h1s0 + n_{k+1}, where h0 and h1 are the complex channel coefficients to the two transmit antennas

The two received signals are combined using the known channel estimates: s0_tilde = h0r_k + h1r_{k+1} and s1_tilde = h1r_k - h0r_{k+1}; each equals (|h0|^2 + |h1|^2) times the symbol plus noise

Choose the symbol s_i from the constellation that minimises |s0_tilde - (|h0|^2 + |h1|^2)*s_i|^2; decoupled decisions can be made independently for s0 and s1

Second-order diversity (diversity order 2), equivalent to 1 Tx and 2 Rx MRC, but achieved with 2 Tx and 1 Rx; the BER curve slope matches that of 2-antenna receive diversity

A technique that adapts the antenna array radiation pattern to direct energy towards specific users rather than radiating in all directions; achieved by switching antennas, adjusting phase, or applying a precoding matrix

Switched array antenna (selective on/off), phase adjustment of signals at each antenna element, or applying a precoding matrix (as used in LTE); more antenna elements produce a sharper beam

A technique used in LTE-A where multiple geographically separated base stations dynamically coordinate transmission and reception to improve performance, especially at cell edges

Joint processing: data transmitted simultaneously to the UE from multiple base stations for improved signal quality (requires high backhaul); Coordinated schedulingeamforming: data sent from one BS but scheduling and beam decisions coordinated across BSs (less backhaul)

Joint reception: multiple base stations receive the UE signal and combine it as a virtual antenna array to improve detection; Coordinated scheduling: base stations coordinate to minimise uplink interference with less backhaul overhead

A MIMO configuration using 100 or more co-located antennas at the base station; enables highly directional beamforming and large spatial multiplexing gains