Design considerations:

- power efficiency
- spectral efficiency
- constant envelope

Linear and nonlinear modulations

Binary and M-ary modulations:

- signal constellations
- modulation/demodulation
- performances in AWGN and Rayleigh fading
- pulse shaping and spectrum

Digital modulations and wireless standards

Two main factors influencing the choice of a digital modulation scheme are **spectral efficiency** (minimum bandwidth occupancy) and **power efficiency**(minimum required transmitted power).

Other requirements are:

- minimum out-of band radiation
- robustness to channel impairments
- low power/low cost implementation
- constant envelope

Often conflicting requirements, tradeoffs are needed (depending on the application).

The ability of a modulation technique to preserve the fidelity of the digital message at low power level.

The amount of signal power required to obtain a certain level of fidelity (i.e., an acceptable BER) depends on the particular type of modulation.

Power efficiency can be measured by the minimum energy contrast γ_{b} required for a certain BER (e.g., BER=10^{-3}).

The ability of a modulation scheme to accommodate data within a limited bandwidth:

- increasing the data rate implies decreasing the signaling interval T
_{s}, which increases bandwidth - some modulation schemes perform better than others in this tradeoff

where:

- R
_{b}= 1/T_{b}bit-rate [bps=b/s] - M = cardinality of the modulation scheme
- T
_{s}= symbol interval - B = one-sided bandwidth of s(t)

Evaluated in bps/Hz, it measures how many bps can be transmitted in 1 Hz of bandwidth.

A modulation scheme with M waveforms is:

**bandwidth-efficient**if the spectral efficiency η**increases**with M**power-efficient**if the power efficiency γ_{b}for a given BER level**decreases**with M

Bandwidth efficiency and power efficiency are conflicting requirements:

- linear modulations are bandwidth-efficient (but not power-efficient)
- nonlinear modulations are power-efficient (but not bandwidth-efficient)

Desirable in wireless communications for several reasons:

- power efficient class C (nonlinear) amplifiers can be used without introducing degradation in the spectrum occupancy of the transmitted signal
- low out-of-band radiation of the order of -60 to -70 dB can be achieved
- limiter-discriminator detection can be used → simplified receiver design

However, constant envelope modulations generally occupy a larger bandwidth.

Linear modulations (ASK, PSK, QAM)

- information coded in amplitude and/or phase
- spectrally efficient
- less robust to channel impairments and amplifier nonlinearities
- more complicated to demodulate

Non linear modulations (FSK and variants)

- information coded in frequency
- power efficient
- more robust to channel impairments and amplifier nonlinearities
- Ssmpler to generate and demodulate

Binary modulations (M=2) are the simplest to analyze.

Binary Amplitude Shift Keying (M=2) → the amplitude of the carrier signal is varied to represent binary 1 or 0.

**Advantage**: simplicity.

**Disadvantage**: amplitude is very susceptible to fading.

Unipolar BASK is also called OOK (On-Off Keying).

Bipolar BASK is more common due to its zero DC.

The bit rate of BASK is R_{b} = 1/Tb.

The bandwidth of BASK is well approximated by B ≈ 1/T_{s} = 1/T_{b}.

The spectral efficiency is:

**Example**: if B=200 kHz → the bit-rate is R_{b}=200 kb/s.

Binary Phase Shift Keying (M=2) → the phase of the carrier signal is varied to represent binary 1 or 0.

**Advantage**: phase is less susceptible to fading, constant envelope property.

**Disadvantage**: more complex demodulation.

The bit rate of BPSK is R_{b} = 1/T_{b.}

The bandwidth of BPSK is well approximated by B ≈ 1/T_{s} = 1/T_{b}.

The spectral efficiency is:

To demodulate BPSK accurate knowledge at the receiver of the carrier phase is required → **coherent demodulation.**

Carrier phase recovery is obtained by using special circuits at the receiver (PLL, phase locked loop).

In many cases it is difficult/expensive to obtain a precise phase reference → one resorts to **differential modulation/demodulation**techniques (differential BPSK=DBPSK):

- the phase in the previous signaling interval is used as phase reference for the present symbol → an absolute phase reference at the receiver is not needed
- the channel phase must remain stable at least over two consecutive signaling intervals (slow fading)

Binary Frequency Shift Keying (M=2) → the frequency of the carrier signal is varied to represent binary 1 or 0.

**Advantage**: less susceptible to noise and fading, constant envelope property, simpler demodulation.

**Disadvantage**: larger bandwidth when M>2.

The signals s_{1}(t) and s_{2}(t) can be made **orthogonal** by appropriate choice of the carrier separation Δf= f_{2} – f_{1
}

Orthogonality simplifies demodulation of BFSK signals.

The minimum carrier separation is Δf = 0.5/T_{b} → the bandwidth of BFSK is well approximated by B ≈ 2Δf = 1/T_{b}.

The bandwidth efficiency is:

When the channel is AWGN (Gaussian noise) the performance of binary modulation techniques can be easily derived: **see the table**.

Since Q(.) is an **exponentially decreasing** function, the power efficiency of BPSK/BASK (bipolar) is 3dB better (a factor of 2) with respect to BFSK/BASK (unipolar).

In Rayleigh fading the performance can be obtained by averaging the AWGN results with respect to fading statistics: **see the table.**

BPSK/BASK (bipolar) has still a 3dB advantage over BFSK/BASK(unipolar) and DBPSK.

In AWGN Pb is **exponentially** decreasing with γ_{b}.In Rayleigh fading P_{b} decreases **linearly** with γ_{b}.

↓

**heavy performance degradation**.

Evaluate the energy contrast γ_{b} needed at the receiver to assure BER = 10^{-3} for BPSK modulation:

(a) over an AWGN channel

(b) over a Rayleigh fading channel

Solution:

(a) .

(b)

**23.98 – 6.82=17.16 dB is the excess power required to combat Rayleigh fading!**

In the previous examples the modulation employed rectangular waveforms:

- simplified implementation of transmitter and receiver
- constant envelope property

A drawback of rectangular waveforms is the high level of out-of-band radiation:

- rectangular waveforms are characterized by sinc spectra in the frequency domain with very strong and slowly decaying sidelobes (20dB/decade)

By appropriately shaping the pulse waveform the sidelobes are reduced → better spectral properties.

The considered binary modulations are all approximately equivalent in terms of spectral efficiency (1 bps/Hz).

In terms of performance, BPSK/ BASK (bipolar) exhibits the best performance both in AWGN and Rayleigh fading channel.

However, in terms of receiver complexity, DBPSK and BFSK are preferable.

Due to their low spectral efficiency, binary modulation are used only in low-rate applications → M-ary modulations with M>2 are needed to implement high-speed modems.

Quadrature Phase Shift Keying.

M=4 → each symbol carries two bits

- θ
_{i}=2π(i-1)/4+Φ_{0}, i=1,…,4 - Φ
_{0}constellation displacement

QPSK modulation can be regarded as two BPSK modulations with orthogonal (sin/cos) carriers:

- the BER of QPSK is practically the same at BPSK
- QPSK carries two bits per symbol, hence T
_{s}= 2*T_{b}

Since the bandwidth of QPSK is well approximated by B ≈ 1/T_{s} = 0.5*1/T_{b}, the spectral efficiency is **doubled**:

QPSK modulation has a constant envelope.

- desirable feature to prevent nonlinear amplifier distortions
- occasional
**phase shift of π radians**cause the envelope to pass from zero, which destroys the constant envelope properties

**Offset QPSK** solve this problem by delaying the Q-channel of a half-symbol period in order to constrain the maximum phase shift to **π**/2 radians.

Uses two different QPSK signal constellation shifted by π/4 and moves from one to the other in every symbol interval:

- pseudo-octonary: uses 8 phases to carry 2 information bits per symbol (not 3)
- maximum phase transition between two adjacent symbols of 135°
- one phase transition of at least π/4 in each interval→ eases symbol synchronization

Easily amenable to differential mo/demodulation (π/4-DQPSK).

Minimum Shift Keying:

- derived from OQPSK by replacing the rectangular pulse with a half-cycle sinusoidal pulse
- can be regarded also as a form of continuous-phase FSK with
**minimum**frequency spacing Δf = 0.5/T_{b} - constant envelope modulation.

The spectrum of MSK is significantly better than BPSK/ QPSK/OQPSK but still too large to satisfy typical bandwidth requirements of wireless communications.

Gaussian Minimum Shift Keying.

Employed in GSM and DECT.

Obtained from MSK by filtering the data before modulation with a **Gaussian-shaped filter**with bandwidth B

- B T
_{b}=0.3 in GSM, B T_{b}=0.5 in DECT

Main advantage is high spectral efficiency coupled with constant envelope property.

In M-PSK the constellation points are equispaced on a circle.

In M-QAM the constellation points are spaced on a square “lattice”.

Increasing the value of M improves spectral efficiency → spectrally efficient modulations.

M-QAM is more power efficient than M-PSK since the distance between the constellation points is higher

*3*. Current and emerging wireless systems

*5*. Shadowing

A. Goldsmith. Wireless Communications. Cambridge University Press, 2005 (selected parts of chaps. 5 and 6)

Supplementary material eventually available on the website

Progetto "Campus Virtuale" dell'Università degli Studi di Napoli Federico II, realizzato con il cofinanziamento dell'Unione europea. Asse V - Società dell'informazione - Obiettivo Operativo 5.1 e-Government ed e-Inclusion