Modulation Techniques Dr. J. Martin Leo Manickam Professor

Challenges in Mobile Communication Channel fading Energy Bandwidth

Digital Modulation Digital signal is converted into analog bit stream Type Constant variable ASK a(t) FSK PSK QAM

Classification Linear modulation Non linear (constant envelope) modulation Amplitude of the transmitted signal varies linearly with message signal Bandwidth efficient QPSK, OQPSK Amplitude of the transmitted signal does not vary with the amplitude of the message signal Power efficient class C amplifiers can be used Low out of band radiation Limiter-discriminator can be used for demodulation FSK,MSK, GMSK

BPSK BPSK is equivalent to a DSB/SC

Binary PSK

PSD of a BPSK signal

Null-to-null bandwidth Observation Pulse shape Null-to-null bandwidth 90 percent energy Rectangular 2Rb 1.6Rb Raised cosine pulse (0.5) < 2Rb 1.5Rb

QPSK

PSD of QPSK signal

Constant Envelope modulation

Binary FSK

Minimum Shift Keying (MSK) Phase information is used to improve the noise performance of the receiver CPFSK signal (0≤t ≤Tb) Eb – transmitted signal energy Tb – Bit duration Θ(0) – value of the phase at t=0, sums up the past history of the modulation process upto t=0.

DPSK signal can also be represented as

Phase tree At time t =Tb,

Phase trellis (h=1/2)

Signal space diagram Quadrature component will be half cycle sine wave In-phase component will be half cycle cosine wave + sign corresponds to - sign corresponds to + sign corresponds to - sign corresponds to

As and can each assume two possible values, any one of four possible values can arise Orthonormal basis functions symbol 1

The MSK signal can represented by Where s1 and s2 are related to the phase states and , respectively. Evaluating s1 and s2:

Signal space of MSK is two dimensional with four message points Observation Both integrals are evaluated for a time interval equal to twice the bit duration Both lower and upper limits of the product integration used to evaluate s1 are shifted by Tb w.r.t those used to evaluate the s2. The time interval , for which the phase states and are defined are common to both intervals Signal space of MSK is two dimensional with four message points

Signal space characterization of MSK Transmitted binary symbol Phase states (radians) Coordinates of message points s1 s2 1

Optimum detection of If x1 > 0, receiver choose the estimate If x1 < 0, receiver choose the estimate if x2 > 0, receiver choose the estimate If x2 < 0, receiver choose the estimate

Estimates Symbol – 0 Symbol – 1 Probability of error Same as that of the BPSK and QPSK

PSD of MSK MSK has lower sidelobes than QPSK and OQPSK Faster roll off Less spectrally efficient Main lobe of MSK is wider Bandlimiting is easier Continuous phase Amplified using non linear amplifiers Constant phase Simple modulation and demodulation

GMSK modulation Sidelobe levels of the spectrum are further reduced Pulse shaping filter requirements Narrow bandwidth Sharp cutoff frequencies Low overshoot Carrier phase must be ±π/2 at odd multiples and two values 0 and π at even multiples Gaussian LPF FM Transmitter NRZ data GMSK output

Impulse response Transfer function parameter related to B, the 3dB baseband bandwidth by GMSK filter may be completely specified by B and the basedand symbol duration T

PSD of a GMSK signal When BT = ∞, GMSK is equivalent to MSK When BT decreases, sidelobe levels falls off rapidly At BT = 0.5, peak of the sidelobe level is 30 db and 20 db below the main lobe for GMSK and MSK Reducing BT increases the error rate produced by the LPF due to ISI

Table 6.3 Occupied RF bandwidth (for GMSK and MSK as a fraction of Rb). Containing the given percentage of power BT 90% 99% 99.9% 99.99% 0.2 GMSK 0.52 0.79 0.99 1.22 0.25GMSK 0.57 0.86 1.09 1.37 0.5 GMSK 0.69 1.04 1.33 2.08 MSK 0.78 1.20 2.76 6.00 GMSK is spectrally tighter than MSK GMSK spectrum is compact at smaller values of BT but degradation due to ISI increases.

GMSK Bit error rate is a constant related to BT by

GMSK Receiver (Fig. 6.43)

Combined Linear and Constant Envelope Modulation Techniques Varying envelope and phase (or frequency) of an RF carrier (M-ary modulation) Two or more bits are grouped together to form symbols and one of M possible symbols are is transmitted during each symbol period Bandwidth efficient Power inefficient Poor error performance (closely located message points

M - ary Phase Shift Keying (MPSK) Carrier phase takes on one of M possible values Where Es is the energy per symbol = (log2M)Eb Ts is the symbol period = (log2M)Tb In quadrature form Orthonormal basis function:

M – ary PSK can be expressed as Signal space is 2D and the M-ary message points are equally spaced on a circle of radius at the origin Distance between the adjacent symbols is equal to Average symbol error prob. Q function defined as 8 - PSK

Bandwidth and power efficiency of M-ary PSK signals 2 4 8 16 32 64 0.5 1 1.5 2.5 3 Eb / No for BER = 10-6 10.5 14 18.5 23.4 28.5 B: First null bandwidth of M-ary PSK signals

M-ary PSK PSD, for M = 8,16 (PSD for both rectangular and RCF pulses for fixed Rb When M increases (fixed Rb) First null bandwidth decreases Bandwidth efficiency increases Constellation is densely packed Power efficiency decreases More sensitive to the timing jitter

M-ary Quadrature amplitude modulation (QAM) Amplitude and phase of the transmitted signal are varied Where Emin - energy of the signal with the lowest amplitude and ai and bi are a pair of independent integers chosen according to the location of the particular point No constant energy per symbol No constant distance between possible symbol states Si(t) is detected with higher probability than others

Ortho normal basis functions Coordinates of ith message point: Where is an element of L by L matrix given by Where

Constellation Diagram for 16-QAM: LXL matrix is given by Probability of Error:

Bandwidth and Power efficiency of QAM 4 16 64 256 1024 4096 1 2 3 5 6 Eb / No for BER = 10-6 10.5 15 18.5 24 28 33.5 Power spectrum and bandwidth efficiency of QAM is identical to M-ary PSK Power efficiency is superior than M-ary PSK

M-ary Frequency Shift Keying (MFSK) Transmitted signal Where for some fixed integer nc Transmitted signals Si(t) themselves can be used as a complete ortho normal basis functions M-dimensional signal space, minimum distance is

Average probability of symbol error: Coherent detection: Non coherent detection: Channel Bandwidth: Coherent MFSK: Non Coherent MFSK:

Bandwidth and Power Efficiency of Coherent MFSK 2 4 8 16 32 64 0.4 0.57 0.55 0.42 0.29 0.18 Eb / No for BER = 10-6 13.5 10.8 9.3 8.2 7.5 6.9 Can be amplified by using non-linear amplifiers with no performance degradation When M increases, bandwidth efficiency decreases Power efficiency increases

Performance of Digital modulation in Slow Flat-fading channels Multiplicative gain variation Received signal can be expressed as - channel gain - phase shift of the channel n(t) - is the additive gaussian noise Assumptions Attenuation and phase shift remains constant

Probability of Error in slow flat-fading channel Choose the possible range for signal strength due to fading Average the probability of error of the particular modulation in AWGN channel over possible range of signal strength - Probability of error for an arbitrary modulation at a specific value of SNR X, - pdf of X due to the fading channel Eb and No are the average energy per bit and noise PSD in a non-fading AWGN channel - instantaneous power values of the fading channel, w.r.t the non fading

For rayleigh fading channels ,fading amplitude has rayleigh distribution is the average value of the signal to noise ratio

For large values of Eb/N0: For GMSK

Observations Flat-fading channel AWGN channel Error rate is inversely proportional to SNR Higher power required BER of 10-3 to 10-6, 30-60 dB SNR AWGN channel Exponential relationship between error rate and SNR Lower power required BER of 10-3 to 10-6, 20-50 dB SNR

Digital Modulation in frequency selective channels Caused by multipath time delay spread or time varying Doppler spread Produces ISI Impose bounds on data rate and BER Errors occurs due to ISI when Main (undelayed) signal component is removed through multipath cancellation Non-zero value of delayed spread (d) Sampling time shifted as a result of delay spread Small delay spread results flat fading Large delay spread results timing errors and ISI

MSK OQPSK QPSK BPSK

MSK OQPSK QPSK BPSK