Digital Modulation – ASK, FSK & PSK

1 Atlanta RFServices, Software & DesignsLink Budget Analysis: DigitalModulation, Part RFServices, Software & : Phase Shift of Constellation Phase Shift Keying: of BPSK Modulated of Spectral Density of Phase Shift Shift Keying: of Spectral Density of & /4-Shifted Modulator & operation & Spectral Density of for Multi-Level : QuadratureAmplitude & Basis of for Multi-Level in Digital Cable & 8-QAM: Transmit : Constellation Transmit Spectral Density of : M-PSK versus Applications: PSK & : Modulation Error : Digital Modulation , Part ContentLink Budget Analysis: Digital Modulation , Part 32 Refer to background material in Atlanta RF s presentations titled:1. Link Budget Getting Started and2. Link Budget: Digital Modulation Part 1 (Overview & M-ASK)3.

2 Link Budget: Digital Modulation Part 2 (M-FSK)which can be downloaded from our website: Atlanta RFServices, Software & DesignsPSK: Phase Shift KeyingLink Budget Analysis: Digital Modulation , Part 3 BPSK can be expanded to a M-arymodulation scheme, employing multiple phases and multiple amplitudes as different Data: m(t)BPSK (M=2) modulated signal : s(t)1100where s(t)0= -Acos( ct) and s(t)1= Acos( ct) s0s0s1s1 TimeTimeAmplitudeTsJuly RFServices, Software & DesignsPSK: Phase Shift KeyingBasis of the baseband signal modulates the phase of the carrier signal , the process is called phase Modulation . For Digital baseband signals, it is called PhaseShift Keying : PSK . Keying (PSK) is a form of Digital modulationthat represents digitaldatasolely through discrete variations in the phaseof a carrier s PSK, the phase of the carrier signal is changed abruptly between 2 (for BPSK) or more (for MPSK) phase states by the baseband Digital message signal : m(t), at the beginning of each signal interval: Ts, to represent binary bits 0 or 1 (or a pair or trio of bits).

3 The carrier signal s amplitude and frequency remain PSK (M-PSK) produces M phase states around a constellation diagram circle, with each phase state separated by 2 is not susceptible to the noise degradations that affects ASK, or to the bandwidth limitations of FSK. PSK is, however, limited by the ability of the equipment to distinguish small differences in phase. This factor limits its potential transmission bit rate. sccb2sb2sscssi/Tnf ; T)M(logT ; E)M(logE ; Mi2 :where to M1 i ; Tt0, tf2cosTE2)t(Sii July RFServices, Software & DesignsMulti-Level PSK: signal Constellation DiagramsTwo-dimensional linear Modulation )(1t 2s1sbE 0 1 bE )(2t 3s7s 110 )(1t 4s2ssE 000 )(2t 6s8s1s5s 001 011 010 101 111 100 )(1t 2s1ssE 00 11 )(2t 3s4s 10 01 )(1t 2s1ssE 00 11 )(2t 3s4s 10 01 BPSK (M = 2)k = 1-bit/stateM = 21 = 2 states = 1800stepQPSK (M = 4)k = 2-bits/stateM = 22= 4 states = 900stepsQPSK alsok = 2-bits/stateM = 22= 4 = 900steps8-PSK (M = 8)k = 3-bits/stateM = 23= 8 states = 450 stepsbsEEd22 bsEEd22min bsEEd22min where the minimum distance between phase states is:and the Energy per symbol is: MsEdsin2minb2bskEMlogEE July 2 Atlanta RFServices, Software & DesignsBPSK.

4 Binary Phase Shift KeyingBasis of PSK (BPSK)is a 2-level Modulation (M = 2) technique, where the Digital message state for a binary 0 and a binary 1 are represented by two different phase states in the carrier s signal : = 00for binary 0 and = 1800for binary 1 (antipodal signals). During Tb, the duration of one information bit during the signaling interval, the two modulated carrier signals can be expressed as:where the carrier frequency: fc= nc/Tbfor fixed integer phases are 1800apart. Constant amplitude the information-bearing data is in the signal s to implement, but inefficient use of PSK is a very robust Modulation technique that is used extensively in satellite Digital communications. '1'binary ,tfTEt EtfAts'0'binary ,tfTE t E tfAtscbbbcccbbbcc 2cos2)(2cos2cos2)(2cos2211 BPSK Constellation Diagram(Phases separated by 180o)2s1sbE 0 1 bE IQJuly RFServices, Software & DesignsTypical Binary PSK Modulated SignalBPSK waveforms shown in the time domainBinary bit 1 and 0 are represented by one carrier frequency with two different phase states: 0 and 180 BasebandMessageSignal: m(t)5 TbTb2Tb3Tb4Tb0 July RFServices, Software & DesignsBPSK: Binary Phase Shift KeyingLink Budget Analysis: Digital Modulation , Part 3 Acos(wct)Implementation of BPSK:m(t)C(t)PSK signalSPSK(t) Digital signalAmplitudeTb2Tb3Tb4Tb5 TbJuly RFServices, Software & DesignsBandpassPower Spectral Density of Binary PSKA ssumes baseband rectangular pulses: Null-to-Null RF bandwidth.

5 BBPSK= (fo+ fb) (fo fb) = 2fb= 2Rb= 2/Tb. 90% power RF bandwidth: B90% = rectangular pulses. 99% power RF bandwidth: B99% = 20fb= 20Rb. 22)()(sin)()(sin2bcbcbcbcbBPSKTffTffTffT ffEPSD2/bE2/)()/)(sin(2 bobobbRffRffREBnull= 2fb= 2 RbJuly RFServices, Software & DesignsDPSK: Differential Phase Shift KeyingBasis of DPSK, the term differential is used because the phase shift is with reference to the previous bit. However, the frequency of the reference signals must be the same as the received signal s information-bearing data is carriedby the phase difference between the current symbol and the previous symbol:. the transmitter, each symbol is modulated relative to the phase of the immediately preceding signal element 0 : signal burst with the same phase as the previous signal 1 : signal burst of opposite phase to the previous signal does not require an accurate receive Local Oscillator that is matched with the transmitter for the phase information, but obviously depends on the preceding phase (information bit) being received Spectral Density (PSD) for DPSK is same as PSD for BPSK.

6 DPSK s Null-to-Null RF transmission bandwidth: Bnull= of bit error for Differential PSK is: 0,exp21 NEPbDPSKbeM/i2 i1k July RFServices, Software & DesignsQPSK: QuadraturePhase Shift KeyingBasis of (QPSK)is a 4-level Modulation technique (M = 22= 4 states), where every two binary bits are combined and mapped ( : encoded) to one of 4 phase states of the carrier signal . These 4 phases are located in 900phase increments. If Tsindicates the duration of one information bit during the signaling interval, the four modulated carrier signals can be expressed as:where: fc= nc/Tbfor fixed integer nc; Es= Eblog2M = 2 Eband Ts= Tblog2M = of 4 possible waveforms is transmitted during each signaling interval: signaling rate ( , the baud rate) is Rs= 1/Ts= 1/(2Tb) = Rb/2 (symbols/sec), can be interpreted as two independent BPSK systems in phase quadrature(one on the in-phase I-channel and one on the quadrature-phase Q-channel), and thus the same performance but twice the bandwidth efficiency of BPSK.

7 10binary for ,t 4/7f2cosTE2)tf2cos(A)t(00binary for ,t 4/5f2cosTE2tf2cosA)t(01binary for ,t 4/3f2cosTE2tf2cosA)t(11binary for ,t 4/f2cosTE2tf2cosA)t(tcss4cc4css3cc3css2c c2csscc1 QPSK sssss Phase constellationdiagram for QPSKJuly RFServices, Software & DesignsBandpassPower Spectral Density of QPSKA ssumes baseband rectangular pulses: Eb= PTs/2 = PTb, where: Ts= Tblog2(22) = 2Tb(M= 22= 4 states). Null-to-Null RF transmission bandwidth: Bnull= (fo+ fb/2) (fo fb/2) = fb= Rb. Bandwidth with 90% of signal power: B90% = 22)()(sin)()(sin2bcbcbcbcsQPSKTffTffTffT ffEPSDS pectrum of QPSK signal : V(f)Bnull=fbJuly RFServices, Software & DesignsTypes of QuadraturePhase Shift Keying (QPSK)When viewed by signal -Space Phase Constellation QPSK has phase transitions through zero ( 1800phase transitions).

8 As such, highly linear amplifiers are Offset QPSK, the phase transitions on the in-phase I-channel and quadrature-phase Q-channel are staggered. Phase transitions are therefore limited to /4 QPSK, the set of phase constellation points are toggled for each symbol, so transitions through zero cannot occur. This Modulation scheme produces the lowest envelope QPSK Modulation schemes require linear power amplifiers .Conventional QPSK /4 QPSKO ffset QPSKJuly cosine roll-off,r= { ( )} {s(t)}with cosine roll-off, r= { ( )} {s(t)}with cosine roll-off, r= RFServices, Software & DesignsOQPSK: Offset QPSK ModulationBasis of Operation: Variant of is 4-level (M = 22= 4) PSK, where the data transition times for the in-phase bit stream and quadrature-phase bit stream are offset by symbol period (or: one bit interval Tb).

9 Has phase transitions between every half-bit time that never exceeds 90 in much less amplitude variation of the bandwidth-limited carrier staggering the bit streams does not change the orthogonalityof the carriers, Offset-QPSK has the same theoretical bit error performance (BER) as BPSK and QPSK. amplified, QPSK results in significant band-width expansion, whereas OQPSK has much less bandwidth expansion, especially if the channel has non-linear RFServices, Software & Designs /4-Shifted QPSK ModulationBasis of Operation: Variant of QPSK1. /4-Shifted QPSK is a variant of 4-phase PSK (QPSK) obtained by introducing an additional /4 phase shift in the carrier phase in each symbol interval. /4 QPSK signal is generated by alternating between two QPSK constellations that are rotated by /4 with respect to each carrier phase transition to odd multiples of /4 (45 ).

10 Elements selected from two QPSK constellationsof four signal points each, with each constellation shifted by phase change is limited to 135 vs. 180 forQPSK, thus maintaining constant envelope ( : Amplitude of a QPSK signal is not constant for the short time interval during 1800phase changes). data bits per symbol. Twice as efficient as GMSK a phase change between symbols, leading to in 2ndGeneration Mobile Communication American Digital Cellular (IS-54): bps/Hz (= 48kbps/30kHz). Digital Cellular System: TETRA System: Personal Handy Phone System (PHP). by PACS (Personal Access Communication System).QIConstellation Diagramof /4 QPSKJuly RFServices, Software & DesignsTransmit ModulatorFor: QuadraturePhase Shift Keying & Offset-QPSK modulationBandpassFilter: fcBasebandLowpassFilterQ-channel (even numbered bit sequence)I-channel (odd numbered bit sequence)BasebandLowpassFilterQPSK-modul ated RF signal out: s(t)BPF added to reduce adjacent channel power ratio (ACPR).