Digital Modulations

Objectives:

  • Define Digital Modulation
  • Enumerate the 3 Categories to Consider in Designing Dig. Mol. System
  • List down & explain why go digital
  • Identify the diff. parameters involve
  • Solve examples involving D.M. in D.M. Parameters.

Digital Modulation

  • Digital Modulation is transmission of digitally modulated signals between transmitter and receivers and requires free space (air) transmission medium. Also, Digital Modulation = Digital Radio
  • Digital Modulation transmittal of digitally modulated analog signal (carrier) between two or more points in a communication system and the process of changing one of the characteristics of an analog signal based on the information in a digital signal (0's and 1's)
  • Refer to the below image for the Analog vs Digital application example.
  • Analog Signal:
    • Amplitude: 10Vp−p10 V_{p-p}
  • Digital Signal:
    • Amplitude: 5V5V

Signal

  • Defined as a function that represents the variation of a physical quantity with respect to any other parameter (time or distance).
  • In the context of electric or electronics, the signal is a function representing the variation of voltage or current or energy with time.

Analog Information Source

  • Definition: Produces messages that are defined on a continuum.
  • Example: Microphone
    • The output voltage describes the information in the sound, and it is distributed over a continuous range of values.

Digital Information Source

  • Definition: Produces a finite set of possible messages
  • Example: Typewriter
    • There is a finite number of characters (messages) that can be emitted by this source.

Analog Communication System

  • Transfers information from analog source to the sink.

Digital Communication System

  • Transfers information from a digital source to the intended receiver(also called the sink).

Why Go Digital?

  • Capacity
  • Controlled Access
  • Consistent Quality
  • Convenient
  • Cool Games
  • Cost Effective
  • Convergence
  • Consumes less Power

Data Storage

  • ANALOG
    • Cassette tape
    • Filmed camera
    • Typewriter
  • DIGITAL
    • DSLR camera
    • iPod
    • Flash disk
    • Big data compute services
    • Security & Identity fundamentals
    • APP application development
    • Google Cloud Kubernetes
    • DevOps VPN
    • AI Services

Controlled Access

  • ANALOG
    • Human intervention
    • Safety Box
  • DIGITAL
    • Biometrics
    • RFID

Consistent Quality

  • ANALOG vs. DIGITAL

Convenience

  • ANALOG
    • Sony Tuner
    • Analog Cellphones
    • Recording
  • DIGITAL
    • Desktop
    • Smart Phones
    • iPhone: Evolution of the iPhone

Cool Games

  • ANALOG
    • New Super Mario Bros.
  • DIGITAL
    • Nintendo
    • DOTA Warcraft

Cost Effective

  • ANALOG
    • Expensive
  • DIGITAL
    • Affordable

Convergence

  • ANALOG
    • Message
    • Computer
    • Telephone
    • Broadcast
      • Rule, Medium, Networks, Agreement, Standard, Devices
  • DIGITAL
    • Multiple services running on multiple networks.

Consumes Less Power

  • ANALOG
    • Analog TV
  • DIGITAL
    • LED TV

3 Categories in Evaluating the Performance of Communication System Design

  • I. Power Efficiency
    • Problem: In order to increase noise immunity, it is necessary to increase the signal power. The amount by which the signal power should be increased to maintain a certain BER depends on the modulation scheme.
    • Power efficiency describes the ability to preserve the fidelity of a digital message at low power levels.
    • This describes the ability of the system to reliably send information at the lowest practical power level
    • The power efficiency expresses the "signal energy over the noise energy" ratio (E<em>b/N</em>0)(E<em>b/N</em>0)
      • required at the receiver to guaranty a certain BER.
  • II. Bandwidth Efficiency
    • Problem: increasing the data rate implies decreasing the pulse width of the digital symbol, which increases the bandwidth of the signal.
    • Bandwidth efficiency describes how efficiently the allocated bandwidth is used.
    • This describes the ability of a modulation scheme to accommodate data within a limited bandwidth.
    • Defined as the ratio of the throughput data rate per Hertz (bps/Hz).
    • Fundamental upper bound: CB=log2(1+SN)\frac{C}{B} = log_2(1 + \frac{S}{N})
      • where C is the channel capacity (bps), B the bandwidth (Hz) and S/N the signal-to-noise ratio.
  • III. Cost Efficiency
    • Problem: cost and the complexity of the receiver. For wireless networks, the robustness under various types of channel impairments such as Rayleigh fading and multipath dispersion is important
    • Very often there is a tradeoff:
      • adding error control coding reduces the bandwidth efficiency (redundancy is transmitted too) but increases the power efficiency (there remain fewer errors).
    • Very often there is a tradeoff:
      • M-ary schemes increase the bandwidth efficiency but require higher transmission power to keep the same BER.

Digital Communications

  • Digital Communications covers a broad area of communications techniques, including:
    • Digital Radio
    • Digital Transmission
    • Information Theory
    • Error Control
    • Source Coding

Digital Radio

  • The transmission of digitally modulated signals between transmitter and receivers and requires free space (air) transmission medium.

Digital Modulation

  • Digital Modulation = Digital Radio
  • SIMPLIFIED BLOCK DIAGRAM OF DIGITAL RADIO SYSTEM
    • TRANSMITTER
      • Input data -> Precoder -> Modulator -> Buffer -> BPF -> Power amplifier
    • TRANSMISSION MEDIA
    • RECEIVER
      • BPF -> LNA -> Demodulator and decoder -> Output data -> Carrier and Clock recovery (loops back to Demodulator)
  • Digital Modulation
    • also known as Digital Radio
    • is the transmittal of digitally modulated analog signal (carrier) between two or more points in a communication system
    • is the process of changing one of the characteristics of an analog signal based on the information in a digital signal (0's and 1's)
  • APPLICATIONS OF DIGITAL MODULATION
    • Morse Code
    • Pager
    • First Telephone Modem
    • Telemetry
    • A cable modem
    • A communications satellite
    • Flight test programs
    • Terrestrial Microwave
    • Code division multiple access (CDMA)
    • EasyTV
  • DEFINITION OF TERMS
    • Modulation
    • Bit Rate
    • Baud Rate
    • Bandwidth
    • Modes of Transmission
    • Constellation Diagram

Bit Rate

  • Bit Rate = FNn\frac{F_N}{n}
    • is the number of bits transmitted during 1 second
    • is the speed at which data is transmitted in a digital communication system
Note:
  • n - # of bits represented by each signal unit

Baud Rate

  • fNf_N = Baud Rate
    • Is the number of signal units per second
    • is the speed at which symbols are transmitted in a digital communication system
  • Symbol Rate = Bit Rate / No. Of Bits transmitted with each symbol
Note:
  • A transmitted signal that can have two or more possible states (called symbol).
  • REMEMBER
    • "Bit rate is the number of bits per second. Baud rate is the number of signal units per second. Bit rate is greater than or equal to the baud rate."
    • "The signal bandwidth for the communications channel needed depends on the symbol rate, not on the bit rate."
  • Nyquist & Root-Raised Cosine Filters
    • The Nyquist bandwidth is the minimum bandwidth than can be used to represent a signal.
    • It is important to limit the spectral occupancy of a signal, to improve bandwidth efficiency and remove adjacent channel interference.
    • Root raised cosine filters allow an approximation to this minimum bandwidth.

Examples

  • 1. An analog signal carries 4 bits in each signal unit. If 1000 signal units are sent per second, find the baud rate and the bit rate.
    • Baud Rate = 1000 band
    • Bit Rate= 4×10004 \times 1000 = 4000 bps
  • 2. The bit rate of a signal is 3000. If each signal unit carries 6 bits, what is the baud rate?
    • Baud Rate= 30006\frac{3000}{6} = 500 band

Types of Digital Modulation

  • ASK
  • FSK
  • PSK
  • QAM
  • BPSK
  • 8-PSK
  • QPSK
  • 16-QAM
  • 8-QAM
  • n-QAM

ASK & FSK

AMPLITUDE SHIFT KEYING

  • Simplest digital modulation techniques, where a binary information signal directly modulates the amplitude of analog carrier
  • ASK sometimes called Digital Amplitude Modulation (DAM)
  • This modulation may be between two levels of amplitude or, more usually, by switching the carrier on and off.
  • known as the on-off ASK, on-off keying (OOK)

ASK Modulated Wave Equation

  • e<em>ASK(t)=E</em>m(t)E<em>csinω</em>cte<em>{ASK}(t) = E</em>m(t) E<em>c sin \omega</em>c t
    • Where:
      • eASK(t) = amplitude shift keying waveform
      • Em(t) = digital information (modulating signal, 1 or 0)
      • Ec(t) = amplitude of the unmodulated carrier, V
      • ωc\omega_c= analog carrier angular frequency, rad/sec

ASK Parameters

  • Bit Rate (fbf_b)
  • Baud Rate (fNf_N)
  • Highest Fundamental Frequency (faf_a)
  • Bandwidth (BW)
  • Output Waveform

ASK = DAM = OOK

  • Logic 1 = +1[V]
    • e<em>ASK(t)=(+1V)(E</em>csinω<em>ct)=E</em>csinωcte<em>{ASK}(t) = (+1V)(E</em>c sin \omega<em>c t) = E</em>c sin \omega_c t
  • Logic 0 = open[V]
    • e<em>ASK(t)=(open[V])(E</em>csinωct)=0e<em>{ASK}(t) = (open[V])(E</em>c sin \omega_c t) = 0
  • f<em>b=f</em>N=BWf<em>b = f</em>N = BW
Note:
  • Noise
  • ASK
    • BW = 2fa2 f_a

ASK

  • ASK IN THE TIME DOMAIN
    • Carrier signal + Multiplier -> Modulated signal
  • ADVANTAGES
    • Simple implementation
    • Less Power
  • DISADVANTAGES
    • Susceptible to sudden gain and changes
    • Noise
  • APPLICATIONS
    • Morse code
    • Laser transmitters
  • EXAMPLES
    • 1. fbf_b = 2000 bps, BW= ?
      • f<em>b=f</em>N=BWf<em>b = f</em>N = BW
    • 2. Given a bandwidth of 5000 Hz for an ASK signal, what are the baud rate and bit rate?
      • f<em>b=f</em>N=BW=5000Hzf<em>b = f</em>N = BW = 5000 Hz
    • 3. Given a bandwidth of 10,000 Hz (1000 to 11,000 Hz), draw the full-duplex ASK diagram of the system.
      • find the carriers and the bandwidths in each direction. Assume there is no gap between the bands in the two directions
      • fc1=3500Hzf_{c1} = 3500 \text{Hz}
      • fc2=8500Hzf_{c2} = 8500 \text{Hz}
      • BW = 5000 Hz

FSK: FREQUENCY SHIFT KEYING, a simple, low performance type of digital modulation

DM-DR

  • is a form of a constant-amplitude angle modulation similar to standard frequency modulation (FM) except the modulating signal is a binary that varies two discrete voltage levels
  • Usually, the instantaneous frequency is shifted between two discrete values termed the "mark" (fm)(f_m)
    • and "space" (fs)(f_s) frequencies
  • Sometimes called binary FSK (BFSK)

Parameters CAP,CA,CQ,CG,Conv,CE

REMEMBER ASK PM Conv CE

Note

fs: 60 MH2
fm: 80MH₂
Data and bps frequency symbols=BW
Simple low performance
Is a form of amplitude similar
Standard frequency
Signal is a binary two
Usually the shift between and discrete mark
Bw method

  • ASK OOK DAM
  • Amplitude variation =noise
  • logic +=+1 V
  • logic 0 = 0 V
  • FSK
    • f<em>mf<em>m = f</em>markf</em>{mark}
    • f<em>sf<em>s = f</em>spacef</em>{space}
    • BW (from) fmf_m theory
  • Laboratory Safety
    • PRECAUTIONS
      • Lab Safety 5S, SAFETY FIRST, WORK SAFELY
    • is a constant-amplitude angle modulation similar to standard frequency modulation (FM) except the modulating signal is a binary that varies two discrete voltage levels
    • Usually, the instantaneous frequency is shifted between two discrete values termed the "mark" (fm)(f_m)
    • and "space" (fs)(f_s) frequencies
    • Sometimes called binary FSK (BFSK)

parameters DM-DR

Remember

  • fs 60MH2
  • fm 80MH₂
  • fo fr 70NH2
  • fb fN and 20Mbaud
  • Convergence.CAPCA, CQ,CGandCE
  • DM parameters
  • fb=data and bps frequency symbols
  • BW Garron's Formula or, Bw2afmN methodBW
    • Binary FSK (BFSK)
  • types
    • BW Garron's Garron's Formula Formulaor, BW Garron's Formula.2afm

Garron's Formula. Exact Method Formula A

BW = 2(δf+fXX)2(\delta f + f_{XX})

  • Formula D. BW = a(δf+fb)a(\delta f + f_b)
FSK MODULATED WAVE EQUATION,

E<em>FSK(t)=E</em>ccos[2πf<em>ct+E</em>m(t)]E<em>{FSK}(t)=E</em>c cos [2\pi f<em>c t + E</em>m(t)]

  • Member: f<em>b=f</em>Nf<em>b = f</em>N
  • FSK PARAMETERS
    • Bit Rate (fbf_b)
    • Baud Rate (fNf_N)
    • Highest Fundamental Frequency (faf_a)
    • Bandwidth (BW)
    • Output Waveform

FSK IN THE TIME DOMAIN

  • FSK TRANSMITTER

    • Binary input FSK Modulator logic 0, Logic 1 then get the FSK output
      A. Bw = 2(δf+fXX)2 (\delta f+f_{XX})

  • D. BW= a(δf+fb)a(\delta f+f_b)

  • EXAMPLES

  • 1. binary FSK modulator with space, rest and mark frequencies of 60, 70, and 80 MHz, respectively and an input bit rate of 20 Mbps, determine the output baud and the minimum required bandwidth.
    */43 objectives FSK mod.

Bessel Function Table (for Frequency Modulation-FM)

FSK modulator
Using Function table
Using exact method of B.WExact Bw - afm. Nfm - thef.Bw - afm.

Mf - fn - f(70MH) = 1:01 220Mbps = B-60MH, Carsons, Formula. Bw - 2 (M/Hz 20Mbps) - 60MH
  • C<em>SC<em>S = f</em>4f</em>4-fof_o =(80−60)2\frac{(80-60)}{2} = 10MH2^2