Digital Modulation and Demodulation

Digital Communication - Chapter 8: Digital Modulation and Demodulation

Introduction

• Focus: Sending digital data (ones and zeros) using sine waves instead of square waves.
• Rationale: Sine waves use less bandwidth, which is a limited and costly resource.
• Pulse waves have wide bandwidths and are not suitable for direct transmission.
• Technological advancements allow sending ones and zeros using sine waves.

Chapter Sections

• Section 1: Digital modulation techniques.
• Section 2: Bandwidth considerations of modulated signals.
• Section 3: M-ary modulation techniques.

Objectives

• Discuss characteristics of:
  • Amplitude Shift Keying (ASK).
  • Frequency Shift Keying (FSK).
  • Phase Shift Keying (PSK).
    • Binary Phase Shift Keying (BPSK).
    • Differential Phase Shift Keying (DPSK).
    • Minimum Shift Keying (MSK).
• Discuss bandwidth and its effects on modulation.
• Discuss characteristics of:
  • M-ary modulation.
  • Quadrature Phase Shift Keying (QPSK).
  • Quadrature Amplitude Modulation (QAM).
• Discuss orthogonal systems.

Wireless Digital Communication Applications

• Cellular/PCS telephone.
• Wireless networking.
• Data transport.
• Cordless devices.
• Digital TV and radio.
• Satellite TV and radio.
• GPS.
• Paging.
• Telemetry.

Baseband vs. Broadband

• Baseband: Digital signals applied directly to the transmission medium (fiber, wire, radio link) without modulation.
• Broadband: Digital signals modulate a carrier (sine wave) for transmission.
• Considerations: Bandwidth, power distribution, and signal-to-noise ratio are the same as analog transmissions.

Digital Modulation Techniques

• Sending digital data using sine waves in various ways:
  • Amplitude Shift Keying (ASK) - a form of AM.
  • Frequency Shift Keying (FSK) - a form of FM.
  • Phase Shift Keying (PSK) - a form of PM.
    • Binary Phase Shift Keying (BPSK).
    • Quadrature Phase Shift Keying (QPSK).
  • Quadrature Amplitude Modulation (QAM) - Combination of AM and PM.

Amplitude Shift Keying (ASK)

• Term "keying" originates from Morse code era.
• Morse code: Early digital transmission using dots, dashes, and spaces.
• Continuous wave transmission is turned on and off to transmit Morse code or binary digits.
• Sharp on and off transitions produce harmonics, requiring a keying filter to slow the rise and fall times.
• Lack of carrier in zero-time leads receiver AGC to increase gain, causing noise processing; manual gain control may be required.
• Simplicity and narrow bandwidth make it attractive to radio amateurs; mainly used for historical development demonstration.
• Not used too often on its own, but in tandem with other keying modulations techniques.

Implementation

• Modulate a carrier frequency between two predetermined frequencies separated by 70 Hz.
• Two different audio frequencies are modulated onto a carrier to represent a one or a zero.
• Carrier is continuous; it is not switched off and on.
• Example: System operates with a 10 MHz carrier.
  • Modulation by 300 Hz produces output frequencies of $10 \text{ MHz} \pm 300 \text{ Hz}$.
  • Modulation by 470 Hz produces output frequencies of $10 \text{ MHz} \pm 470 \text{ Hz}$.
  • Required bandwidth = $470 \text{ Hz} \times 2$, so 1 kHz channel is adequate (similar to AM receivers).

Frequency Shift Keying (FSK)

• Form of frequency modulation where the modulating wave shifts the output between two predetermined frequencies.
• The two frequencies are termed a "mark" (for a one) and a "space" (for a zero).
• Carrier frequency is in between the mark and space frequencies, similar to FM.
• Frequency shift can be as little as 85 Hz for narrowband or 850 Hz for wideband.
• Bandwidth depends on the modulating frequency and deviation.
• Modulation index $(\text{deviation} / \text{intelligence frequency})$ determines channel bandwidth.
• FSK generation involves shunting a capacitance around an oscillator tank circuit to produce frequency shifts; could be used for Morse code wireless transmission.
• Modulating bits can vary a voltage-controlled oscillator (VCO) to produce FSK.
• Phase-locked loops (PLL) can demonstrate FSK and recover data bits.

Example

• Narrowband FSK shifts a total of 85 Hz, but bandwidth is not simply 85 Hz.
• Shifting creates an infinite number of sidebands; significant sidebands determined by the modulation index.

Phase Shift Keying (PSK)

• Incoming data is used to phase shift the carrier by a predetermined amount.

Binary Phase Shift Keying (BPSK)

• Simplest form of PSK; carrier is phase-shifted 180 degrees to send a one or a zero.
• Mathematically represented as $\sin(\omega t)$ (one) or $-\sin(\omega t)$ (zero), where $\omega$ is the angular velocity of the carrier.
• One bit gives two allowable phase states:
  • Formula: $2^m = \text{number of allowable phase states}$, where $m$ is the number of bits (1 in this case).
  • Constellation diagram: Represents the phase states (one or zero).
• If the signal is in phase with the reference signal, it represents a one.
• If the signal is out of phase by 180 degrees, it represents a zero.

Generation

• Sine wave input goes through an inverter (producing an inverted sine wave) and a non-inverter.
• Binary data goes into a one-of-two selector.
  • The selector outputs a sine wave in phase for a one and out of phase for a zero.

Receiver

• Binary PSK receiver detects the phase shift in the received signal.
• Signal is fed into a mixer circuit.
• The other input to the mixer circuit is driven by a reference oscillator synchronized to the carrier (coherent carrier recovery).
• If the sine wave is in phase with coherent carrier recovery, it represents a one; if out of phase, a zero.
• Output goes through a low-pass filter to remove harmonics.

• Synchronization and carrier reinsertion.
• Positive and negative sine functions produce sidebands at frequencies above $\text{f}<em>o + \text{data rate}$ and below the carrier $\text{f}</em>o - \text{data rate}$, but the carrier is suppressed.
• A frequency doubler mixes the carrier plus data rate and the carrier minus data rate to produce a multiple of the carrier frequency and data rate.
• The phase-locked loop (PLL) locks onto the multiple (doubling) of the carrier frequency.
• A divide-by-two circuit restores the carrier.

Differential Phase Shift Keying (DPSK)

• Widely used form of PSK that uses the BPSK vector relationship but does not require coherent carrier recovery.
• Data bits are compared to previous bits; changes are registered as negative sine functions, while no change is a positive sine function.
• Data is exclusive NOR gated through a delay in a feedback network to create DPSK.
• Receiver: Incoming data is exclusive NOR gated with a one-bit delay of itself.
• Advantage: Carrier recovery circuitry not required.
• Disadvantage: Requires good signal-to-noise ratio to achieve a bit error rate equivalent to QPSK.

Minimum Shift Keying (MSK)

• Variation of FSK and PSK; used in cell phones (GSM).
• Gaussian Minimum Shift Keying (GMSK) used in 3G cellular technology.
• Output of a BPSK modulator has sharp edges, which generate high-frequency components and increase bandwidth.
• Careful selection of mark and space frequencies (multiples of bit rate) allows transition points to occur at zero degrees on the sine waves.
• MSK uses a modulation index of 0.5.
• Mark and space frequencies separated by half the bit rate: $\text{Mark} - \text{Space} = \frac{1}{2} f_b$, where the Mark frequency has a binary one and the space frequency is a binary zero.
• Carrier phase shifts by a quarter cycle $\pm 90$ degrees during each bit.
• Can be implemented as DPSK with a phase shift of 90 degrees.

Example

• FSK system with a bit clock frequency of 1800 bits per second and mark and space frequencies set at 1800 Hz and 2700 Hz, respectively.
• Modulation index should be 0.5, and mark and space frequencies should be integer multiples of the bit clock frequency.
• Deviation: $2700 \text{ Hz} - 1800 \text{ Hz} = 900 \text{ Hz}$.
• Period: $1 / 1800 = 0.0005555 \text{ seconds}$.
• Modulation index: $900 \times 0.0005555 = 0.5$.

Gaussian Minimum Shift Keying (GMSK)

• Modulating bits are filtered prior to modulation to remove high-frequency harmonics, lowering bandwidth requirements.
• A Gaussian filter (bell-shaped curve response) is used.
• Used in GSM cellular systems (AT&T, T-Mobile).

Bandwidth Considerations of Modulated Signals

• Available bandwidth of a transmission channel dictates how much data can be transmitted.
• Bandwidth is in hertz (Hz); data throughput is in bits per second (bps).
• Bandwidth and throughput may differ depending on modulation type and data compression.

Bandwidth Calculation

• Baseband signal's throughput in bits per second is twice the bandwidth.
• $\text{Bit Time} = \text{Period} = 1/ \text{Frequency}$
• One bit for each half cycle at the highest frequency of the bandwidth.

Example

• An 8 kilobit per second data stream used in a digital communication link.
• Bit time: $1 / (8 \text{ kilobits/second}) = 125 \text{ microseconds}$.
• Bandwidth is 4 kHz.

Broadband

• When a baseband signal modulates a carrier, sidebands are created, increasing bandwidth requirements.
• Available bandwidth is scarce.
• Methods of modulating more bits at a time onto a carrier are desirable.

M-ary Modulation Techniques

• M-ary systems group bits together; groups modulate the carrier.
• Allows higher bit rates for a given bandwidth; groups are called symbols.
• The symbol rate is known as the baud.

M-ary Phase Shift Keying

• $m$ is the number of allowable phase states, depending on the number of bits sent.
• $n$ Number of Data Bits determines each Phase State.
• Binary PSK: 1 bit, 2 allowable phase states; quadrature PSK: 4 allowable phase states.
• 8-PSK: 8 allowable phase states; 16-PSK: 16 phase states; 16 is the practical limit.

Quadrature Amplitude Modulation (QAM)

• Combines phase and amplitude modulation to achieve up to 256 phase states.
• Formula: $m = 2^n$, where $m$ is the number of allowable phase states and $n$ represents the number of bits sent.
• M-ary can be accomplished with digital signal processing.

M-ary Examples

• Incoming data phase shifts the carrier by a predetermined amount.
• Use of quadrature systems increases bit rate for a given bandwidth.

Three Most Common PSK Signals

• Binary PSK: Represents one phase state, when a one or zero is sent, creating two allowable states
• Quadrature PSK: Represents two phase states that allows for four allowable states: 00, 01, 10, 11
• Eight PSK: Sends three bits at a time, creating eight allowable phase states: 000 - 111.

Quadrature Phase Shift Keying

• Data bits are grouped into two-bit symbols known as divots.
• In-phase (I) and quadrature (Q) channels; Q is out of phase by 90 degrees.
• Each channel contributes to the direction of the vector in the phase constellation.
• I and Q data channels modulate the carrier at 0 and 90 degrees, respectively.
• Signals out of phase by 90 degrees will not interfere with each other.
• Four bit states can be contained within each cycle, doubling the bit rate over binary PSK.

Modulator

• Incoming data is split into in-phase (I) and out-of-phase (Q) channels.
• Carrier provides a carrier frequency.
• A 90 degree phase shifter mixes the data.
• A signal is known to be quadrature. Also is a signal that mixes with the carrier, in phase, that add together to get quadrature phase shift.

Receiver

• Having a Quadrature Phase Shift Key that runs through carrier recovery.
• Going through a phase detector that then proceeds to low pass filter.
• Undoing the transmitting sequence, putting the receiving lines together.
• Signals in quadrature are orthogonal; they will not interfere with each other, leading to frequencies residing on a transmission without disturbance.
• Constellation with noise results in clusters, not exact points; decision boundaries indicated by shaded areas.

Quadrature Amplitude Modulation

• Combines PSK and ASK; achieves high data rates in limited bandwidth channels.
• 8-QAM (eight phase states), 16-QAM (16 phase states), 256-QAM (256 phase states).
• Number of states depends on the amount of phases states or amount of bits one is sending.
• $n$ = number of data sets that specifies the phase state.

16 QAM

• You're sending 4 bits at a time
• In phase channels and out of phase channels

Offset Modulation

• Using Amplitude Modulation (AM), one may experience susceptibility to noice interference and more!
• Linear amplifier requirements and distortions may cause spectral regrowth.

Orthogonal Offset

• Helps avoid zero trajectory point by in/out phase channels.
  • Verizon/Sprint are example manufactures of such things.
  • Zero-Intersecting Points may affect amplitude issues. This issue results in a need to not regenerate.

Determining the Bits for QAM

• 128 QAM requires number of odd bits split. Three-bits on one and four-bits on another. Total number of seven bits are needed.
• Utilizes this formula: $m=2^n$ one may easily compute for it.

Conclusion

• Studying digital communication provides one with a rough knowledge of the behind the scenes of digital signals.
• Discussing components such as AKS, FSK, PSK, BPSK, DPSK, MSK, etc. provide a rough understanding needed for acronym understanding.
• Complex systems are needed that help send less and receive less data bandwidth.