6.003: Signal Processing

Communications Systems

7 May 2019

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Communications Systems

Some of largest and fastest growing applications of signal processing.

Examples: cellular communications • wifi • broadband • cable • bluetooth • GPS (the Global Positioning System) • private networks: fire departments, police • radar and navigation systems • IOT (the Internet of Things) • smart house / smart appliances − smart car − medical devices − many more • Telephone

Popular thirst for communications has been evident since the early days of telephony.

mic amp telephone wire amp speaker

Patented by Alexander Graham Bell (1876) this technology flour- ished first as a network of copper wires and later as optical fibers (“long-distance” network) connecting virtually every household in the US by the 1980’s.

Bell Labs became a premier research facility, developing information theory and a host of wired and wireless communications technologies that built on that theory, as well has hadware inovations such as the transistor and the laser.

Cellular Communication

First demonstrated by Motorola in 1973, cellular communications quickly revolutionized the field. There are now more cell phones than people in the world.

sound out

sound in

sound cell E/M optic E/M cell sound tower tower in phone fiber phone out

Much of the popularity and convenience of cellular communications is that the communication is wireless (at least to the local tower).

Check Yourself

For energy-efficient transmission and reception, the length of the antenna should be on the order of the wavelength.

Telephone-quality speech contains frequencies between 200 Hz and 3000 Hz.

How long should the antenna be?

1. < 1 mm 2. cm ∼ 3. m ∼ 4. km ∼ 5. > 100 km Check Yourself

What frequency E/M wave is well matched to an antenna with a length of 10 cm (about 4 inches)?

1. < 100 kHz 2. 1 MHz 3. 10 MHz 4. 100 MHz 5. > 1 GHz

Wireless Communication

Speech is not well matched to the wireless medium.

Matching the message to the medium is important in all communi- cations systems.

Example media: radio (E/M) waves • cable (coaxial wires) • fiber optics •

Today we will introduce simple matching strategies based on modulation, which underlie virtually all communication schemes.

Check Yourself

Construct a signal Y that codes the audio frequency information in X using frequency components near 2 GHz. X(ω) | |

ω Y (ω) | |

ω ωc

Determine an expression for y( ) in terms of x( ). · ·

1. y(t) = x(t) e jωct 2. y(t) = x(t) e jωct ∗ 3. y(t) = x(t) cos(ωct) 4. y(t) = x(t) cos(ωct) ∗ 5. none of the above Amplitude Modulation (Time Domain)

Multiplying a signal by a sinusoidal carrier signal is called amplitude modulation. The signal “modulates” the amplitude of the carrier.

x(t) y(t) ×

cos(ωct)

x(t) t

cos(ωct) t

x(t) cos(ωct) t

Check Yourself!

Multiplying a signal by a sinusoidal carrier signal is called amplitude modulation. The signal “modulates” the amplitude of the carrier.

x(t) y(t) ×

cos(ωct)

X(ω) | |

ω

What does the resulting signal’s CTFT Y ( ) look like? ·

Amplitude Modulation

How could you recover x(t) from y(t)?

x(t) y(t) ×

cos(ωct) Frequency-Division Multiplexing

Multiple transmitters can co-exist, as long as the frequencies that they transmit do not overlap.

z1(t) x1(t)

cos w1t

z2(t) z(t) x2(t) LPF y(t)

cos w2t cos wct

z3(t) x3(t)

cos w3t

Frequency-Division Multiplexing

Multiple transmitters can co-exist, as long as the frequencies that they transmit do not overlap.

X1(ω)

ω

X2(ω)

ω

X3(ω)

ω

Frequency-Division Multiplexing

Multiple transmitters can co-exist, as long as the frequencies that they transmit do not overlap.

Z1(ω)

ω ω1 Z2(ω)

ω ω2 Z3(ω)

ω ω3 Z(ω)

ω ω1 ω2 ω3 Broadcast Radio

“Broadcast” radio was championed by David Sarnoff, who previously worked at Marconi Wireless Telegraphy Company (point-to-point).

envisioned “radio music boxes” • analogous to newspaper, but at speed of light • receiver must be cheap (as with newsprint) • transmitter can be expensive (as with printing press) •

Sarnoff (left) and Marconi (right)

Modernity: What About Sending Digital Data?

Consider input stream x[n] of 1’s and 0’s. Transmitter: Construct new stream by replicating each bit some number of • times. Modulate with a cosine. • Transmit. •

Receiver: Multiply received stream with a cosine (demodulate). • Low-pass filter. • Threshold result to find 1’s and 0’s, and decimate. •

Check Yourself

The problem with making the simple strategy we’ve discussed is that you must know the carrier signal exactly!

x[n]z[n] LPF y[n]

cos(Ωcn) cos(Ωcn + φ)

What happens if there is a phase shift φ between the signal used to modulate and that used to demodulate? Fixing Phase Problems

Phase errors (and channel delay) result in scaling the output ampli- tude, where the magnitude of the scaling can’t be determined when we design the system: channel delay varies on mobile devices • phase difference between transmitter and receiver is arbitrary •

One strategy to mitigate this effect is quadrature demodulation: Multiply by cosine to find I[n] = x[n D] cos(φ) • − × Multiply by cosine to find Q[n] = x[n D] sin(φ) • − × Then, if we let w[n] = I[n] + jQ[n], we have: w[n] = I[n]2 + Q[n]2 | | q 2 2 = (x[n D] cos(φ)) + (x[n D] sin(φ)) − − q = x[n D] cos2(φ) + sin2(φ) = x[n D] | − | | − | q

Quadrature Demodulation

We can do better (in terms of mitigating noise) if we encode our bitsream as +1 and 1 instead of as 1 and 0. Called binary phase- − shift keying because the carrier changes phase when x[n] switches from 0 to 1 (and vice versa).

However, this introduces an ambiguity between 0’s and 1’s! However, we can fix this multiple ways: Send an agreed-on preamble (known bit sequence) at the start • of each message, or Use a different encoding (for example, a 1 corresponds to step- • ping the phase, and a 0 corresponds to keep the phase the same.

Example: Sending Data via Audio

Example: audio-based communication link WiFi

Brief overview of WiFi.

Additional challenges! AM radio is single source multiple receivers. → WiFi needs to be: multiple source (computers) single receiver (access point) • → single sender (access point) single receiver (computers) • →

How is this accomplished (simple version)? Frequency division multiplexing • Medium access control protocols for effectively sharing a channel •