A (NAIVE) DIGITAL RADIO

ò An Illustrative Digital Communication ò System ò Transmitter and Transmitted Pulse Sequence ò Received Signal and Receiver ò Synchronization Issues ò Spectrum Sharing ò RF Communication System ò Practical Obstacles ò Analog/Digital Signal Processing Split

Digital Communication System

ò Objective: Send text converted to a stream of bits from place 1 to place 2 through the analog medium in between. ò Coding: Use standard ASCII code to convert text to bits (using 8 bits per character) ò Transmitter: Use sequence of scaled rectangular

pulses to convey bits,

ò singly 1 +1 and 0 −1 or

ò in clusters, 10 +1, 01 −1, 00 +3, and 11 −3. ò We choose pairs, so groups of 8 bits become clumps of 4 symbols. ò Receiver: Sample received pulse and convert symbols to bits, e.g., 1, 3,−1, 1,−3 ¡ 1000011011, and then back to text.

1 Transmitted Pulse Sequence

ò An idealized baseband transmitter and the transmitted signal consists of a sequence of pulses

ò Each pulse has the same rectangular shape ò Each one corresponding to each symbol. ò Though offset in time and scaled in magnitude.

Received Signal and Receiver ò In the ideal case, the received signal is the same as the transmitted signal though attenuated in magnitude and delayed in time.

ò An idealized baseband receiver

2 Synchronization Issues

ò Baud (symbol) timing selection for fixed T top-dead-center = τ + δ + T/2 ò Frame start determination ò grouping symbols to decoder ò example: −1,−1, 1,−3,−1; first 4 symbols decode to “X” and last four decode to “a”

Radio Frequency (RF) Communication System

ò An RF transmitter

ò An RF receiver

3 Practical Issues

ò Precise frequency translation required in receiver ò precise timing required in receiver ò multi-user interference occurs in received signal, e.g. since each user is not strictly bandlimited in frequency ò noise contamination of transmitted signal: in-band, out-of- band, narrowband, or broadband ò Channel distortion: fading or multipath

Analog/Digital Signal Processing Split

ò Due to cost and flexibility benefits, modern radio design is pushing the sampler (and subsequent digital signal processing) closer to the received signal, i.e. the output of the low noise amplifier driven

by the antenna signal.

ò Sample period Ts symbol period T.

4 An ASP/DSP Division of Labor

ò ASP: ò frequency translation to intermediate frequency ò out-of-band signal attenuation ò automatic gain control ò DSP: ò downconversion to baseband ò carrier tracking ò symbol timing (via interpolation) ò channel compensation (via linear filtering) ò symbol decision (via quantization) ò frame synchronization (via correlation) ò decode symbols to message text

Modulation and Demodulation

ò For upconversion mixer multiplies input waveform with a sinusoid

ò – s(t) = w(t)cos(2 f0t) ò – w(t): message waveform ò – s(t): transmitted waveform (mixer output) ò We want to compute the Fourier transform of the transmitted waveform s(t) using: ò Exponential definition of a cosine (A.2)

ò Fourier transform definition

5 Mixing

Bandwidth Definitions

ò Measures of Bandwidth (BW): ò 99% BW‰ freq. range where 99% of power is ò Absolute BW : Range of frequencies over a non-zero spectrum ò Null-to-Null BW : Width of the main spectral lobe ò Half-power bandwidth: 3dB bandwidth Half-power bandwidth

dB

6 Mixing

ò Assume transmitted signal arrives unimpaired ò For downconversion use mixer with frequency and phase matching transmitter’s

ò Using linearity of Fourier transform (A.31) and previously extracted result on Fourier transform of mixer output also included in (A.33)

Illustration of Mixing

(a) original spectrum of the message

(b) message modulated by the carrier

(c) demodulated signal has original spectrum after ideal low pass filtering

7 Frequency Division MUX (FDM)

ò Compose transmitted FDM signal as sum of message signals with same bandwidth f using

carriers with appropriately separated frequencies f1, f2, f3 ò Resulting spectrum of sum shows threedifferent upconverted signals in their assigned frequency bands.

FDM

ò Mixing transmitted/received FDM signal with cosine

with frequency f3 followed by ideal lowpass filtering with a cutoff frequency f recovers baseband message signal 3.

ò Time division multiplexing (TDM) is amultiple-user channel capacity allotment alternative.

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