Baseband Digital Communications

1

Baseband Digital Communications

• Characteristics and Constraints of Wireless Channels

• Baseband Pulse Transmission: Line Signal Codings [NRZ, AMI, Manchester,2B1Q, ...]

• Pulse Amplitude Modulation [PAM]: Transmitter and Receiver pulse shaping

• Intersymbol Interference [ISI]: Eye Pattern

• The Nyquist Criterion:

– Raised Cosine Pulses

– Multipath

– Performance: Mean-Square Error

– Probability of Error

2

Baseband Modulation

• An information bearing-signal must conform to the limits of its channel

• Generally modulation is a two-step process– baseband: shaping the spectrum of input bits to fit in a limited spectrum

– passband: modulating the baseband signal to the system rf carrier

• Most common baseband modulation is Pulse Amplitude Modulation (PAM)– data amplitude modulates a sequence of time translates of basic pulse

– PAM is a linear form of modulation: easy to equalize, BW is pulse BW

– Typically baseband data will modulate in-phase [cos] and quadrature [sine] datastreams to the carrier passband

• Special cases of modulated PAM include– phase shift keying (PSK)

– quadrature amplitude modulation (QAM)

3

Need for Baseband Modulation

• An analog signal has a finite bandwidth.

• A digital stream or signal, with sharp transitions, has an infinitebandwidth.

• Due to the limited available system bandwidth, only the major portion ofa digital signal spectrum can be transmitted and restored. Even if there isno loss or noise in the communication system, the received signal willhave distortion due to the limited channel bandwidth.

To avoid or to reduce this signal distortion, weuse baseband modulation techniques

time

time

Typical Baseband PAM Signals

1 0 0 0 01 1RZ

s(t)g(t)anM

T0NRZ

2

2

2

4

3

01

01

01

00011110

01

01

-11

-11

-3113

0±1

→→→→

→→→→

→→→→

→→→→→→→→

→→→→

BANDLIMITED

4-LEVEL

BIPOLAR/AMI [Alternate Mark Inversion]

T0

T0

T0 2T

T0

an

S(t)

Each technique will have different spectrum (at DC and band edge),ease of timing recovery

S(t) = ΣΣ ang(t-nT)an represents data (M-ary)1/T = symbol (baud) rateBit rate = log2 M=RT

1

n

= a0g(t) + a1g(t-T) + ...

5

State Diagram for AMI Signaling

State “+” State “-”

1/-p(t)

Branch Labels: Input bit (an)/output waveform or symbol [dnp(t)]

1/p(t)

0/0 0/0

The modulator has two states, labeled “+” and “-”. The modulator responds to a source symbol0 with a zero waveform and to a source symbol 1 with the waveform p(t) or -p(t) depending on whether its state is “-” or “+” respectively.

Note that the choice of the states is not obvious. A common mistake is to choose the output levels,0, 1, and -1 as states. But, if you make this choice, it is hard/impossible(?) to capture the memoryof the system.

6

Examples of Baseband Impulse Responses

(1) NRZ (non return to zero)

(2) Raised Cosine

(3) Bipolar (AMI)

(4) Manchester

0 T 2T

0 T t

0

T 2T

0 T

0 1/T f

0 1/T1/2T

0 1/T1/2T

3T

1T

0 2T

E.g Equalized Voiceband,Cellular or MicrowaveLOS Modem

e.g. 1.544/2.048 MbpsT1 /E1 Carrier on Twisted-Pair

e.g. Ethernet on CoaxialCable (3-10 Mbps)

h (t) |H(f)|

7

Examples of Baseband Impulse Responses (continued)

(5) Multipath: Class I Partial Response(Duobinary)

(6) Multipath: Class IV Partial Response

T 2T

0 T 0

• Multipath Nulls at DC and Nyquist frequency

h (t) |H(f)|

(7) Minimum - Bandwidth Nyquist Pulse

12T

0 12T

• Multipath (Cellular)

• Need Powerful Equalizer(DFE, VA)

• Regularly spaced zero crossings• Not Realized in Practice

0 12T

= W

0

sin2ππ Wt2ππ WT

Typical Linear Channel Characteristics

Voiceband Telephone After Demodulation

0

Frequency ResponseH(f)

Impulse Responseh(t)

Twisted Copper Pair with Transformers (DSL)

Radio

Gitlin1_8

f

0 f

0 ff0

h(t)Linear Equalizer

I/Q Equalizer

~DFE

t

t

t

h(t)

h(t)

|H(f)| ang H(f)

|H(f)|

ang H(f)

|H(f)|ang H(f)

~10 ms

Nulls require a non-linearequalizer: DFE or MLSE/VA

9

Pulse Distortion Due to MultiPath

10

Digital Baseband Modulation Techniques

• NR (Non-Return-to-zero)• Bipolar (AMI)• Partial response• Manchester

• Baseband (PAM): Baseband Channels

Typical Power Spectra:

Bipolar, Partial Reponse,or Manchester

Examples: Twisted-Pair and Coaxial Cable Channels

12T

1T

toFreq.0

Freq.0

NRZ

11

Doubling the Data Rate

• Date Rate =

• If SNR limited ----> double the symbol rate [3 dB SNR penalty]

• If bandwidth limited ----> only choice is to double the number of bits/symbolby increasing the number of points

– For example: going from 4-QAM to 16-QAM [from 2 to 4 bits/symbol]

– This has a ~6-7 dB penalty

• So, assuming that the bandwidth is available it is always better to double thesymbol rate

• The above also assumes that the background noise and/or interference is flatwith frequency

NT 2log1 Recall that 1/T is the symbol rate

and N is the number of modulation levels

12

Coded Baseband Digital Modulation Techniques

• Can be combined with any of the above• Performance improvement at the cost of increased receiver delay

and complexity• Allows rate to approach channel capacity• Types: - block coding

- convolutional or trellis coding

• Coded Systems

Signal-to-Noise Ratio

Uncoded System

Coded Systems withIncreasing Complexity

Channel Capacity Limit

ErrorProbability

Examples of Application: - Cellular Phones- Satellite Channels- High Speed Voiceband

Telephone Modems

13

Example of a Baseband PAM System

QuantizeReceive

FilterBasebandChannel

Trans.Filter

0 → → 10 → −→ −1

r(t)

B C

r(nT)

A

an

1/T persec.

Overall Impulse Response = x(t) Sample att = nT + ττ

ân

At A:{an}

T

• Baud = Symbols/sec x(t) ISI

0 T

At C:{r(nt)}

At D:{ân}

At B:r(t)

Timing Margin

T 2T 3T 4T 5T 6T 7T 8T

Margin Against Noise

anx(t-nT)r(t) =n∑∑

PAM

anδδ(t-nT)n∑∑

Intersymbol Interference (ISI) Can Cause Errors Without Noise

14

Band-Limited Signal for No Intersymbol Interference

-3T -2T -T T 2T 3T0-4T 4T t

t

x(t)

• Ideal Pulse

ππWt

sinππWt

• Minimum Bandwidth Pulse

0-W =2T1- W =

2T1

2W1

X(f)

f

1/T Symbols/sec

Don’t Need Time Limited Pulses for “0” ISI

Nyquist (1928)

15

Why Equalization Is Needed

(A)

Transmitted Pulse

(B)

(C)

Amplitude

0 F1Frequency

Amplitude

-3T -2T -T T 2T 3T0

P(t)

P(t) + P(t-T)

Time

-3T -2T -T T 2T 3T0

Time

16

INTERSYMBOL INTERFERENCE: ISI

• Cause of ISI:

• Elimination or reduction of ISI

- filtering

- equalization

17

EQUALIZATION: Pulse Shaping

Ideal pulse shaping [to satisfy the Nyquis tcriterion]:

y(t) = 0 at t = nT [n = 1, 2, 3, . . . ]

18

The Eye Pattern [as a measure of distortion]

0 T 2T 3T 4T 5T 6T 7T 8T

nT)(t (t) : WaveformPAMn

n −∑= xar

mmkk xaxakTr (0) )(0m

∑+=≠

−

Desired Intersymbol Interference = is a random variable(pdf is difficult to compute)

By the Central Limit Theorem the ISI can be approximated by a Gaussian Random Variable of zero mean and variance ∑

∞

≠0

2

nnx

19

Eye Pattern

“Bad” - Closed

Eye Pattern Display

“Good” - Open

ThresholdLevel

Marginfor ErrorDue ToNoise

Marginfor ErrorDue toTiming

Sample Instant

Symbol Timing Wave

Scope TriggerFrom Modem

20

The Raised Cosine Family of Nyquist Pulses

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

-3T -2T -T T 2T 3T

0.5

0

αα = 00

0.51

Raised Cosine

(a)

Excess Bandwidth

(b)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

α α = 0

X (ωω)

ππ/T 2ππ/T

Raised Cosine Pulse Shaping: (a) Frequency Response, (b) Time Response

1

==ωω

T

)(X

T2T

sin12T

ππ−−ωω

αα−−

)1(T

0 αα−−ππ

≤≤ωω≤≤

222 T/t4-1t/T cos

T/tT/tsin

)t(xαα

απαπππ

ππ==

1

0.5Fequency

Time

)1(T

)1(T

αα++ππ≤≤ωω≤≤αα−−ππ

,

,

21

Performance of PAM Systems: No ISI/Multipath(Gaussian Noise)

L = 2 4 8 16

1

10-1

10-2

10-3

10-4

10-5

10-6

5 10 15 20 25 30 350

Ps / PN [SNR], dB

Pe

Probability of error Ps for L-level PAM, where Ps / PN is thesignal-to-noise power ratio in the Nyquist bandwidth. Notethat doubling the bit rate requires about 6-7 dB of SNR

For Nyquist Pulse

{{ }}

∫∫∞∞ππ

==

−−==>>ηη

−−==

−−==−−======

−−

==∑∑

x dte 2

1)x(Q

PP

1-L3

Q L1

12dPr L1

1P

31L

Td

1)]d(2i[LT2

IT aPOWER XMITTP

22t

2/1

N

s2e

222

L12

1i

2s

L/2

/ T

22

ΣΣ

Adaptive Equalization

Inputbinarydata

Pulsegenerator

Transmittingfilter Channel Receiving

filterAdaptiveequalizer

Decisiondevice

{a(n)} y(n)

Outputbinarydata

Block diagram of a baseband data transmission system.

Transmitter Noise Receiver

Adaptive equalizer with a decision-directed mode of operation.

Adaptiveequalizer

Decisiondevice

Switch Stored referencegenerator

ΣΣ +

-

Inputsignal

Desired Response = Replica of transmitted signal

Sampler

Error