10/17/2006

Digital I/Q Transceiver• Constellation Diagram• SNR• Eye DiagramLab 5• Transmitter• Analog Receiver • Digital Receiver

Lecture 10Digital I/Q Transceiver

L10/17/2006 2Lecture 10 Fall 2006

Digital Modulation

• I/Q signals take on discrete values at discrete time instants corresponding to digital data– Receiver samples I/Q channels

• Uses decision boundaries to evaluate value of data at each time instant

• I/Q signals may be binary or multi-bit– Multi-bit shown above

Receiver Output

2cos(2πf1t)2sin(2πf1t)

Lowpassir(t)

Lowpassqr(t)

it(t)

qt(t)

2cos(2πf1t)2sin(2πf1t)

t

t

t

Baseband Input

tDecisionBoundaries Sample

Times

L10/17/2006 3Lecture 10 Fall 2006

Constellation Diagram-16QAM

• We can view I/Q values at sample instants on a two-dimensional coordinate system

• Decision boundaries mark up regions corresponding to different data values

• Gray coding used to minimize number of bit errors that occur if wrong decisions made due to noise

DecisionBoundaries I

Q

DecisionBoundaries

00 01 11 10

00

01

11

10

Receiver Output

t

tSampleTimes

L10/17/2006 4Lecture 10 Fall 2006

Impact of Noise on Constellation Diagram

Low PowerHigh Power

• Sampled data values no longer land in exact same location across all sample instants while decision boundaries remain fixed

• Significant noise causes bit errors to be made• Increasing signal power increases distance between decision boundaries

i.e., increased SNR

L10/17/2006 5Lecture 10 Fall 2006

Transition Behavior Between Constellation Points

• Constellation diagrams provide us with a snapshot of I/Q signals at sample instants

• Transition behavior between sample points depends on modulation scheme and transmit filter

DecisionBoundaries I

Q

DecisionBoundaries

00 01 11 10

00

01

11

10

L10/17/2006 6Lecture 10 Fall 2006

Need for Transmit Filter

• Steps in waveform x(t) have high frequency components. (Recall Fourier Series applet)

• We want spectral efficiency (i.e. narrow bandwidth signals) to conserve spectrum

t

Td

data(t)

t

x(t)

O-Order

Track & Hold

L10/17/2006 7Lecture 10 Fall 2006

Transmit Filter

• Special low pass filtering (e.g. raised cosine filter) removes high-frequency content but preserves signal levels as sampling points.

• Trade-off bandwidth and signal integrity

t

Td

data(t)

t

x(t)|P(f)|2

f1/(2Td)0

L10/17/2006 8Lecture 10 Fall 2006

Lab 5 Transmitter Block

L10/17/2006 9Lecture 10 Fall 2006

Σ−Δ Modulator Pushes Quantization Noise to High Frequency

• Allows music to be encoded digitally• LPF at receiver is used to remove quantization noise while

preserving the signal. Tradeoff is noise vs. signal integrity

Time Domain Frequency Domain

L10/17/2006 10Lecture 10 Fall 2006

Lab 5 Analog Receiver Block Diagram

Neglecting higher frequency termsrxa = it (t)cos Δω ct + φOFF (t)[ ]

Difference between transmitter and receiver modulation frequency

Difference in phase between transmitter and receiver. It is a function of time.

Where Δω c :φOFF (t) :

rxb = qt (t)cos Δω ct +φOFF (t)[ ]If we can measure Δωc and φOFF(t) we can remove both frequency and phase offset.

rx = rxa + jrxb

L10/17/2006 11Lecture 10 Fall 2006

Complex ModulationWrite

in exponential form

rx = rxa + jrxb where rxa = RE rx( ); rxb = IM rx( )

rx = [it (t)+ jqt (t)]ej Δωct+θOFF (t )( )

rx by e− j Δωct+φOFF (t )( )

I = ir (t)Q = qr (t)

× ××××

Σ

Σ

I

Q

cos ω ct( )rxa

sin ω ct( )rxb

cos( )

sin( )

cos( )

+−

+ +

Where ( ) = Δω ct + φOFF (t)

Multiply

L10/17/2006 12Lecture 10 Fall 2006

Lab 5 Digital Receiver Block Diagram

USRP

Receiverx_a (I)

rx_b (Q)

250 kSample/s

Complex

Mixer

250 kSample/s

cos(ωct)

sin(ωct)

rx_a (I)

rx_b (Q)

in

ωc = 2π(vco_freq + dco_freq)

freq

offset

phase

offset I

Q

listen to

song I

listen to

song Q

analog extract filter

analog extract filter

matchedfilter

matchedfilter

Digital

receiver

operations

i_sliced_data

q_sliced_data

i_raw

q_raw

Output i_raw & q_raw

L10/17/2006 13Lecture 10 Fall 2006

Eye Diagram for 1 Gb/s Data Rate [2-level -it(t)]

• Wrap signal back onto itself every 2*Td seconds– Same as an oscilloscope would do

• Allows immediate assessment of the quality of the signal at the receiver (look at eye opening)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 10−9

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time (seconds)

out

Eye Diagram

0 0.5 1 1.5 2 2.5

x 10−8

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

out

TIME

Snapshot in Time

L10/17/2006 14Lecture 10 Fall 2006

Relationship of Eye to Sampling Time and Slice Level

• Horizontal portion of eye indicates sensitivity to timing jitter

• Vertical portion of eye indicates sensitivity to additional noise

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 109

0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time (seconds)

out

Eye Diagram

SliceLevel

SamplingInstant

L10/17/2006 15Lecture 10 Fall 2006

Realistic Eye Diagram

• Eye more closed due to amplitude noise and timing variation

• Line denotes best time to sample

0 2 4 6 8

x 10−11

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Time (seconds)

out

Eye Diagram

L10/17/2006 16Lecture 10 Fall 2006

Multi-Level Signaling• Increase spectral efficiency by sending more than one bit

during a symbol interval• Example: 4-Level PAM on each channel I and Q

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

x 10−10

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Time (seconds)

out

Eye Diagram