EECS 4214, F15 1

L15: Bandpass Detection

Sebastian Magierowski York University

L15: Bandpass Detection

LE/EECS 4214 Fall 2015

EECS 4214, F15 2

•  15.1 Coherent Detection of BPSK •  15.2 Coherent Detection of Multiple PSK •  15.3 Non-coherent Detection of DPSK •  15.4 Non-coherent FSK

Outline

L15: Bandpass Detection

EECS 4214, F15 3

•  Recall BPSK

•  Modulation-wise

Bandpass Modulation: BPSK

L15: Bandpass Detection

pE�

pE

1

s1(t) =

r2E

Tcos(!

o

t)�r

2E

Tcos(!

o

t) = s2(t)

1(t) =

r2

Tcos(!

o

t)

±pE

1

si(t) si(t) =NX

j=1

aij j(t)

EECS 4214, F15 4

•  For a 2D system

Bandpass Modulation: QPSK

L15: Bandpass Detection

𝛴

±pE

±pE

pE

1

2

si(t)

1(t) =

r2

Tcos(!

o

t)

2(t) =

r2

Tsin(!

o

t)

EECS 4214, F15 5

•  Same idea as with baseband

•  Send a signal and extract maximum SNR from it –  Correlator example

•  Note how this matches up with our abstract signal-space mapping ideas

Bandpass Detection: BPSK

L15: Bandpass Detection

±pE

1

si(t)

1

si(t)Z T

0

ai1 = ±pE

si(t) =NX

j=1

aij j(t) aij =

Z Tf

Ti

si(t) j(t)dt

EECS 4214, F15 6

•  Using related receive architectures gives us the same basic result

Bandpass Detection: BPSK

L15: Bandpass Detection

±pE

1

si(t)

1

si(t)Z T

0

ai1 = ±pE

Bandpass Matched

Filter si(t) ai1 = ±

pE

1

si(t) ai1 = ±pEMF

EECS 4214, F15 7

•  What if we sent…

•  But received…

•  If the phase is not right –  Easy to get garbage –  The challenge of coherent detection

Coherent Detection

L15: Bandpass Detection

±pE si(t) = ±

r2E

Tcos(!

o

t)

1(t) =

r2

Tcos(!

o

t)

Z T

0

si

(t) = ±r

2E

Tcos

⇣!o

t+⇡

2

⌘

1(t) =

r2

Tcos(!

o

t)

ai1 = ???

EECS 4214, F15 8

•  Picking up signals over a 2-D space

•  Formal decision procedure: based on proximity

A (More) General BP Detection Scheme

L15: Bandpass Detection

Z T

0

Z T

0

1

2

r(t)

choose si(t) based on proximity

of projection to (ai1,ai2)

projection

z2(T ) =

Z T

0r(t) 2(t)dt

z1(T ) =

Z T

0r(t) 1(t)dt

arg min[si � zi(T )]2si

EECS 4214, F15 9

More Specifics: M-ary PSK Detection

L15: Bandpass Detection

Z T

0

Z T

0

r(t)

choose si(t) based on proximity

of projection to (ai1,ai2)

z2(T ) =

Z T

0r(t) 2(t)dt

z1(T ) =

Z T

0r(t) 1(t)dt

1(t) =

r2

Tcos(!

o

t)

2(t) =

r2

Tsin(!

o

t)

r(t) = si

(t) =

r2E

Tcos

✓!o

t+2⇡i

M

◆, i = 0, . . . ,M � 1

EECS 4214, F15 10

More Specifics: M-ary PSK Detection

L15: Bandpass Detection

Z T

0

Z T

0

r(t)

choose si(t) based on proximity

of projection to (ai1,ai2)

z2(T ) =

Z T

0r(t) 2(t)dt

z1(T ) =

Z T

0r(t) 1(t)dt

1(t) =

r2

Tcos(!

o

t)

2(t) =

r2

Tsin(!

o

t)

r(t) = si(t) =pE cos

✓2⇡i

M

◆ 1(t) +

pE sin

✓2⇡i

M

◆ 2(t)

Xi =pE cos (2⇡i/M)

Yi =pE sin (2⇡i/M)

EECS 4214, F15 11

•  Detect signals by looking at:

More Specifics: M-ary PSK Detection

L15: Bandpass Detection

Z T

0

Z T

0

r(t)

choose si(t) based on proximity

of projection to (ai1,ai2)

1(t) =

r2

Tcos(!

o

t)

2(t) =

r2

Tsin(!

o

t)

Xi =pE cos (2⇡i/M)

Yi =pE sin (2⇡i/M)

pE

1

2

Xi

Yi

�i�i

EECS 4214, F15 12

M-ary PSK Receiver

L15: Bandpass Detection

Z T

0

Z T

0

1

2

r(t) atan(Y/X) �̂

|�i � �̂|ŝi = arg mini(·)

pE

1

2

Xi

Yi �i

Xi

Yi

EECS 4214, F15 13

QPSK Transmitter

L15: Bandpass Detection

( & LdL1WA’.

1-v-i-

—‘I)

sQf)

t1 (+i w4)

1(-1)

I-I

/‘ ‘L

i—ih() 0

0

+1--1

13 50

2.

-I

of£7.0 0

3

--1

II

00 10

( & LdL1WA’.

1-v-i-

—‘I)

sQf)

t1 (+i w4)

1(-1)

I-I

/‘ ‘L

i—ih() 0

0

+1--1

13 50

2.

-I

of£7.0 0

3

--1

II

00 10

EECS 4214, F15 14

QPSK Receiver

L15: Bandpass Detection

‘IC.’

\L)

.—

;

Ii.

cji

LA

Q:7;;:\j

(AI

c’ 0 LA

V

1•/

LA%J

‘4

/

/

j

4,

‘IC.’

\L)

.—

;

Ii.

cji

LA

Q:7;;:\j

(AI

c’ 0 LA

V

1•/

LA%J

‘4

/

/

j

4,

EECS 4214, F15 15

•  Instead of mapping data to phase: 𝜃k –  BPSK: 𝜃k = 0, 𝜋 –  QPSK: 𝜃k = 𝜋/4, 3𝜋/4, 5𝜋/4, 7𝜋/4

•  Map it to phase shift: 𝜃k = 𝜃k-1 + 𝛥𝜃k –  DPSK: 𝛥𝜃k = 0, 𝜋 –  DQPSK: 𝛥𝜃k = 0, 𝜋/2, 𝜋, 3𝜋/2

Non-Coherent Detection: DPSK

L15: Bandpass Detection

EECS 4214, F15 16

DPSK Transmitter

L15: Bandpass Detection

1(t) =

r2

Tcos(!0t)

p(t)

DQ

m(k) c(k) p(k)

k 0 1 2 3 4 5 6 7 8

m 1 1 0 1 0 1 1 0

c 0 1 0 0 1 1 0 1 1

p -1 1 -1 -1 1 1 -1 1 1

𝜃 𝜋 0 𝜋 𝜋 0 0 𝜋 0 0

r(t)

EECS 4214, F15 17

DPSK Receiver

L15: Bandpass Detection

Z T

0

T

k 0 1 2 3 4 5 6 7 8

m 1 1 0 1 0 1 1 0

c 0 1 0 0 1 1 0 1 1

p -1 1 -1 -1 1 1 -1 1 1

𝜃 𝜋 0 𝜋 𝜋 0 0 𝜋 0 0

z -1 -1 1 -1 1 -1 -1 1

r(t) z(k)

EECS 4214, F15 18

Differential Drawback

•  Higher noise

•  In coherent reception –  Demodulate with clean

reference signal

•  In non-coherent reception –  Demodulate using a noisy

reference (the previously received signal)

–  2X the noise

L15: Bandpass Detection

• I1 L ‘Q-t7’(QJLA4 ‘2 ,V

-,‘, DP Si UL fl -r p57’ I’€&!-‘ Lt /1Lf g- 744Q A1Li’S (/‘p S/n’

Pi

e___

bPS

/c Z/ rs/<1c- 11?LtIf2/r

r(+)

S’fl.iba5Icv

1 VJ

1(t) =

r2

Tcos(!0t)

EECS 4214, F15 19

•  Energy detection method

•  Envelope detection

Non-Coherent FSK

L15: Bandpass Detection

• I1 L ‘Q-t7’(QJLA4 ‘2 ,V

-,‘, DP Si UL fl -r p57’ I’€&!-‘ Lt /1Lf g- 744Q A1Li’S (/‘p S/n’

Pi

e___

bPS

/c Z/ rs/<1c- 11?LtIf2/r

r(+)

S’fl.iba5Icv

1 VJ

• I1 L ‘Q-t7’(QJLA4 ‘2 ,V

-,‘, DP Si UL fl -r p57’ I’€&!-‘ Lt /1Lf g- 744Q A1Li’S (/‘p S/n’

Pi

e___

bPS

/c Z/ rs/<1c- 11?LtIf2/r

r(+)

S’fl.iba5Icv

1 VJ

EECS 4214, F15 20

•  Another receiver example

Non-Coherent FSK

L15: Bandpass Detection

.LWL

111

____