Information Theory

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Unit-II
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Digital CW Modulation Techniques

• Desirable features
• Low bit error rate at low received S/N
• Performs well in multipath conditions
• Occupies a minimum of BW
• Easy and cost-effective to implement
• None of existing techniques satisfy all of these
  requirements
• Depending upon application some of the above
  features are prioritized over other and
  accordingly modulation technique is selected

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• Bandwidth efficiency (R/B maxlog2(1S/N))
• Ability to accommodate data within a limited
  bandwidth. (may be greater than 1)
• In general increasing data rate implies
  decreasing pulse width i.e. increase in BW of
  signal.
• Power efficiency (Eb/N0)
• Ability to keep the minimum error at low power
  levels (may be greater than 1)
• With decrease in power BER increases but rate of
  increase depends upon modulation tech.
• Phase characteristics
• If phase change is smooth then nonlinear
  amplifiers can be used which reduces
  implementation complexity.

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Amplitude Shift Keying (ASK)
Baseband Data
ASK modulated signal
A cos wct
A cos wct
0
0

• Pulse shaping can be employed to remove spectral
  spreading.
• ASK demonstrates poor performance, as it is
  heavily affected by noise and interference.
• Long string of zeros causes synchronization loss.

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Frequency Shift Keying (FSK)
Baseband Data
FSK modulated signal
f1
f1
f0
f0
where f0 A cos(wc-Dw)t and f1 A
cos(wcDw)t

• Bandwidth occupancy of FSK is dependant on the
  spacing of the two symbols. A frequency spacing
  of 0.5 times the symbol period is typically used.
• FSK can be expanded to a M-ary scheme, employing
  multiple frequencies as different states.

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Phase Shift Keying (PSK)
Baseband Data
Binary PSK modulated signal
s1
s1
s0
s0
where s0 -A cos wct and s1 A cos wct

• Binary Phase Shift Keying (BPSK) demonstrates
  better performance than ASK and FSK.
• PSK can be expanded to a M-ary scheme, employing
  multiple phases and amplitudes as different
  states.
• Filtering can be employed to avoid spectral
  spreading.

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Quadrature phase shift keying (QPSK)
Wc Carrier Frequency, I In phase channel, Q
Quadrature channel

• Quadrature Phase Shift Keying is effectively two
  independent BPSK systems (I and Q), and therefore
  exhibits the same performance but twice the
  bandwidth efficiency.
• Quadrature Phase Shift Keying can be filtered
  using raised cosine filters to achieve excellent
  out of band suppression.
• Large envelope variations occur during phase
  transitions, thus requiring linear amplification.

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Geometric Representation

• Digital modulation involves choosing a particular
  signal si(t) form a finite set S of possible
  signals.
• For binary modulation schemes a binary
  information bit is mapped directly to a signal
  and S contains only 2 signals, representing 0 and
  1.
• For M-ary keying S contains more than 2 signals
  and each represents more than a single bit of
  information. With a signal set of size M, it is
  possible to transmit up to log2M bits per signal.

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• Any element of set S can be represented as a
  point in a signal space whose coordinates are
  basis signals ?j(t) such that

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Example BPSK Constellation Diagram
Q
I
?Eb
-?Eb
Constellation diagram
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Constellation diagram

• It is a graphical representation of the complex
  envelope of each possible symbol state
• The x-axis represents the in-phase component and
  the y-axis the quadrature component of the
  complex envelope
• The distance between signals on a constellation
  diagram relates to how different the modulation
  waveforms are and how easily a receiver can
  differentiate between them.

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QPSK Constellation Diagram
Q
Q
I
I
Carrier phases 0, ?/2, ?, 3?/2
Carrier phases ?/4, 3?/4, 5?/4, 7?/4

• Quadrature Phase Shift Keying has twice the
  bandwidth efficiency of BPSK since 2 bits are
  transmitted in a single modulation symbol

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Distortions
Perfect channel
White noise
Phase jitter
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Types of QPSK

• Conventional QPSK has transitions through zero
  (ie. 180o phase transition). Highly linear
  amplifier required.
• In Offset QPSK, the transitions on the I and Q
  channels are staggered. Phase transitions are
  therefore limited to 90o.
• In p/4-QPSK the set of constellation points are
  toggled each symbol, so transitions through zero
  cannot occur. This scheme produces the lowest
  envelope variations.
• All QPSK schemes require linear power amplifiers.

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M-ary Phase and Amplitude Modulation

• Amplitude and phase shift keying can be combined
  to transmit several bits per symbol (in this case
  M4). These modulation schemes are often
  referred to as linear, as they require linear
  amplification.
• 16QAM has the largest distance between points,
  but requires very linear amplification. 16PSK
  has less stringent linearity requirements, but
  has less spacing between constellation points,
  and is therefore more affected by noise.
• M-ary schemes are more bandwidth efficient, but
  more susceptible to noise.

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Minimum Shift Keying (MSK)
MSK possible phase transitions
MSK phase transitions for data (00111000...)

• In MSK phase ramps up through 90 degrees for a
  binary one, and down 90 degrees for a binary
  zero.
• For GMSK transmission, a Gaussian pre-modulation
  baseband filter is used to suppress the high
  frequency components in the data. The degree of
  out-of-band suppression is controlled by the BT
  product.

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GMSK- Gaussian MSK

• GMSK is a form of continuous-phase FSK, in which
  the phase is changed between symbols to provide a
  constant envelope.
• The RF bandwidth is controlled by the Gaussian
  low-pass filter bandwidth.
• The degree of filtering is expressed by
  multiplying the filter 3dB bandwidth by the bit
  period of the transmission, ie. by BT.
• As bandwidth of this filter is lowered the amount
  of intersymbol-interference introduced increases.
• GMSK allows efficient class C non-linear
  amplifiers to be used, however even with a low BT
  value its bandwidth efficiency is less than
  filtered QPSK.
• - GMSK generally achieves a bandwidth efficiency
  less than 0.7 bits per second per Hz (QPSK can be
  as high as 1.6 bits per second per Hz).

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GMSK Signals

• In MSK , the BT is infinity and this allows the
  square bit transients to directly modulate the
  VCO.
• In GMSK, low values of BT create significant
  intersymbol interference (ISI). In the diagram,
  the portion of the symbol energy a acts as ISI
  for adjacent symbols.
• If BT is less than 0.3, some form of combating
  the ISI is required.

GMSK conceptual transmitter
MSK
GMSK, BT0.5
GMSK BT0.3
GMSK Pulse Shapes and ISI
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GMSK Spectra

• GMSK has a main lobe 1.5 times that of QPSK.
• GMSK generally achieves a bandwidth efficiency
  less than 0.7 bits per second per Hz (QPSK can be
  as high as 1.6 bits per second per Hz).

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Demodulation Detection

• Demodulation
• Is process of removing the carrier signal to
  obtain the original signal waveform
• Detection extracts the symbols from the
  waveform
• Coherent detection
• Non-coherent detection

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Coherent Detection

• An estimate of the channel phase and attenuation
  is recovered. It is then possible to reproduce
  the transmitted signal and demodulate.
• Requires a replica carrier wave of the same
  frequency and phase at the receiver.
• The received signal and replica carrier are
  cross-correlated using information contained in
  their amplitudes and phases.
• Also known as synchronous detection

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• Carrier recovery methods include
• Pilot Tone (such as Transparent Tone in Band)
• Less power in the information bearing signal,
  High peak-to-mean power ratio
• Carrier recovery from the information signal
• E.g. Costas loop
• Applicable to
• Phase Shift Keying (PSK)
• Frequency Shift Keying (FSK)
• Amplitude Shift Keying (ASK)

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Optimum binary detection (a) parallel matched
filters (b) correlation detector Figure 14.2-3
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Non-Coherent Detection

• Requires no reference wave does not exploit
  phase reference information (envelope detection)
• Differential Phase Shift Keying (DPSK)
• Frequency Shift Keying (FSK)
• Amplitude Shift Keying (ASK)
• Non coherent detection is less complex than
  coherent detection (easier to implement), but has
  worse performance.

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Noncoherent detection of bianry FSK Figure 14.3-5
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Modulation Summary

• Phase Shift Keying is often used, as it provides
  a highly bandwidth efficient modulation scheme.
• QPSK, modulation is very robust, but requires
  some form of linear amplification. Alternatives
  (e.g. Offset QPSK and p/4-QPSK) can be
  implemented, and reduce the envelope variations
  of the signal.
• High level M-ary schemes (such as 64-QAM) are
  very bandwidth-efficient, but more susceptible to
  noise and require linear amplification.
• Constant envelope schemes (such as GMSK) can be
  employed since an efficient, non-linear amplifier
  can be used.
• Coherent reception provides better performance
  than differential, but requires a more complex
  receiver.

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Spread Spectrum Technology

• Low power high bandwidth transmission.
• Better performance in noisy condition.
• Anti jamming feature
• Security, etc.

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Types of SS techniques

• Direct Sequence Spread Spectrum (DS-SS) e.g. CDMA
• Frequency Hopping Spread Spectrum (FH-SS)
• Time hopping Spread Spectrum (TH-SS)
• Hybrid (DS/FH, DS/TH, FH/TH,DS/FH/TH)

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Direct Sequence Spread Spectrum (DS-SS)

• This figure shows BPSK-DS transmitter and
  receiver (multiplication can be realized by
  RF-mixers)

spreading
DS-CDMA is used in WCDMA, cdma2000 and IS-95
systems
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• Effect of narrowband noise signal

Effect of wideband Interference
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Basic principle of CDMA

• Assumptions
• Polar line coding is used.
• All the users are synchronized
• All the users produce same power level at the
  base station.
• Base station has a copy of all chipcodes of its
  network
• All the codes should be either PN-sequence or
  orthogonal codes (preferable) i.e.
• ?CxCy 1 if x y
• -1 if x complement (y)
• 0 otherwise.

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• Algorithm
• A unique codeword of same length Cx(c1,c2,c3)
  is assigned to each user.
• A user transmits its codeword for transmitting
  logic 1 and its compliment for 0.
• The base station receives the algebraic sum of
  chips D(d1,d2,) transmitted by all the active
  users.
• The BS calculates Sx ?Cx(i)D(i) for all users.
• If it is above ve (-ve) threshold user x has
  transmitted logic 1 (0)

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• Problem
• There are three users A,B,C in a CDMA network
  with corresponding chip sequences Ca
  1,-1,-1,1,-1,1, Cb 1,1,-1,-1,1,1, Cc
  1,1,-1,1,1,-1. If both the thresholds are set
  at 0 volts, find the data decoded by BS when
• A transmits logic 1.
• A and B transmit logic 1
• A and C transmit logic 1.

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PN - sequences

• Uniform distribution and independence.
• Period 2n 1 bits n length of shift register
• To identify a PN both algorithm (interconnection
  of taps) and seed (starting point) must be known.
• Seed can change the starting and ending point of
  a PN sequence but the contents remains the same.
  (this property is used for cell identification in
  CDMA mobile systems.)
• Walsh codes are known to be orthogonal codes.

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Frequency Hopping Transmitter and Receiver

• Hopping frequencies are determined by the code.
• This method is applied in BlueTooth

• May be slow (two or more symbols are tx at same
  fc) or fast (two or more frequencies are used to
  transmit single symbol)

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Frequency Hopping Spread Spectrum (FH-SS) (ex tx
of two symbols/chip)
4-level FSK modulation
Hopped frequency slot determined by hopping code
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DS and FH compared

• FH is applicable in environments where there
  exist tone jammers that can be overcame by
  avoiding hopping on those frequencies
• DS is applicable for multiple access because it
  allows statistical multiplexing (resource
  reallocation) to other users (power control)
• FH applies usually non-coherent modulation due to
  carrier synchronization difficulties -gt
  modulation method degrades performance

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• Both methods were first used in military comm,
• FH can be advantageous because the hopping span
  can be very large (makes eavesdropping difficult)
  
• DS can be advantageous because spectral density
  can be much smaller than background noise density
  (transmission is unnoticed)
• By using hybrid systems some benefits can be
  combined The system can have a low probability
  of interception and negligible near-far effect at
  the same time. (Differentially coherent
  modulation is applicable)

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FDMA, TDMA and CDMA compared

• TDMA and FDMA principle
• TDMA allocates a time instant for a user
• FDMA allocates a frequency band for a user
• CDMA allocates a code for user
• CDMA-system can be synchronous or asynchronous
• Synchronous CDMA difficult to apply in multipath
  channels that destroy code orthogonality
• Therefore, in wireless CDMA-systems as in
  IS-95,cdma2000, WCDMA and IEEE 802.11 users are
  asynchronous

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• FDMA, TDMA and CDMA yield conceptually the same
  capacity
• However, in wireless communications CDMA has
  improved capacity due to
• statistical multiplexing
• graceful degradation
• Performance can still be improved by adaptive
  antennas, multiuser detection, FEC, and
  multi-rate encoding