EE 615 Lecture 6

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EE 615 Lecture 6

• Diversity
• Space (Antenna)
• Time (Coding)

Dr. Uf Tureli Department of Electrical and
Computer Engineering Stevens Institute of
Technology Hoboken NJ 07030
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HW

• Due today,
• Channel estimation

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Diversity (Background)

• Potential for capacity through change of the
  channel (either different channels or variation)
• Increase link performance or throughput
• Limits of Capacity?

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Capacity

• Shannon Maximum achievable throughput without
  distortion (asymptotically error free data)
• Multiple parallel channel capacity.
• If HnI

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Additive White Gaussian Noise Channel

• Capacity scales linearly with number of channels
  rather than logarithmically
• Benefit of parallel transmission!
• The assumption independent channels, in reality
  interference / correlation between channels
• What to do if channel is not AWGN?

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Modulation

• mapping the digital information to analog form
• demodulation, done by the receiver to recover the
  transmitted digital information
• constellation is the set of points that can be
  transmitted on a single symbol

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Modulation

• Bit error rate (BER) of PB of a constellation
  given by calculating Q-function
• Different constellations have different dmin
  values for the same
• Constellation with the largest dmin for a given
  has the best performance.
• To make comparisons between constellations fair,
  averaging the power of all the M points Ck of the
  constellation

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Constellation
set of points located in one dimensional or
larger space spanned by the transmitted symbols.
PSK modulations are also called constant
amplitude modulations.

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Distance properties of PSK
.

Symbol error rate of PSK modulations can be
derived exactly for BPSK and QPSK
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BER performance PSK

• BPSK
• Higher order PSK modulation Ps appoximated

k log2 M
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Quadrature Amplitude Mod.
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Distance properties QAM
Symbol error rate of QAM modulation is
approximated by considering QAM as two
independent ASK modulation on both I- and
Q-carriers.
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Detection
A hard decision demodulator or slicer
If the demodulator can output more information
than the input to the modulator, the system uses
soft decision Soft decision demodulator outputs
"soft" bits, that in addition to indicating a
zero or one bit retain information about the
reliability of the decision.
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Channel coding

• Capacity is a rate limit for error free
  communications.
• The channel codes that can achieve this bound is
  not given!
• GOAL Enable signal to counter channel
  impairments, noise, fading, jamming
• Block coding vs Channel coding

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Channel Coding (ctnued)

• Decrease BER of power/bandwidth limited channel
• Add structured redundancy into signal
• Examples Linear Block Codes

Syndrome test determines error. One-to-one
mapping between correctable error patterns and
associated syndrome s
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Interleaving

• Most codes are designed for AWGN channel.
  Performance rapidly degrades in frequency
  selective channels with correlated channels.

Interleaving basically a matrix which you write
data in columns and read in rows 6x8 block
interleaver shown Has interleaving depth 48
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Convolutional Interleaver
A convolutional interleaver is another possible
interleaving solution that is most suitable for
systems that operate on continuous stream of
bits.
Deinterleaving of convolutional interleaver is
achieved by flipping the interleaver along its
horizontal axis
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Interleaving in IEEE 802.11a

• Block interleaver, limited to one OFDM symbol
  (read the book for details)
• Performance effect of interleaving in IEEE
  802.11a is due to frequency diversity.
• Channel assumed to be quasi static and assumed to
  stay the same for duration of a transmitted
  packet.

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Interleaving in 802.11a
Interleaving depth equal to one OFDM symbol.
(block interleaver )
performance effect of interleaving in IEEE
802.11a is a consequence of frequency diversity.
combined effect of interleaving and convolutional
channel coding takes advantage of the frequency
diversity provided by the wideband nature of the
transmitted signal.
because the channel is assumed to be
quasi-static that is, the channel is assumed to
stay essentially the same for the duration of a
transmitted packet.
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IEEE 802.11a 12 Mbits mode with and without
interleaving in 75ns rms delay spread Rayleigh
fading channel.
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Interleaving in OFDM

• Interleaver from OFDM Wireless LANS
• A Theoretical and Practical Guide
• function interleaved_bits tx_interleaver(in_bits
  , sim_options)
• global sim_consts
• interleaver_depth sim_consts.NumDataSubc
  get_bits_per_symbol(sim_options.Modulation)
• num_symbols length(in_bits)/interleaver_depth
• Get interleaver pattern for symbols
• single_intlvr_patt tx_gen_intlvr_patt(interleave
  r_depth, sim_options)
• Generate intereleaver pattern for the whole
  packet
• intlvr_patt interleaver_depthones(interleaver_d
  epth, num_symbols)
• intlvr_patt intlvr_pattdiag(0num_symbols-1)
• intlvr_patt intlvr_pattrepmat(single_intlvr_pat
  t', 1, num_symbols)
• intlvr_patt intlvr_patt()

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OFDM Standard 802.11a

• Generating 12 Mbit/s involves
• a. Encoding the 24 bit signal field with a rate
  ½ convolutional encoder (yields 48 bits)
• b. Interleaving the encoded bits with a 2 step
  interleaver
• c. QPSK modulating of the interleaved bits
• d. Padding the modulated bits with zeros, and
  skipping 4 locations (yields a total of 64 bits)
• e. Inserting pilots in the 4 skipped locations
• f. Applying the IFFT to the final bits.

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Systemview OFDM w/ interlea.
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Deinterleaving (MATLAB)

• Deinterleaving is exactly same as interleaving
  reversed

• function out_bits rx_deinterleave(in_bits,
  sim_options)
• global sim_consts
• interleaver_depth sim_consts.NumDataSubc
  get_bits_per_symbol(sim_options.Modulation)
• num_symbols length(in_bits)/interleaver_depth
• single_deintlvr_patt rx_gen_deintlvr_patt(interl
  eaver_depth)
• deintlvr_patt interleaver_depthones(interleaver
  _depth, num_symbols)
• deintlvr_patt deintlvr_pattdiag(0num_symbols-1
  )
• deintlvr_patt deintlvr_pattrepmat(single_deintl
  vr_patt', 1, num_symbols)
• deintlvr_patt deintlvr_patt()
• out_bits(deintlvr_patt) in_bits

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Convolutional Coding

• Most widely used channel codes
• (GSM, IS-95), IEEE 802.11a has eight different
  data rates (conv. Coding rate adjustment)

(1338,1818) rate ½, 64 state convolutional encoder
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Punctured Codes
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Ddistances of the 64 State Convolutional Codes
Used in IEEE 802.11a
64 state rate 1/2 convolutional encoder used in
IEEE 802.11a.                                   
                                                  
                                                  
  
64 state rate 1/2 convolutional encoder used in
IEEE 802.11a.
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Decoding Convolutional Code

• Viterbi algorithm, ML sequential detector (hard
  or soft decision decode)
• In coherent OFDM system channel estimate is
  necessary. This can be incorporated ito Viterbi
  algorithm to improve channel by weighting the
  squared Euclidean distance

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Decoding Conv. Code

• Hard or Soft decision demodulation
• Coherent OFDM system needs to estimate frequency
  response of system.
• Performance effect of weighting matters because
  of frequency diversity

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Viterbi Decoding

• Trellis, using state transition. For K memory
  element conv. Encoder, there are 2K states.

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Effect of Soft vs Hard decode
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Effect of Interleaving

• Interleaving improves BER for convolutionaly
  coded (r1/2)

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Coding Gain

• BER and PER w/ and w/out coding

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Decoding

• BER and PER improvement due to soft decoding

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Effect of metric weighting

• The performance of coding changes in fading
  channel.

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Next time

• Space Diversity (receiver, transmit diversity)
• HW due next week
• Read Chapter 3, (see below)
• Implement OFDM with 9Mbits/sec (1/3 code), and
  check performance with different rms delay spread
  values.
• (Use the code simulator.gz of OFDM Wireless Lans
  A Theoretical and Practical Guide (Sams
  Publishing)