Multi-user%20CDMA

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Multi-user CDMA

• Enhancing capacity of wireless cellular CDMA

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Topics Today

• Dealing without multi-user reception
  asynchronous CDMA
• SNR
• power balance - near-far effect
• Multi-user detection (MUD) classification and
  properties
• The conventional detector (non-MUD, denotations)
• Maximum likelihood sequence detection
• Linear detectors
• Decorrelating detector
• Minimum mean-square error detector
• Polynomial expansion detector
• Subtractive interference cancellation
• Serial and parallel cancellation techniques

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Asynchronous CDMA
voltage at the ID at the decision instant
signalvoltage
ISI noise voltage
signal power for the jth user

• The jth user experiences the SNR

channel noise
MAI
Integrate and dump receiver
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Practical CDMA receiver
Effective BW is defined by
for rectangular spectra

• Hence, SNR upper bound for the jth user is

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Perfect power control

• Equal received powers for U users means that
• Therefore the jth user SNR equalsand the
  number of users is
• where (for BPSK)
• Number of users is determined by
• channel AWGN level N0
• processing gain Lc
• received power Pr

Eb/No (SNR1/2)
AWGN level decreases
SNR1 received SNR without multiple access
interference
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Unequal received powers - the near-far -effect

• Assume all users apply the same power but their
  distance to the receiving node is different.
  Hence the power from the ith node iswhere d
  is the distance, and a is the propagation
  attenuation coefficient (a 2 for free space, in
  urban area a 35 )
• Express the power ratio of the ith and jth user
  at the common reception point
• Therefore, the SNR of the jth user is

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The near-far effect in asynchronous CDMA

• Grouping the previous yields condition
• Multiple-access interference (MAI) power should
  not be larger than what the receiver sensitivity
  can accommodate
• Note the manifestation of near-far -effect
  because just one larger sum term on the left side
  of the equation voids it
• Example Assume that all but one transmitter have
  the same distance to the receiving node. The one
  transmitter has the distance d1dj /2.5 and
  a3.68, SNR014, SNR125, Rb 30 kb/s, Beff
  20 MHz, then

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• By using the perfect power balance the number of
  users is
• Hence the presence of a single user so near has
  dropped the number of users into almost 1/3 part
  of the maximum number
• If this user comes closer thanall the other
  users will be rejected, e.g. they can not
  communicate in the system in the required SNR
  level. This illustrates the near-far effect
• To minimize the near-far effect efficient power
  control is should be adaptively realized in
  asynchronous CDMA-systems

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Fighting against Multiple Access Interference

• CDMA system can be realized by spreading codes
  having low cross -correlation as Gold codes
  (asynchronous usage) or Walsh codes (synchronous
  usage)
• Multipath channel with large delay spread can
  destroy code cross-correlation properties
• a remedy asynchronous systems with large code
  gain assume other users to behave as Gaussian
  noise (as just analyzed!)
• Additional compensation of MAI yields further
  capacity (increases receiver sensitivity). This
  can be achieved by
• Code waveform design (BW-rate/trade-off)
• Power control (minimizes near-far effect)
• FEC- and ARQ-systems
• Diversity-systems - Spatial - Frequency - Time
• multi-user detection

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MAI versus ISI (Inter-Symbolic Interference)

• Note that there exists a strong parallelism
  between the problem of MAI and that of ISI
• Hence, a number of multi-user detectors have
  their equalizer counter parts as
• maximum likelihood
• zero-forcing
• minimum mean square
• decision feedback
• General classification of multi-user detectors
• linear
• subtractive

Asynchronous channel of K-users behaves the same
way as a single user channel having ISI with
memory depth of K-1
This could be generated for instance by a
multipath channel having K-1 taps
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Maximum-likelihood sequence detection

• Optimum multi-user detection applies
  maximum-likelihood principle
• The ML principle
• has the optimum performance
• has large computational complexity - In
  exhaustive search 2NK vectors to be considered!
  (K users, N bits)
• requires estimation of received amplitudes and
  phases that takes still more computational power
• can be implemented by using Viterbi-decoder that
  is practically optimum ML-detection scheme to
  reduce computational complexity by surviving path
  selections
• We discuss first the conventional detector (by
  following the approach we already had to
  familiarize to denotations)

Considering the whole received sequence, find the
estimate for the received sequence that has the
minimum distance to the allowed sequences
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Formulation Received signal

• Assume
• single path AWGN channel
• perfect carrier synchronization
• BPSK modulation
• Received signal is thereforewhere for K users
• Note that there are Lc chips/bit (Lc processing
  gain)

is the amplitude
is the spreading code waveform
is the data modulation of the kth user
is the AWGN with N0/2 PSD
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Conventional detection (without MUD) for
multiple access

• The conventional BS receiver for K users consists
  of K matched filters or correlators
• Each user is detected without considering
  background noise (generated by the spreading
  codes of the other users) to be deterministic
  (Assumed to be genuine AWGN)

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Output for the Kth user without MUD

• Detection quality depends on code cross- and
  autocorrelation
• Hence we require a large autocorrelation and
  small crosscorrelation
• The output for the Kth user consist of the
  signal, MAI and filtered Gaussian noise terms (as
  discussed earlier)
• Received SNR of this was considered earlier in
  this lecture

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Matrix notations to consider detection for
multiple access

• Assume a three user synchronous system with a
  matched filter receiverthat is
  expressed by the matrix-vector notation as

noise
matched filter outputs
data
received amplitudes
correlations between each pair of codes
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The data-term and the MAI-term

• Matrix R can be partitioned into two parts by
  setting Note that hence Q contains
  off-diagonal elements or R (or the
  crosscorrelations)
• and therefore MF outputs can
  be expressed as
• Therefore the term Ad contains the decoupled data
  and QAd represents the MAI
• Objective of all MUD schemes is to cancel out the
  MAI-term as effectively as possible (constraints
  to hardware/software complexity and computational
  efficiency)

with
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Asynchronous and synchronous channel

• In synchronous detection decisions can be made
  bit-by-bit
• In asynchronous detection bits overlap and
  multi-user detection is based on taking all the
  bits into account
• The matrix R contains now partial correlations
  that exist between every pair of the NK code
  words (K users, N bits)

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Asynchronous channel correlation matrix

• In this example the correlation matrix extends to
  6x6 dimension
• Note that the resulting matrix is sparse because
  most of the bits do not overlap
• Sparse matrix - algorithms can be utilized to
  reduce computational difficulties (memory size
  computational time)

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Decorrelating detector

• The decorrelating detector applies the inverse of
  the correlation matrix to suppress MAIand the
  data estimate is therefore
• We note that the decorrelating detector
  eliminates the MAI completely!
• However, channel noise is filtered by the inverse
  of correlation matrix - This results in noise
  enhancement!
• Decorrelating detector is mathematically similar
  to zero forcing equalizer as applied to
  compensate ISI

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Decorrelating detector properties summarized

• PROS
• Provides substantial performance improvement over
  conventional detector under most conditions
• Does not need received amplitude estimation
• Has computational complexity substantially lower
  that the ML detector (linear with respect of
  number of users)
• Corresponds ML detection when the energies of the
  users are not know at the receiver
• Has probability of error independent of the
  signal energies
• CONS
• Noise enhancement
• High computational complexity in inverting matrix
  R

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Polynomial expansion (PE) detector

• Many MUD techniques require inversion of R. This
  can be obtained efficiently by PE
• For finite length message a finite length PE
  series can synthesize R-1 exactly. However, in
  practice a truncated series must be used for
  continuous signaling

Weight multiplication
Weight multiplication
Weight multiplication
matched filter bank
R
R
R
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Mathcad-example
series expansion of R-1 (to 2. degree)
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Minimum mean-square error (MMSE) detector

• Based on solving MMSE optimization problem
  withthat should be minimized
• This leads into the solution
• One notes that under high SNR this solution is
  the same as decorrelating receiver
• This multi-user technique is equal to MMSE linear
  equalizer used to combat ISI
• PROS Provides improved noise behavior with
  respect of decorrelating detector
• CONS
• Requires estimation of received amplitudes and
  noise level
• Performance depends also on powers of
  interfering users

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Successive interference cancellation (SIC)
MF user 1
To the next stage
decision
-

• Each stage detects, regenerates and cancels out a
  user
• First the strongest user is cancelled because
• it is easiest to synchronize and demodulate
• this gives the highest benefit for canceling out
  the other users
• Note that the strongest user has therefore no use
  for this MAI canceling scheme!
• PROS Small HW requirements and large performance
  improvement when compared to conventional
  detector
• CONS Processing delay, signal reordered if their
  powers changes, in low SNRs performance suddenly
  drops

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Parallel interference cancellation (PIC)
spreader
matched filter bank
decisions and stage weights

amplitude estimation
parallel summer

• With equal weights for all stages the data
  estimates for each stages are
• Number of stages determined by required accuracy
  (Stage-by-stage decision-variance can be
  monitored)

initial data estimates
minimization tends to cancel MAI
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PIC properties

• SIC performs better in non-power controlled
  channels
• PIC performs better in power balanced channels
• Using decorrelating detector as the first stage
• improving first estimates improves total
  performance
• simplifies system analysis
• Doing a partial MAI cancellation at each stage
  with the amount of cancellation increasing for
  each successive stage
• tentative decisions of the earlier stages are
  less reliable - hence they should have a lower
  weight
• very large performance improvements have achieved
  by this method
• probably the most promising suboptimal MUD

PIC variations
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Benefits and limitations of multi-user detection
PROS

• Significant capacity improvement - usually
  signals of the own cell are included
• More efficient uplink spectrum utilization -
  hence for downlink a wider spectrum may be
  allocated
• Reduced MAI and near-far effect - reduced
  precision requirements for power control
• More efficient power utilization because near-far
  effect is reduced
• If the neighboring cells are not included
  interference cancellation efficiency is greatly
  reduced
• Interference cancellation is very difficult to
  implement in downlink reception where, however,
  larger capacity requirements exist (DL traffic
  tends to be larger)

CONS