1. Enhancing capacity of wireless cellular CDMA
Multiuser CDMA
Enhancing capacity of wireless cellular CDMA

2. Topics Today Asynchronous CDMA SNR power balance
The conventional detector
Multi-user detection (MUD) classification and properties
Maximum likelihood sequence detection
Linear detectors
Decorrelating detector
Minimum mean-square error detector
Polynomial expansion detector
Subtractive interference cancellation
Serial and parallel cancellation techniques
Zero-forcing decision feedback detector

3. user cross correlation
Asynchronous CDMA
Integrate and dump (I&D) yields at the decision time:
I&D signal for the j:th user:
I&D user interference (MAI):
I&D channel noise:
user cross correlation
ref: G.R. Cooper, D. McGillem: Modern Communications and Spread Spectrum

4. SNR for the j:th user Sum effect of user interference is a function of
applied codes (crosscorrelation)
modulation method
user power balance
code synchronization
channel characteristics
The j:th user experiences the SNR
signal
ISI & noise

5. The j:th user experiences SNR of
Here the effective bandwidth Beff is defined by (GS(f) equals spread spectrum signal magnitude spectra)
Beff is about the same as pulse BN for strictly band limited signal
for BPSK 2tmBeff equals processing gain
Pj :received power
MAI component
AWGN component

6. reception sensitivity
Perfect power control
Equal received powers for U users means that
Therefore the j:th user SNR equals and the number of users is where
Number of users is determined by
reception sensitivity Eb/No
code gain 2tmBeff
Note that reception sensitivity is comparable to SNR1
reception sensitivity

7. 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 i:th node is where d is the distance, and a: propagation attenuation coefficient, a = 2 for free space
In multipath environment in UHF range (300 MHz… 3 GHz), a = 3 … 4
Express the power ratio of the i:th and j:th user at the common reception point

8. The near-far effect in asynchronous CDMA
Solving from the previous the MAI power yields
This means in practice that the MAI power should not be larger than what the receiver can accommodate
Note that the near-far -effect is manifested here because just one sum term on the left side of this equation voids it
Example: Assume that all but one transmitter have the same distance to the receiving node. The one transmitter has the distance d1=dj /2.5 and a=3.68, SNR0=14, SNR1=25, Rb = 30 kb/s, Beff = 20 MHz, then

9. By using the perfect power control the number of users is
Hence the presence of this single user so near has dropped the number of users into almost 1/3 part of the maximum number
If this user comes closer than all 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 realized in asynchronous CDMA-systems. (Closed and open loop power control)

10. Fighting against Multiple Access Interference
For multiple access codes often have relatively good crosscorrelations as Gold codes (asynchronous usage) or Walsh codes (synchronous usage)
Quite often, however, correlation properties destroyed by multipath (as happens often in wireless communications)
Also Near-far-effect has a tendency to increase MAI into harmful levels
Hence compensation of MAI would yield additional capacity. This can be achieved by
Code waveform design
Power control
FEC codes
Adaptivity: - spatial - frequency - time
Multiuser detection

11. MAI versus ISI (Inter-Symbolic Interference)
Multiuser detection main classification:
linear
subtractive
Note that there exist a strong parallelism between the problem of MAI and that of ISI:
For this reason a number of multiuser detectors have their equalizer counter parts as:
maximum likelihood
zero-forcing
minimum mean square
decision feedback
Asynchronous K-user channel can be modeled with a single user ISI channel with memory of K-1

12. Maximum-likelihood sequence detection
Optimum multiuser detection uses maximum-likelihood principle:
The ML principle
has the optimum performance
has severe computational complexity - In exhaustive search 2NK vectors to consider! (K users, N bits)
can be implemented by using Viterbi-decoder that reduces computations
requires estimation of received amplitudes and phases that takes still more computational power
Considering the whole received sequence find the sequence estimate that has the minimum distance to the received sequence

13. Received signal Assume single path AWGN channel
perfect carrier synchronization
BPSK modulation
Received signal is therefore where for K users
Note that there are Gp chips/bit (Gp:processing gain)
is the amplitude
is the signature code waveform
is the modulation of the k:th user
is the AWGN with N0/2 PSD

14. Conventional detection (without MUD)
The conventional BS receiver for K users consists of K matched filters or correlators:
Assumed that background noise is Gaussian, each user is detected without considering deterministic noise of the other users
decision

15. Output for the K:th user without MUD
Detection quality depends on code cross- and autocorrelation
Hence we require a large autocorrelation and small crosscorrelation
The output for the K:th user consist of the signal, MAI and filtered Gaussian noise terms
Received SNR of this was considered earlier in this lecture

16. Multiple access notations
Assume a three user synchronous system with the matched filter received signals that is expressed by the matrix-vector notation as
noise
matched filter outputs
data
correlations between each pair of codes
received amplitudes

17. 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)

18. Asynchronous and synchronous channel
In synchronous detection decisions can be made bit-by-bit
In asynchronous detection bits overlap and multiuser detection is based on taking all the bits into account
The matrix R contains now the partial correlations that exist between every pair of the NK code words (K users, N bits)
User 1 1 3 5
User 1 1 3 5
User 2 2 4 6
User 2 2 4 6

19. 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 alleviate computational difficulties

20. Decorrelating detector
The decorrelation detector applies the inverse of the correlation matrix and the data estimate is therefore
We note therefore that the decorrelating detector completely eliminates the MAI
Note that the noise is filtered by the inverse of correlation matrix - This results in noise enhancement
Mathematically decorrelating detector is similar to zero forcing equalizer used to compensate ISI

21. 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 R

22. 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

23. Minimum mean-square error (MMSE) detector
Based on solving MMSE optimization problem where should be minimized
This leads into solution
One notes that under high SNR this solution is the same as decorrelating receiver
This multiuser 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
Performance depends on powers of interfering users

24. 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: minimal HW and significant performance improvement when compared to conventional detector
CONS: Processing delay, signal reordered if their powers changes, in low SNR:s performance suddenly drops

25. 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

26. PIC properties PIC variations
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

27. Benefits and limitations of multiuser 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 where, however, larger capacity requirements exist (DL traffic larger)
CONS: