1. Enhancing capacity of wireless cellular CDMA
Multi-user CDMA
Enhancing capacity of wireless cellular CDMA

2. 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

3. Asynchronous CDMA The j:th user experiences the SNR:
voltage at the I&D* at the decision instant
signal voltage
ISI & noise voltage
signal power for the j:th user
The j:th user experiences the SNR:
channel noise
MAI
*Integrate and dump receiver

4. Practical CDMA receiver
Effective BW
is defined by:
LPF
local code
from channel
decision
phasing of
sampling
for rectangular
spectra:
Hence, SNR upper bound for the j:th user is

5. *SNR1: received SNR without multiple access interference
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* (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

6. 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 is the propagation attenuation coefficient (a = 2 for free space, in urban area a = 3…5 )
Express the power ratio of the i:th and j:th user at the common reception point
Therefore, the SNR of the j:th user is

7. 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 d1=dj /2.5 and a=3.68, SNR0=14, SNR1=25, Rb = 30 kb/s, Beff = 20 MHz, then

8. 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 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 should be adaptively realized in asynchronous CDMA-systems

9. 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

10. 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

11. 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

12. Formulation: Received signal
Assume
single path AWGN channel
perfect carrier synchronization
BPSK modulation
Received signal is therefore where 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 k:th user
is the AWGN with N0/2 PSD

13. 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)
decision

14. 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 (as discussed earlier)
Received SNR of this was considered earlier in this lecture

15. Matrix notations to consider detection for multiple access
Assume a three user synchronous system with a matched filter receiver that is expressed by the matrix-vector notation as
noise
matched filter outputs
data
correlations between each pair of codes
received amplitudes

16. 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

17. 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) 4 3 6 5 2 1
User 1
User 2
asynchronous ch.
synchronous ch.

18. 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)

19. Decorrelating detector
The decorrelating detector applies the inverse of the correlation matrix to suppress MAI and 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

20. 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

21. 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

22. Mathcad-example
= series expansion
of R-1 (to 2. degree)

23. Minimum mean-square error (MMSE) detector
Based on solving MMSE optimization problem with that 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

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: Small HW requirements and large 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 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: