Multi-user CDMA

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

2. Characterizing asynchronous CDMA system • Normalize power for each user: • Integrate and dump yields at the decision time: • Intended signal for the j:th user: • User interference (MAI):

3. Characterizing asynchronous CDMA system (cont.) • The AWGN component is at the the decision time • Sum effect of user interference is a function of (1) applied codes crosscorrelation, (2) modulation method, (3) user power balance, (4) code synchronization, (5) channel characteristics • The j:th user experiences the SNR:

4. Evaluating different interference and noise components for multiple access • The background noise power is filtered by the code matched filter or correlator: • The crossproduct component is averaged into zero. • The user interference assuming equal rates and code autocorrelations: where

5. SNR for the asynchronous CDMA • The user crosscorrelation power can be expressed by using the effective bandwidth: that evaluates for the code matched filter asand finally • Therefore the j:th user experiences SNR of Received power MAI component AWGN component

6. Perfect power control • Equal received powers for U users means that • Thereforeand the number of users is • Example: SNRO = 11.5 dBR=30 kb/s • Note that there exist the limit for the maximum number of users that is not a function of Eb/N0 where

7. Unequal received powers and 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 iswhere 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 node at the common reception point

8. The near-far effect in asynchronous CDMA • In order to have the required (SNR)0 it is therefore required that • Note that the near-far -effect is manifested here because just one sum term on the left side of this equation is adequate to fulfill the condition • Example: Assume that all but one transmitter have the same distance to the receiving node . The one transmitter has the distance • Assume further a=3.68, SNR=11.5 dB, Rb = 30 kb/s, Beff = 20 MHz and received Eb/N0= 12.5, now

9. Near-far effect (example cont.) • By using 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 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 realized in asynchronous CDMA-systems. (Closed and open loop power control.)

10. Multiple Access Interference (MAI) • 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 in wireless communications) • Also Near-far-effect has a tendency to increase MAI into harmful levels • Hence compensation of MAI would yields additional capacity. This can be achieved by • Code waveform design • Power control • FEC codes • Adaptivity: - spatial - frequency - time • Multiuser detection

11. Multi-user CDMA • The conventional detector • Mitigating the effect of MAI • Multi-user detection (MUD) limitations and potential benefits • Matrix-vector notations • Synchronous and asynchronous channels • Detector 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

12. Background • CDMA capacity is in great deal limited by multiple access interference (MAI) • MAI is introduced by • breaking down code orthogonality due to • code design • always by multipath propagation • other cells build up interference • Multiuser detection is a method by which MAI can be suppressed • Multiuser detection is computationally demanding, thus it has become applicable quite lately • WCDMA-system has a provision for using multiuser detection at base stations

13. Received signal • Assume • single path AWGN channel • perfect carrier synchronization • BPSK • Received signal is thereforewhere for K users • Note that there are PG chips/bit (PG: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. decision decision decision Conventional detection • 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

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

16. 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

17. Zero forcing equalizer for ISI cancellation • Classical technique to combat ISI is to use zero-forcing equalizer (ZFE) • Principle used also in decorrelating MUD • ZFE is a time domain linear filter (or convolver) whose discrete convolution sum can be required • to yield zero values outside of sampling instances • to be maximized at the sampling instant

20. 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, largest capacity requirements exist CONS:

21. Matrix-vector notation • Assume a three user synchronous system with the outputsthat is expressed by the matrix-vector notation as noise matched filter outputs data correlations between each pair of codes received amplitudes

22. The data-term and the MAI-term • Matrix R can be partitioned into two parts by settingand therefore MF outputs can be expressed as • Note that hence Q contains off-diagonal elements or R (or the crosscorrelations) • Therefore the term Ad contains decoupled data and QAd represents the MAI • Objective of all MUD schemes is to cancel out the MAI-term as effectively as possible (with respect of HW and computational efficiency)

23. 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 2 4 6 User 2

24. 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 can be utilized to alleviate computational difficulties

25. Maximum-likelihood sequence detection • Optimum multiuser detection uses maximum-likelihood principle: • The ML principle • has the optimum performance • has severe computational difficulties - In exhaustive search 2NK vectors to consider! (K users, N bits) • can be implemented by using Viterbi-decoder that reduces computations approximately to 215xN • 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

26. Decorrelating detector • The decorrelation detector applies the inverse of the correlation matrixand 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

27. Decorrelating detector properties summarized Advantages • 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 • Optimal near-far resistance metric • Noise enhancement • High computational complexity in inverting R Disadvantages

28. Minimum mean-square error (MMSE) detector • Based on solving MMSE optimization problem whereshould be minimized • This leads into solution • One notes that under high SNR this solution is the same as decorrelating receiver • This multiuser technique is exactly 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

29. Successive interference cancellation (SIC) • 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 MF user 1 To the next stage decision - +

30. - - - Parallel interference cancellation (PIC) • With equal weights for all stages the data estimates for each state are • Number of stages determined by required accuracy (Stage-by-stage decision variance can be monitored) spreader matched filter bank decisions and stage weights + amplitude estimation parallel summer

31. 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 • Linearly combining the soft-decision outputs of different stages of the PIC detector • noise correlations between stages can be used to cancel out each other improving performance greatly • 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

32. matched filter bank dec* - dec - - dec - - - dec Zero-forcing decision-feedback (ZF-DF) detector • An enhanced SIC technique consisting of • pre-whitening that removes noise correlations and partially removes signal correlations • SIC performed in the descending order of signal power • The pre-whitening is realized by decomposingwhere after *decision device

33. Some properties of ZF-DF detector • Pre-whitening can be shown to cause the first detected bit to contain no MAI • Under the assumption that all past decisions are correct, the ZF-DF eliminates all MAI and maximizes SNR. • ZF-DF principle can be used also to combat ISI • An important difficulty is is to calculate the whitening filter (FT)-1. This can be simplified similar techniques than the Polynomial expansion (PE) detector (next slide) • ZF-DF needs the estimates of received amplitudes • If the soft output of the decorrelating detector are used for amplitude estimation, ZF-DF performance equals decorrelating detector • If still improved amplitude estimates exists, ZF-DF performance can be even higher

34. 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

35. Summary of MUD techniques • MAI limits significantly performance of CDMA systems and enhances near-far effect • MAI can be compensated by using MUD-techniques • MUD is especially applicable in cellular uplink • Optimum MUD (maximum likelihood) is too complicated to realize, hence suboptimum techniques developed: • Linear • MMSE • PE • Subtractive • SIC • PIC • ZF-DF