Multiuser CDMA

1. 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. 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. Perfect power control • Equal received powers for U users means that • Therefore the j:th user SNR equalsand the number of users iswhere • Number of users is determined by • reception sensitivity Eb/No • code gain 2tmBeff • Note that reception sensitivityis 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 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 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 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. 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 thereforewhere 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. decision decision decision 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

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 signalsthat 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 2 4 6 User 2

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 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

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 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 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) • 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 - +

25. - - - Parallel interference cancellation (PIC) • 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) spreader matched filter bank decisions and stage weights + amplitude estimation parallel summer initial data estimates minimization tends to cancel MAI

26. 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

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: