Multi-user CDMA

1. 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 voltage at the I&D* at the decision instant signalvoltage 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. from channel LPF decision phasing of sampling local code Practical CDMA receiver Effective BW is defined by: • Hence, SNR upper bound for the j:th user is for rectangular spectra:

5. Perfect power control • Equal received powers for U users means that • Therefore the j:th user’s SNR equalsand the number of users is • where* (for BPSK) • Number of users is limited 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 iswhere 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 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

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 provided transmitted symbols equal alike • 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 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 k:th user is the AWGN with N0/2 PSD

13. decision decision decision Conventional detection (without MUD) for multiple access • The conventional DS receiver for K users consists of K matched filters or correlators: • Each user is detected without considering backgroundnoise (generated by the spreading codes of the other users) to be deterministic (Assumed to be genuine AWGN)

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 (small ISI) • 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 receiverthat 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 ch. synchronous ch. User 1 1 3 5 User 1 1 3 5 User 2 2 4 6 2 4 6 User 2 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)

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 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

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 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

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: 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 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 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: