Eugene Golovins Neco Ventura egolovins@crg.ee.uct.ac.za neco@crg.ee.uct.ac.za

1. Optimisation of the Pilot-to-Data Power Ratio in SM-MIMO-OFDM Systems with Low-Complexity Channel Estimation Eugene Golovins Neco Ventura egolovins@crg.ee.uct.ac.za neco@crg.ee.uct.ac.za

2. Outline -- Introduction -- System model (transceiver + channel) -- Low-complexity channel estimation -- PDR optimisation in numerical examples -- Conclusions

3. Introduction • OFDM is the most spectrally efficient block-wise modulation technology • OFDM capacity can be increased by extension to the spatial multiplexing multiple-input-multiple-output (SM-MIMO) framework • The overall performance (error rate) of the SM-MIMO-OFDM system depends on: • CSI acquisition at each spatial layer (SL) – Tx-Rx antenna link • SM data detection algorithm • PDR is known as a transceiver design parameter, which being optimal guarantees the least error rate

4. Methodology

5. Channel estimation problems • Practically reliable CSI acquisition methods rely on training-based CIR/CFR measurements • Optimal training scheme for the block-wise multicarrier systems is the frequency-separated constant-power pilot symbols, ideally equally spaced (but not always possible) • MIMO extension makes the low complexity of the channel estimation algorithm a crucial requirement towards hardware cost reduction • Performance of some channel estimation algorithms (e.g., optimal MMSE) depends on the channel, in particular its deterministic and statistical properties

6. MIMO detection challenges • Ensure that MIMO transceiver design guarantees non-correlatedness of channel response between different SLs (only under this condition capacity requirements are satisfied) • Performance is directly influenced by precision of channel estimates • Complexity is also an issue of concern • Optimal detector for the system with many antennas: V-BLAST architecture

7. Problem of research • What? • Under total transmit energy constraint there is a trade-off between boosting power of pilots to gain more accurate channel estimates and maintaining higher SNR at data subcarriers to minimise probability of detection error in the assumption of sufficiently reliable CSI • Why? • Optimal power allocation between pilot and data symbols ensures the best system performance for given configuration (taking into account block size, number of pilots, channel model order, number of antennas, SNR) • How? • Derive closed-form expressionof pilot-to-data power ratio (PDR)

8. Baseband SM-MIMO-OFDM system

9. Channel model (discrete-time, bandlimited) • Channel represents a set of uncorrelated links (SLs) defined for each TXa-RXa pair (homogeneity assumption) • Each individual SL is affected by: • dispersion (frequency selectivity) due to multipath propagation • interblock channel response variation (time selectivity) due to Doppler effect • Adopted multipath fading model – WSSUS block-wise stochastic process that specifies independently generated lowpass random variable sequences for each of K propagation paths at each SL

10. Transmit signal format • Pilots should be equipowered and equispaced for optimal performance • Empty symbols are necessary to decouple channel estimation process on different SLs

11. Low-complexity channel estimators • Intrablock estimators • compute channel response for each OFDM block individually • 2D estimators • exploit interblock correlation of channel response in addition to intrablock processing Pilot subcarrier Data subcarrier Frequency (subcarriers) N Time (OFDM blocks)

12. CLS estimator (intrablock)

13. Recursive CMMSE estimator (intrablock) CLS weighting Smoothing module

14. Recursive CLS-MMSE estimator (2D) CLS weighting Wiener filter-bank

15. Recursive CMMSE-MMSE estimator (2D) CLS weighting Wiener filter-bank Smoothing module

16. Case study • 64-subcarrier system with 16 pilots • Modelled CIR length equal to 16 samples • Equicomplex CMMSE and CLS-MMSE configurations • Channel.1: sample-spaced with 16 equipowered multipath components • Channel.4: non-sample-spaced with 3 equipowered multipath components

17. Summary of channel estimators • CLS • needs minimum information about channel (only CIR length) • attractive for the lowest-complexity solutions • exhibits worse performance than its counterparts • suitable for non-stationary (e.g., heterogeneous mobile) environments • CMMSE • requires info on CIR intrablock correlation and SNR • beneficial for sparse multipath channels • suitable for non-stationary environments characterised by invariant intrablock CIR correlation

18. Summary of channel estimators (cont’d) • CLS-MMSE • requires info on channel PDP and SNR • suffers from initialisation delay needed to fill up filter-bank buffer • designated to operate in stationary environments (e.g., fixed wireless or homogeneous vehicular with low to moderate speeds) • guarantees equally good performance gain for both sparse and dense multipath channels • CMMSE-MMSE • requires info on CIR intrablock correlation and SNR • shares same pros and cons as CLS-MMSE • improves performance in sparse multipath channels

19. PDR optimisation • Idea: express performance as seen at the output of cascade of two linear systems (channel estimator and data detector) • Use NMSE of ZF detection as a function for optimisation • Wherever the exact closed-form solution does not exist, find an approximate one – upper bound on optimal PDR • Derived analytical expressions reveal that (sub)optimal PDR is a function of: • total number of subcarriers • number of pilot subcarriers • number of Tx antennas • effective order of multipath model (CMMSE and CMMSE-MMSE) • order of Doppler model adopted for estimator design (2D only) • SNR at receiver input

20. Numerical examples • System configuration: • 64-subcarrier system with 8 pilots per Tx antenna • Modelled CIR length equal to 8 samples • 4 Tx antennas and 6 Rx antennas • operational SNR at receiver input 15 or 30 dB

21. SNR gain of detector output in case of CMMSE estimator • Channel.1: sample-spaced with 8 equipowered multipath components • Channel.2: non-sample-spaced with 3 equipowered multipath components • Channel.3: sample-spaced with 8 multipath components characterised by exponential power decay of factor 2

22. SNR gain of detector output in case of CLS-MMSE estimator • Channel.1: non-sample-spaced with 3 equipowered multipath components • Channel.2: sample-spaced with 8 multipath components characterised by exponential power decay of factor 2

23. SNR gain of detector output in case of CMMSE-MMSE estimator • Channel.1: non-sample-spaced with 3 equipowered multipath components • Channel.2: sample-spaced with 8 multipath components characterised by exponential power decay of factor 2

24. Conclusions • Suboptimal PDR has been derived in the closed form for SM-MIMO-OFDM system with various channel estimation algorithms and pilot patterns • These results are useful for reconfigurable transceiver design to meet channel requirements (optimised PDR is dependent on operational mode)

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