SYSC 4607 – Lecture 21 Outline

1. SYSC 4607 – Lecture 21 Outline • Review of Previous Lecture • ISI Countermeasures • Multicarrier Modulation • Overlapping Substreams • Fading Across Subcarriers • Discrete implementation of MCM • FFT Implementation of MCM- OFDM

2. Review of Previous Lecture • MIMO channels greatly improve capacity and performance through array gain, diversity gain, interference reduction, and spatial multiplexing. • MIMO channel can be decomposed into RH parallel SISO channels, where RH is rank of channel matrix H. • Capacity is the sum of capacities of parallel channels. • Greatest capacity improvement is obtained under rich scattering conditions (H full rank).

3. Review of Previous Lecture • MIMO capacity depends on the degree of channel knowledge at transmitter and receiver • For static channel with perfect CSI at TX and RX, power water-filling over space is optimal. • In fading, water-filling over space (based on short-term power constraint) or space-time (long-term constraint) • Without transmitter channel knowledge, capacity metric is based on an outage probability • MIMO can be used for antenna diversity. This leads to capacity versus diversity tradeoff

4. ISI Countermeasures • Equalization - Signal processing at receiver to eliminate ISI - Can be very complex at high data rates, and performs poorly in fast-changing channels • Multicarrier Modulation - Breaks data stream into narrowband lower-rate substreams, modulated onto narrowband flat-fading subchannels • Spread spectrum - Superimpose a wideband spreading sequence on top of data sequence, allows individual multipath components to be resolved and removed/combined

5. Flat and Frequency-SelectiveFading Channels

6. Multicarrier Modulation

7. Multicarrier ModulationNon-Overlapping Subchannels

8. Multicarrier Transmitter

9. Multicarrier Receiver

10. Drawbacks of Standard MCM

11. MCM - Overlapping Subchannels

12. MCM - Overlapping SubchannelsOrthogonality

13. MCM - Overlapping SubchannelsReceiver Structure

14. MCM - Overlapping SubchannelsSignal Recovery

15. Fading Across Subcarriers • Leads to different BERS due to different channel gains αi for different subcarrier bands. • Compensation techniques - Frequency equalization - Precoding - Coding across subcarriers - Adaptive loading (power and rate)

16. Subcarrier Fading - Compensations • Frequency equalization - Channel inversion at the receiver (1/αi) ■ Requires channel knowledge at receiver only ■ Impact of fading removed, but noise is proportionately enhanced • Precoding - Frequency equalization, with fading inverted at the transmitter ■ Requires transmitter knowledge of channel gains αi . ■ No noise enhancement ■ Obtaining accurate and frequent channel estimates difficult for high bit rate applications

17. Subcarrier Fading - Compensations • Coding Across Subcarriers - Coding with interleaving over time and frequency ■ Transmission of coded bits over different subchannels (bits in a codeword experience different fading) ■ Errors associated with few bad subchannels can be corrected ■ Takes advantage of frequency diversity inherent in multicarrier ■ Works best for uncorrelated subcarrier fading (small Bc) • Adaptive Loading (Power and Rate) - Adapts power and rate on subcarriers relative to their gain ■ Optimization similar to that of adaptive modulation in time (variable rate-variable power MQAM)

18. Multicarrier Modulation DiscreteImplementation based on DFT • Implementing N separate modulators and demodulators is very complex and costly • MCM can be effectively implemented using IFFT at transmitter and FFT at receiver • The IFFT shifts modulated symbols to desired subcarriers • A Cyclic Prefix (CP) is inserted in data blocks at transmitter to remove ISI between blocks. It also makes the linear convolution with the channel circular • Popularity of OFDM is due to the use of IFFT/FFT which have efficient implementations

19. Discrete Fourier Transform(DFT)

20. Discrete LTI System

21. Multipath-Induced ISI

22. ISI Removal - The Cyclic Prefix • A multipath channel results in ISI • The Cyclic Prefix (CP) is a block of symbols added at the beginning of each data block • CP converts a linear convolution channel into a circular convolution channel. It helps to remove the ISI. • Drawbacks of CP are a reduction in data rate due to the CP overhead and waste of power in the cyclic prefix samples. The latter can be avoided by transmitting all zeros (no power)

23. ISI Removal - The Cyclic Prefix

24. Receiver Data Blocks

25. Orthogonal Frequency DivisionMultiplexing (OFDM)

26. OFDM with IFFT/FFT

27. OFDM with IFFT/FFT

28. Main Points • ISI can be mitigated through equalization, multicarrier modulation, or spread spectrum • Multicarrier is alternative to equalization - Splits data stream into N flat fading substreams - Subchannels can overlap and still maintain orthogonality • Fading across subcarriers degrades performance. - Can be compensated through frequency equalization, precoding, or adaptive loading • Discrete implementation of MCM involves the use of DFT - Cyclic Prefix eliminates ISI and restores orthogonality at RX • OFDM is efficiently implemented using IFFT/FFT