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SYSC 4607 – Lecture 18 Outline. Review of Previous Lecture MIMO Systems Advantages of MIMO over SISO Parallel Decomposition of MIMO channels Capacity of MIMO Channels. Review of Previous Lecture Variable-Rate Variable-Power MQAM.
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SYSC 4607 – Lecture 18 Outline • Review of Previous Lecture • MIMO Systems • Advantages of MIMO over SISO • Parallel Decomposition of MIMO channels • Capacity of MIMO Channels
Review of Previous LectureSpectral Efficiency in Rayleigh Fading
Review of Previous Lecture • Adaptive MQAM uses capacity-achieving power and rate adaptation, with power penalty K. • Adaptive MQAM comes within 5-6 dB of capacity • Discretizing the constellation size results in negligible performance loss. • Constellations cannot be updated faster than 10s to 100s of symbol times: OK for most Dopplers. • Estimation error and delay can lead to irreducible error floors.
MIMO Principles • Array and diversity gains increase coverage and QoS • Multiplexing gain increases spectral efficiency • Co–channel interference is reduced and cellular capacity increases
MIMO Systems (Flat Fading) • MIMO systems have multiple transmit and receive antennas • With perfect channel estimates at Tx and Rx, decomposes into independent channels - RH -fold capacity increase over SISO system - Demodulation complexity reduction - Can also use antennas for diversity and beamforming - Leads to capacity versus diversity tradeoff in MIMO
MIMO Performance Improvements • MIMO results in four major Performance improvements: - Array Gain - Diversity Gain - Spatial Multiplexing Gain - Interference Reduction Gain • In general it is not possible to take advantage of all the above improvements due to Conflicting demands
MIMO Performance Improvements • Array Gain - Increase in average SNR due to coherent combining - Requires channel knowledge of transmitter and receiver - Depends on number of transmit and receive antennas • Diversity Gain - Diversity mitigates fading in wireless links - ‘MtMr’ links of independently faded channels can lead to MtMr-th order diversity as compared to SISO link (diversity order is slope of BER curve) - Can be achieved in the absence of channel knowledge at the transmitter by designing suitable transmit signals (space-time coding)
MIMO Performance Improvements • Spatial Multiplexing Gain - Transmit independent data signals from individual antennas - Receiver can extract different streams under uncorrelated fading channel conditions – rich scattering - A linear increase (in min(Mt, Mr)) in capacity for no additional power or bandwidth cost is obtained • Interference Reduction - Differentiation between the spatial signatures of the desired channel and co-channel signals is exploited to reduce interference - Requires knowledge of desired signal’s channel (spatial filtering) - Smart antenna system: Beam-forming at transmitter through switched beam or adaptive array - Aggressive frequency reuse and increase in multi-cell capacity.
Capacity of MIMO Systems • Capacity of multiple antennas at input or output (but not both) increases with the log of number of antennas, while MIMO capacity can increases LINEARLY with number of antennas. • For a full-rank channel matrix, RH - fold capacity increase is possible, where RH = min(Mt,Mr).
Spatial Multiplexing Gain • Transmitters use same frequency and modulation • Sub-streams are independent (no coding across the transmit antennas - each sub-stream can be individually coded) • Individual transmit powers scaled by 1/Mt , so the total power is kept constant • Channel estimation burst by burst using a training sequence • Requires near–independent channel coefficients
MIMO ChannelParallel Decomposition • Multiplexing gain is realized through parallel decomposition: MIMO channel is decomposed to RH parallel independent channels.
Capacity of MIMO Systems • Is the sum of capacity of parallel channels • Channel is static or fading • Channel knowledge: CSIR, CSIT, or Channel distribution only • For static channel with perfect channel knowledge at TX and RX, waterfilling over space is optimal power allocation • Similar idea in fading, based on short-term or long-term power constraint • Without channel knowledge, capacity is based on an outage probability
Main Points • 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. • Greatest capacity improvements are obtained under rich scattering conditions (H full rank). • Capacity depends on the degree of channel knowledge at transmitter and receiver
