ELEC E721: Communication Theory Lecture 7: Adaptive modulation and coding
Adaptive modulation and coding (1) Change modulation and coding relative to fading AMC enable robust and spectrally efficient transmission over time varying radio channels The basic premuse is to estimate the channel at Rx and feed this estimate back to TX in order to adapt the transmission scheme to the channel state.
Adaptive modulation and coding (2) Modulation and coding techniques that don t adapt to fading conditions require a fixed link margin to maintain an acceptable performance when the channel quality is poor. These systems are designed for worst case channel conditions
Requirements Feedback path between Tx and Rx, which may be not feasible for some systems AMC perform poorly for fast changing channels Hardware constraints may dictate how often Tx may change its rate and/or power Limits the performance gains of AMC
Adaptive transmission system(1) System model Decoder ŵ w Encoder Power control x i g i n i y i Channel estimator ĝ i Transmitter Delay Feedback Channel Receiver
Assumptions (1) Linear modulatin where the adaptation takes place at a multiple of the symbol rate Rs 1/ Ts. Ideal Nyquist filter ( h t) sinc( t / T )). ( s Flat fading radio channel with the channel use at t nt s Stationary and ergodic power gain with the PDF p(g) Feedback path doesn t introduce errors g i
Assumptions (2) n / 2 AWGN with the power spectral density i N The average transmit power P ~ The signal bandwidth B 1/ T s The average channel gain g The instantaneous receiver SNR i Pg i / N B with the distribution p( ) ~
Parameters to adapt: Constellation size/symbol time Transmit power Instantaneous BER Coding rate/scheme Only 1-2 degrees of freedom needed for good performance Optimization criterions: Maximize throughput Minimize average power Minimize average BER
Adaptive techniques 1. Variable rate techniques R Data rate is varied depending on the channel gain : either by fixing the symbol rate Rs 1/ Ts and using multiple modulation schemes or constellation sizes, or by fixing the modulation and changing the symbol rate. The former technique is easier to implement. These methods are used in current systems (GSM, IS 136 EDGE system, 812.11a wireless LANs) If a discrete set of modulation types or conslellation sizes are used, each value of is mapped to one of the possible modulation schemes. This is done to maintain the BER below a given value.
Variable rate techniques: Example Task Adaptive modulation system uses QPSK and 8 PSK Target BER is Pb 1 3 If neither scheme achieves the target BER, no data is transmitted Find the range of values associated with 3 possible transmission schemes Find the average spectral efficiency over Rayleigh fading with 2dB
Solution (1) QPSK: P b Q, (1.85)1.35 db 8 PSK: No transmission if 1.35 db 3 Pb 1 P b.666q 2 sin, (3.1)14. 79 db 8 3 Pb 1 Average rate R / B log2 4 2 QPSK bps/hz. Fraction of time when QPSK is used P QPSK 3.1 1.85 1 1 exp( /1) d.157
Solution (2) 8 PSK R / B log2 8 3 bps/hz. Fraction of time when 8 PSK is used QPSK 1 1 3.1 exp( /1) d.74 The average spectral efficiency P 3.74 2.157 2.534 bps/hz
Variable power techniques Water filling Channel inversion The goal to compensate for SNR variations due to fading, i.e. to maintain a fixed error probability a constant received SNR. The power adaptation transforms a fading channel into AWGN channel. P ~ P P ~ P p d / p d 1 1/ E 1/
Truncated channel inversion TCI P ~ P /,, The cut off value is defined on the basis of a desired outage probability or on a desired target BER above a cutoff.
Variable error probability The instantaneous BER is adapted subject to an average BER constraint Pb P b p d In adaptive modulation, error probability is typically adapted along with some other form of adaptation such as constellation size or modulation type.
Variable Rate Variable Power M QAM (1) P b.2exp 1.5 /( M 1) Consider adapting the transmit power S( ) relative to, subject to the average power constraint S and P an instantaneous BER constraint b P. b The received SNR is then S ( ) / S
Variable Rate Variable Power M QAM (2) M 1.5 S 1 1 K ln 5P S b S S K 1.5 ln 5 P b 1 E log2 M log21 KS S p d p S( ) S
Variable Rate Variable Power M QAM (3) Adaptive Rate and Power Schemes The power adaptation policy where is the optimized cut off fade depth below which the channel is not used. It must satisfy the power constraint: K K K S S /, /, / 1/ K d p K K / 1 K /
Variable Rate Variable Power M QAM (5) Adaptive Rate and Power Schemes Corresponding average spectral eviciency is R B K p log 2 / K d The effective power loss of K for adaptive M QAM as compared to the capacity achieving scheme. If the capacity of a fading channel is R bps/hz at SNR, uncoded adaptive MQAM requires a received SNR of / K to achieve the same rate. The power loss K is independent of the fading distribution.
Variable Rate Variable Power MQAM Rayleigh fading (6)
Variable Rate Variable Power MQAM (7) Log normal shadowing ( 8dB )
Channel Inversion with Fixed Rate We apply channel inversion power adaptation to maintain a fixed received SNR. We transmit a single fixed rate M QAM that achieves the target P b. The spectral efficiency under the channel inversion P (with the power adaptation 1 is P E1/ R B log2m log2 1 ln 1.5 5P E1/ b
Truncated Channel Inversion Max spectral efficiency R B max log 1 1.5 2 ln5p E 1/ b p