Adaptive Modulation and Coding Master Universitario en Ingeniería de Telecomunicación I. Santamaría Universidad de Cantabria
Contents Introduction Rate adaptation Power adaptation Adaptive coding Hybrid techniques Adaptive Modulation and Coding 0/17
Estimación del canal Canal de retorno Adaptive Modulation and Coding 1/17 Introduction Goal: to adapt the transmitted power, constellation size, and/or coding technique in order Esquema to maintain general a given fixed instantaneous BER for each symbol while maximizing the average data rate
System model SISO system with symbol period T s and thus symbol rate R s = 1/T s We assume ideal Nyquist pulses so the bandwidth is also W = 1/T s We assume a flat fading channel in which each channel use corresponds to one symbol The channel power gain is g[n] = h[n] 2, with pdf p(g) (exponential for a Rayleigh channel) The noise is AWGN with psd N 0 /2 The average transmitted power is P, and hence the instantaneous SNR is γ[n] = Pg[n] N 0 W Adaptive Modulation and Coding 2/17
The average SNR is γ = PE[g] N 0 W We estimate the power gain at time n, ĝ[n], (or received SNR ˆγ[n]) and then adapt the data rate R[n], coding parameters C[n] and transmit power P[n] Adaptive Mod. Power Adapt. & Coding g[n] P[n] R[ n], C[ n] r[n] Demod & Decoding gˆ [ n] or ˆ[ γ n] gˆ [ n] or ˆ[ γ n] Channel Est. We assume that the estimate is perfect and that the feedback channel involves no delay: ĝ[n] = g[n], ˆγ[n] = γ[n] Adaptive Modulation and Coding 3/17
For M-ary modulations R[n] = log(m[n])/t s bps, where M[n] is the constellation size The spectral efficiency (note that it might change with time) is R[n]/W bps/hz For simplicity, and to stress the dependence of the rate, coding, and transmitted power with the SNR, we will omit the time index and denote P(γ), R(γ), C(γ) The rate of channel variation dictates how often the Tx must adapt its transmission parameters To further proceed we need to review the BER expressions for the AWGN as a function of the SNR = γ for different constellations Adaptive Modulation and Coding 4/17
BER expressions for the AWGN channel We assume that the average symbol energy is divided equally among all bits and that Gray encoding is used, so P b P s log(m) BPSK QPSK MPSK ( ) P b = P s = Q 2γ P s = 2Q ( γ) ( ) P s = 2Q 2γ sin(π/m) Adaptive Modulation and Coding 5/17
MPAM P s = ( ) 2(M 1) 6γ M Q M 2 1 MQAM P s = 4Q ( ) 3γ M 1 A useful approximation for the BER for MQAM modulations is P b 0.2e 1.5γ/(M 1), which allows us to obtain M as a function of the target P b Adaptive Modulation and Coding 6/17
Rate adaptation R(γ) is changed depending on the received SNR γ. How? 1. We fix the modulation (e.g., QPSK) and change the symbol period difficult to implement 2. We fix the symbol rate and change the constellation size or modulation type much simpler to implement, preferred option The modulation parameters are typically fixed over a block of symbols or frame The goal os to maintain a minimum BER: each constellation is selected for a range of values of γ Adaptive Modulation and Coding 7/17
Example An adaptive modulation system with a target Pb = 10 3, uses two modulation formats: QPSK and 8-PSK. If the target P b cannot be met, no data is transmitted. Find the range of SNR (γ) values associated to the 3 possible transmission schemes (8PSK, QPSK, and no transmission) Find the average spectral efficiency of the system, assuming a Rayleigh fading channel with γ = 20dB Adaptive Modulation and Coding 8/17
Continuous power adaptation P(γ) is changed depending on the received SNR γ The goal is to maintain a fixed BER or, equivalently, a constant received SNR We ve seen that the solution is channel inversion, which converts the fading channel into an equivalent fixed-snr AWGN channel P(γ) = β h 2 = β γ where β is the constant (target) received SNR The average power constraint implies that β P(γ)f (γ)dγ = γ f (γ)dγ = P The constant SNR achieved with channel inversion is β = P/E[1/γ] Adaptive Modulation and Coding 9/17
Suppose we have a target BER of P b, and we use a fixed modulation. Then, if the value of β (constant SNR) needed to meet that target is greater than P/E[1/γ] then this target cannot be met Remember that for a Rayleigh channel 1/E[1/γ] = and no BER target can be met A more practical alternative was truncated channel inversion { 0, γ < γ0, P(γ) = β γ, γ γ 0. where the cutoff value γ 0 can be based on a desired outage probability P out = Prob(γ γ 0 ) or on a desired target BER The constant SNR achieved when the channel is in use is β = P γ 0 1 γ f (γ)dγ Adaptive Modulation and Coding 10/17
Example Find the power adaptation for BPSK modulation that maintains a fixed P b = 10 3 in non-outage for a Rayleigh fading channel with γ = 10dB. The average power is P = 1 W. Find the resulting outage probability. Adaptive Modulation and Coding 11/17
Discrete power adaptation For channel inversion or truncated channel inversion we assume a continuous power variation, but sometimes only a discrete set of power values is possible at the Tx side P Tx = {0, P 1,..., P Np } where P Tx = 0 means no transmission, and P 1 >... > P Np The solution in this case consists of discretizing the fading states of the channel and assign to each channel state a transmitted power γ γ 3 γ 2 γ 1 P 3 P 2 P 1 = P max 0 Decreasing power P3, P2, P( γ ) = P1, 0, γ γ < 3 γ γ < γ 2 γ γ < γ 1 0 γ < γ 2 1 3 Adaptive Modulation and Coding 12/17
Discrete power adaptation For a given M-ary modulation (fixed), the levels are chosen to guarantee the target BER: P b ( ) Pn γ n BER = P b, n = 1,..., N p N 0 W γ n = N 0W P n BER 1 (P b ), n = 1,..., N p The average transmitted power is N p P = P n Prob(S n ), Prob(S n ) = n=1 γn+1 The spectral efficiency is (1 Prob(E 1 )) log(m) γ n p(γ)dγ Adaptive Modulation and Coding 13/17
Example Consider a transmitter with a set of discrete powers P Tx = {0, 0.1W, 0.05W, 0.01W } The transmitter uses QPSK, the bandwidth is W = 1 MHz, and N 0 = 10 9 W/Hz. The channel is Rayleigh with γ = 5dB. 1. Find the rule to assign the power levels as a function of the channel states to maintain a fixed P b = 10 3. 2. Find the probability of no transmission. 3. Find the average transmitted power. Adaptive Modulation and Coding 14/17
Adaptive coding In adaptive coding, different channel codes,c(γ), are used to provide different amounts of channel protection against errors to the transmitted bits Intuition: stronger error protection should be provided when γ is small, whereas a weaker coder should be used when γ is large Adaptive coding is typically achieved by puncturing: not transmitting certain coded bits in convolutional encoders Adaptive Modulation and Coding 15/17
Hybrid techniques Hybrid techniques can adapt multiple parameters of the transmission scheme: rate, coding scheme, power, and even the target BER Typical examples include Rate and power adaptation Adaptive modulation and coding (MCS) Adaptive Modulation and Coding 16/17
Adaptive Modulation and Coding 17/17