Constant Envelope OFDM Phase Modulation - Dr. James R. Zeidler

3Figure 1.2, interference is caused from symbol to symbol. This intersymbol interference(ISI) is illustrated in Figure 1.3. For simplicity, g(t) is rectangular. The channel isrepresented by its time-variant impulse response h(τ, t), where τ is a propagation delayvariable. The received signal is expressed mathematically as [387, p. 97]r(t) = s(t) ∗ h(τ, t) + n(t)=∫ ∞−∞h(τ, t)s(t − τ)dτ + n(t),(1.2)where ∗ represents the linear convolution operator and n(t) is additive noise. The effect ofthe time-dispersive channel is shown to smear symbol 1 into symbol 2, therefore creatingintersymbol interference.s(t)r(t)Transmitter Channel Receivers(t)... symbol 1 symbol 2 ...0 T s 2T st|h(τ, t)|τ0r(t)ISIT s2T stFigure 1.3: Intersymbol interference.The severity of the ISI depends on the symbol period relative to the channel’s maximumpropagation delay, τ max . Consider transmitting the signal in (1.1) over the 2MHz channel in Figure 1.2. The signal bandwidth is roughly proportional to the symbolrate 1/T s Hz. Therefore making s(t) a 2 MHz signal, T s = (2 × 10 6 ) −1 = 0.5 µs.Since the maximum propagation delay of the channel is τ max = 14 µs, the ISI spansτ max /T s = (14 µs) / (0.5 µs) = 28 symbols. (For comparison, the ISI in Figure 1.3 spansless than one symbol.) Such severe ISI must be corrected at the receiver in order toprovide reliable communication.The traditional approach to combating intersymbol interference is with time-domainequalizers [421]. There are many types, ranging in complexity and in effectiveness.The optimum maximum-likelihood (ML) receiver is the most effective but is typicallyimpractical due to its high complexity, which grows exponentially with the ISI length.Linear equalizers are much simpler, having a complexity which grows roughly linearlywith ISI length, but perform much worse than the optimum receiver. Nonlinear decisionfeedback equalizers (DFEs) have similar complexity as the linear type and have betterperformance.