9.1 Digital receivers: symbol-timing recovery for qpsk

Introduction

This receiver exercise introduces the primary components of a QPSK receiver with specific focus on symbol-timing recovery.In a receiver, the received signal is first coherently demodulated and low-pass filtered (see Digital Receivers: Carrier Recovery for QPSK ) to recover the message signals (in-phase and quadrature channels). The next step for the receiver is tosample the message signals at the symbol rate and decide which symbols were sent. Although the symbol rate is typicallyknown to the receiver, the receiver does not know when to sample the signal for the best noise performance. Theobjective of the symbol-timing recovery loop is to find the best time to sample the received signal.

illustrates the digital receiver system. The transmitted signal coherently demodulated with both a sineand cosine, then low-pass filtered to remove the double-frequency terms, yielding the recovered in-phase andquadrature signals, $\stackrel{}{s_I}(n)$ and $\stackrel{}{s_Q}(n)$ . These operations are explained in Digital Receivers: Carrier Recovery for QPSK . The remaining operations are explained in this module. Both branches are fed through a matched filter and re-sampled at the symbol rate. The matched filter is simply an FIR filter with an impulse responsematched to the transmitted pulse. It aids in timing recovery and helps suppress the effects of noise.

If we consider the square wave shown in as a potential recovered in-phase (or quadrature) signal ( i.e. , we sent the data $$

+1 -1 +1 -1

However, in the presence of noise, the received waveform may look like that shown in . In this case, sampling at any point other than the symboltransitions does not guarantee a correct data decision. By averaging over the symbol duration we can obtain a betterestimate of the true data bit being sent ( $+1$ or $-1$ ). The best averaging filter is the matched filter, which has the impulse response $u(n)-u(n-T_{\mathrm{symb}})$ , where $u(n)$ is the unit step function, for the simple rectangular pulse shape used in Digital Transmitter: Introduction to Quadrature Phase-ShiftKeying .

Note that in both cases the output of the matched filter has peaks where the matched filter exactly lines up with thesymbol, and a positive peak indicates a $+1$ was sent; likewise, a negative peak indicates a $-1$ was sent. Although there is still some noise in second figure, the peaks are relatively easy to distinguishand yield considerably more accurate estimation of the data ( $+1$ or $-1$ ) than we could get by sampling the original noisy signal in .