0.9 Carrier recovery

The current layer describes all the practical fixes that are required in order to create a workable radio.One by one the various pragmatic problems are studied and solutions are proposed, implemented, and tested. These include fixesfor additive noise, for timing offset problems, for clock frequency mismatches and jitter, and for multipath reflections.The order in which topics are discussed is the order in which they appear in our receiver.

A man with one watch knows what time it is. A man with two watches is never sure.

—Segal's law

[link] shows a generic transmitter and receiver pair that emphasizes the modulation and corresponding demodulation.Even assuming that the transmission path is ideal (as in [link] ), the signal that arrives at the receiver is a complicatedanalog waveform that must be downconverted and sampled before the message can be recovered.For the demodulation to be successful, the receiver must be able to figure outboth the frequency and phase of the modulating sinusoid used in the transmitter, aswas shown in [link] and [link] and graphically illustrated in Figures  [link] and [link] . This chapter discusses a variety of strategiesthat can be used to estimate the phase and frequency of the carrier and to fix the gain problem(of [link] and [link] ) and the problem of vanishing amplitudes(in [link] and [link] ).This process of estimating the frequency and phase of the carrier is called carrier recovery .

[link] shows two downconversion steps: one analog and one digital. In a purely analog system,no sampler or digital downconversion would be needed. The problem is that accurate analog downconversion requires highly precise analogcomponents, which can be expensive. In a purely digital receiver, the sampler would directly digitize the received signal,and no analog downconversion would be required. The problem is that sampling this fast can be prohibitively expensive.The happy compromise is to use an inexpensive analog downconverter to translate to some lower intermediate frequency, where it ispossible to sample cheaply enough. At the same time, sophisticated digital processing can be used to compensate for inaccuracies inthe cheap analog components. Indeed, the same adaptive elements that estimate and remove the unknown phase offset betweenthe transmitter and the receiver automatically compensate for any additional phase inaccuracies in the analog portion of the receiver.

Normally, the transmitter and receiver agree to use a particular frequency for the carrier, and in an ideal world,the frequency of the carrier of the transmitted signal would be known exactly.But even expensive oscillators may drift apart in frequency over time, and cheap (inaccurate) oscillatorsmay be an economic necessity. Thus, there needs to be a way to align the frequency of the oscillator at the transmitter with thefrequency of the oscillator at the receiver. Since the goal is to find the frequency and phase of a signal,why not use a Fourier Transform (or, more properly, an FFT)? "Phase and Frequency Estimation via an FFT" shows how to isolate a sinusoid that is at twice the frequency of the carrierby squaring and filtering the received signal. The frequency and phase of this sinusoid can then be found in astraightforward manner by using the FFT, and the frequency and phase of the carrier can then be simply deduced.Though feasible, this method is rarely used because of the computational cost.