Rake Demodulator:
It is named so, because it reminds the function of “Gardner Rake”.
The design of a rake receiver can be visualized as a series of time delayed correlator taps fed from a
common antenna. If each correlator tap is delayed to match the arrival of a particular transmitted
signal, then the outputs of each tap can be recombined in phase. Once an RF signal with a particular
travel time is locked onto by the correlator tap, an estimate of the gain or loss experienced by that
signal must be made. The weighting of the taps perform this gain normalization function. Once
adjusted, the outputs of each finger of the rake can be combined to form a better version of the
transmitted signal.
Fig 1: Optimum demodulator for wideband binary signals
The above diagram represents the optimum demodulator for wideband binary signals. Here we
consider two equal wideband binary energy signals 𝑠𝑙1 (𝑡) and 𝑠𝑙2 (𝑡). These two binary signals are
delayed at different times and multiplied with time-variant tap weights {Cn(t)}. Since the transmitted
signal is received from multiple paths with different delays, the Rake receiver uses this multipath
received signal to detect the signal efficiently. Wherein the received signal is correlated with multiple
delayed reference signals, thus for which ever delayed version of signal the received signal matches
and has highest SNR value we are able to acquire the transmitted signal.
Consider the below example to understand the working of Rake receiver, let us say that we have a
waveform which is represented as g1 and let the delayed version of g1 be represented as g2. Now at
the rake receiver, we will have the filter taps matched to g1 (i.e. g1*) and its delayed version g2 (i.e.
g2*). Thus if g1(t)is received, the signal at the summer will be maximum from upper arm as shown in
fig 3., such a combination of multiple arms is termed as a finger in this receiver. If g2(t) is received the
then summer will have maximum output from lower arm. Thus we will be able to detect g1(t) even
though it is delayed due to multipath effects. For each transmitted signal if a finger is used and the
one having the maximum value can be obtained by correlating it with filter matched to transmitted
signal for various delays. Other fingers may be having lower information, but this information can be
combined to get the maximum output at the summer thus enabling to detect signals by using
multipath property of the channel.
Fig 2: Two signals delayed by Δ𝑡
Fig 3: Detecting the waveform using matched filter and summing the signal amplitudes.
This we have done for single signal waveform, similarly we can place multiple fingers for each signal
waveform to get detect the signal at the receiver.
Now consider the demodulator in Fig 1, here we can see the two binary signals are delayed multiple
times by “1/W’ and multiplied by time-variant tap-weights {cn(t)} which forms a matched filter, and
the received signal is correlated with each delayed matched filter coefficients. The signal matching
the matched filter will have maximum output. Each correlator output is summed, thus we have two
decision making quantities U1 and U2. If U1 is maximum we say s1(t) is transmitted else s2(t) is
transmitted. Thus we will be able to detect the signal even in case of multipath channel effects.
Another approach is to use single delay line as shown in below figure, here the received signal is
delayed and correlated with the reference signal waveforms to make the decisions.
Fig 4: Single Delay Optimum Demodulator for Wideband Binary Signals
