Rake receiver

If, in a mobile radio channel reflected waves arrive with small relative time delays, self interference occurs. Direct Sequence (DS) Spread Spectrum is often claimed to have particular properties that makes it less vulnerable to multipath reception. In particular, the rake receiver architecture allows an optimal combining of energy received over paths with different. It avoids wave cancellation (fades) if delayed paths arrive with phase differences and appropriately weighs signals coming in with different signal-to-noise ratios.

The rake receiver consists of multiple correlators, in which the receive signal is multiplied by time-shifted versions of a locally generated code sequence. The intention is to separate signals such that each finger only sees signals coming in over a single (resolvable) path. The spreading code is chosen to have a very small autocorrelation value for any nonzero time offset. This avoids crosstalk between fingers.In practice, the situation is less ideal. It is not the full periodic autocorrelation that determines the crosstalk between signals in different fingers, but rather two partial correlations, with contributions from two consecutive bits or symbols. It has been attempted to find sequences that have satisfactory partial correlation values, but the crosstalk due to partial (non-periodic) correlations remains substantially more difficult to reduce than the effects of periodic correlations.

The rake receiver is designed to optimally detected a DS-CDMA signal transmitted over a dispersive multipath channel. It is an extension of the concept of the matched filter.

Figure: Matched filter receiver for AWGN channel.

In the matched filter receiver, the signal is correlated with a locally generated copy of the signal waveform. If, however, the signal is distorted by the channel, the receiver should correlate the incoming signal by a copy of the expected received signal, rather than by a copy of transmitted waveform. Thus the receiver should estimate the delay profile of channel, and adapt its locally generated copy according to this estimate.

In a multipath channel, delayed reflections interfere with the direct signal. However, a DS-CDMA signal suffering from multipath dispersion can be detected by a rake receiver. This receiver optimally combines signals received over multiple paths.

Figure: Rake receiver with 5 fingers

Like a garden rake, the rake receiver gathers the energy received over the various delayed propagation paths. According to the maximum ratio combining principle, the SNR at the output is the sum of the SNRs in the individual branches, provided that

we assume that only AWGN is present (no interference)
codes with a time offset are truly orthogonal

Different reflected waves arrive with different delays. A rake receiver can detect these different signals separately. These signals are then combined, using the diversity technique called maximum ratio combining.
Signals arriving with the same excess propagation delay as the time offset in the receiver are retrieved accurately, because

This reception concept is repeated for every delayed path that is received with relevant power. Considering a single correlator branch, multipath self-interference from other paths is attenuated here, because one can choose codes such that

Rake Performance

A spread spectrum receiver with rake outperforms a simple receiver with a single correlator.

Rake Facts

In an interference-free system, each attenuation/amplification coefficient in the Rake receiver is proportional to the received amplitude in the corresponding "bin" of the delay spread.
One can compare the choice of the coefficients in the rake receiver with maximum ratio combining diversity receiver.
The rake receiver can also be used to support soft handovers in CDMA cellular networks.

The Number of Resolvable Paths

The order of diversity achieved by the rake receiver depends on the number of resolvable paths L with

             T_max
L  =  round(------)  + 1
             T_chip

where T_max is the maximum delay spread of the multipath channel.

Exercise

Use the Nyquist Theorem for bandpass signals to explain that only delays of integer multiples of the chip time are needed in a rake receiver.

Implementation Example for Broadband CDMA

The infopad research project implemented a broadband CDMA system for downlink transmission, with a monolithic radio receiver. The rake filtering is done at base band.

Novel receivers for CDMA

An overview of various techniques by Ahmet Tewfik: MP3 files: 1, 2, 3

Array Processing for CDMA by Peter Grant: html

Multiuser Detection by Sergio Verdu: Real-Audio

JPL's Wireless Communication Reference Website

Chapter: Analog and Digital Transmission Section: CDMA