Hi Miguel,
You're correct that the rake receiver combines multipath effects. If there is little or no multipath then a rake receiver is not necessary.
However, in any real world system a receiver needs to track timing offset with respect to the transmitter. To do this the receiver needs to correlate against the transmitted scrambling code at a series of lags to find the peak. The result of these correlations is the channel impulse response, so in reality implementing a rake receiver isn't much more difficult than a single path receiver.
There actually is a pilot "channel" on the uplink, just not a dedicated one. For the standard QPSK uplink transmission, the control information is on the Q (imaginary) axis (see 3GPP TS 25.213 section 4.2.1.1). Uplink control channel formatting varies (see 3GPP TS 25.211 Section 5.2.11), but at least some of the control bits in a frame are pilot bits. You can use these bits to derotate the data channel, similar to the way the CPICH is used on the downlink.
Furthermore your signal processing chain isn't correct. You need to first descramble, then despread, then you can use a QPSK slicer/demodulator. You might consider first implementing a UMTS downlink receiever as it's similar to the uplink, but a bit simpler.
Finally, if you plan on using this receiver to receive actual UMTS uplink signals keep in mind there are 2^24 possible codes (if the system is using long codes). If you don't know the code number, it will take a very long time to crunch through all the possibilities.
Good luck!
Michael Johnson
Software Radio Architect
Epiq Solutions
www.eqiqsolutions.com