McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. The CDMA Principle The CDMA Principle D+E+G E+F+H F+G+I G+H+J H+I+K I+J+L J+K+M Three Rake Fingers A+B+D B+C+E C+D+F D+E+G E+F+H F+G+I G+H+J +C+D+F +D+E+G +E+F+H +F+G+I +G+H+J +H+I+K +I+J+L +D+E+G +E+F+H +F+G+I +G+H+J +H+I+K +I+J+L +J+K+M 9D+6x 9E+6x 9F+6x 9G+6x 9H+6x 9I+6x 9J+6x Figure 8.7 Rake filter reconstructing the signal. cussion, an adaptive matched filter. Each of the representations of the signal in the rake filter is called a finger of the rake. It is a nice mathematical result that the time reverse of the delay spread is, in fact, the optimal receiver for the multipath radio channel. In Fig. 8.7 we show a three-finger rake receiver recombining the three paths in Fig. 8.6. Consider the E chip leaving the transmitter. The three E-chip arrivals at the receiver are B + C + E, D + E + G, and E + F + H. The rake receiver combines these three triple-chip sums to get (B + C + E) + (D + E +G) + (E + F + H), equal weight for equal signal paths in this example. This works out to 3E + B + C + D F + H. The sum of the three received chips generates the desired chip with triple amplitude and six time sidelobe cross-terms. Triple amplitude is a ninefold power increase, so the total result of multipath and rake filter is nine signal units and six time-shifted units. 8 This is a 40 percent loss of S/N or Eb/No, a 2-dB loss. In this example, the rake filter re- covers 3 dB of the damage caused by multipath. In our example we knew that the delay was spread over three chips. How does an adaptive matched filter figure out the delay spread SO that it can time-reverse it? The receiver measures the signal over many chips and does a mathematical maximization of signal strength. In the forward direction, the adaptive matched filter of the user ter- minal uses the known characteristics of the pilot signal. When the results from the adaptive filter match the pilot signal as closely as possible, they are also matching the da