Diversity Technique

Diversity exploits the random nature of radio propagation by finding independent (or at least highly uncorrelated) signal paths for communication. The diversity concept can be explained simply. If one radio path undergoes a deep fade, another independent path may have a strong signal. By having more than one path to select from, both the instantaneous and average SNRs at the receiver may be improved, often by as much as 20dB to 30dB.

There are two types of fading, one is small-scale fading and the other is large-scale fading. Small-scale fades are characterized by deep and rapid amplitude fluctuations which occur as the mobile moves over distances of just a few wavelength. These fades are caused by multiple reflections from the surroundings in the vicinity of the mobile. In order to prevent deep fades from occurring, microscopic diversity techniques can exploit the rapidly changing signal. For example, if two antennas are separated by a fraction of a meter, one may receive a null while the other receives a strong signal. By selecting the best signal at all times, a receiver can mitigate small-scale fading effect.

Large scale fading is caused by shadowing due to variations in both the terrain profile and the nature of the surrounding. By selecting a base station which is not shadowed when others are, the mobile can improve the average SNR, this is called macroscopic diversity, since the mobile is taking advantage of large separations(the macro system differences) between the serving base stations.

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Derivation of Selection Diversity Improvement

Consider M independent Rayleigh fading channels available at a receiver, assume each channel has the same average SNR given by

                                                                          (1-3)

where we assume

If each channel has an instantaneous , then the PDF of  is

                                                                      (1-4)

where  is the mean SNR of each channel.

The probability that a channel has a instantaneous SNR less than  is

                                                            (1-5)

Then the probability that all M independent diversity channels SNR are less than  is

                                        (1-6)

The probability that  is given by

                                            (1-7)

the PDF of  is

                                                     (1-8)

Then the mean SNR  may be expressed as

                                    (1-9)

where . Equation (1-9) is evaluated to yield the average SNR improvement offered by selection diversity

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Derivation of Maximal Ratio Combining Improvement

In maximal ration combining, the resulting signal envelope applied to the detector is

where  is the signal voltage from branch I, and  is the gain of each branch.

Assume that each branch has the same average noise power N, the total noise power applied to the detector is

the SNR  applied to the detector is given by .

Using Chebyshev inequality,  is maximized when

Thus the SNR out of the diversity combiner is simply the sum of the SNRs in each branch.

Time diversity repeatedly transmits information at time spacings that exceed the coherence time of the channel, so that multiple repetitions of the signal will be received with independent fading conditions, thereby providing for diversity. One modern implementation of time diversity involves the use of the RAKE receiver for spread spectrum CDMA.

Often the time-varying impulse response channel model is too complex for simple analysis. In this case a discrete time approximation for the wideband multipath model can be used. This discrete-time model is especially useful in the study of spread spectrum systems and RAKE receivers. This discrete-time model is based on a physical propagation environment consisting of a composition of isolated point scatterers, as shown in Figure 1-5. In this model, the multipath components are assumed to form subpath clusters: incoming paths on a given subpath with approximate delay  are combined, and incoming paths on different subpath clusters with delaysandwhere can be resolved, wheredenotes the signal bandwidth.

                      Point Scatterer Channel Model 

For a fixed t, the time axis is divided into  equal intervals of duration T such that  where  is the rms delay spread of the channel, which is derived empirically. The subpaths are restricted to lie in one of thetime interval bins, as shown in Figure 3.17. The multipath spread of this discrete model is, and the resolution between paths is . This resolution is based on the transmitted signal bandwidth: . The statistics for the nth bin are that , 1 ≤ n ≤ M, is a binary indicator of the existence of a multipath component in the nth bin: so  is one if there is a multipath component in the nth bin and zero otherwise. If then (), the amplitude and phase corresponding to this multipath component, follow an empirically determined distribution. This distribution is obtained by sample averages of () for each  at different locations in the propagation environment. The empirical distribution of () and (),, is generally different, it may correspond to the same family of fading but with different parameters (e.g. Ricean fading with differentfactors), or it may correspond to different fading distributions altogether (e.g. Rayleigh fading for the nth bin, Nakagami fading for the mth bin).

This completes the statistical model for the discrete time approximation for a single snapshot. A sequence of profiles will model the signal over time as the channel impulse response changes, e.g. the impulse response seen by a receiver moving at some nonzero velocity through a city. Thus, the model must include both the first order statistics of () for each profile (equivalently, each t), but also the temporal and spatial correlations (assumed Markov) between them.

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RAKE receivers

The spread spectrum receiver shown in Figure 13.5 will synchronize to one of the multipath components in the received signal. The multipath component to which it is synchronized is typically the first one acquired during the coarse synchronization that is above a given threshold. This may not be the strongest multipath component, and also treats all other multipath components as interference. A more complicated receiver can have several branches, with each branch synchronized to a different multipath component. This receiver structure is called a RAKE receiver 4 and typically assumes there is a multipath component at each integer multiple of a chip time. Thus, the time delay of the spreading code between branches is, as shown in Figure XXXX. The RAKE is essentially another form of diversity combining, since the spreading code induces a path diversity on the transmitted signal so that independent multipath components separated by more than a chip time can be resolved. Any of the combining techniques discussed above may be used.

In order to study the behavior of RAKE receivers, assume a channel model with impulse response  where is the gain associated with the jth multipath component. This model can approximate a wide range of multipath environments by matching the statistics of the complex gains to those of the desired environment. The statistics of the ’s have been characterized empirically in for outdoor wireless channels. With this model, each branch of the RAKE receiver in Figure XXXX synchronizes to a different multipath component and coherently demodulates its associated signal. A larger J implies a higher receiver complexity but also increased diversity. Then the output of the ith branch demodulator is

where  is the symbol transmitted over symbol time [], and we assume , so  is also transmitted over []. If  then the ISI term in (13.22)is more complicated and involves partial autocorrelations. However, in all cases the ISI is reduced by roughly the autocorrelation . The diversity combiner coherently combines the demodulator outputs. If for then we can neglect the ISI terms in each branch, and the performance of the RAKE receiver with J branches is identical to any other J-branch diversity technique.

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