Monday, March 24, 2008

Now for the Various Techniques...

**ZF-This is an equalization technique in which the received signal is multiplied by a weighted vector such that the Inter Symbol Interference (ISI) is forced to zero. This value is chosen from the Channel Matrix (H) which provides the channel state information. The disadvantage in Zf is that since it amplifies the noise components along with he signal it is not much preferred.

**MMSE-The MMSE receiver suppresses both the interference and noise components, whereas the ZF receiver removes only the interference components. This implies that the mean square error between the transmitted symbols and the estimate of the receiver is minimized. Hence, MMSE is superior to ZF in the presence of noise.

**MAP-This algorithm is used to obtain a point estimate of an unobserved quantity on the basis of empirical data. It is optimum as it minimizes the probability of error. MAP instead of selecting the next symbol to be detected according to the rule, here the set of all potential symbol decisions are ranked with respect to their a posteriori probabilities of being correct. The index permutation produced by MAP depends on both H (Channel Matrix) and r(received signal) , unlike ZF where permutation depends only on H . So the major complexity in MAP is that the weighting vector must be computed in real time since it also depends on r.

**ML-It brings out the optimal performance. It is a special case of MAP detection when all possible inputs are equally likely. The major advantage of ML over MAP is that the likelihood is easily computed for each possible symbol knowing the statistics of noise generator and not statistics of data symbol. ML and MAP are different detection techniques, but yield the same result when the priori probabilities are equal. However If priori probabilities are different, MAP yields lower probability of error.

**N/C-Nulling and cancelling (NC) uses a serial decision-feedback approach to detect each layer separately. When a layer has been detected, an estimate of the corresponding contribution to the received vector r is subtracted from; the result is then used to detect the next layer and so on. N/C progressively clears r from the interference corresponding to the layers already detected. To detect a specific layer, the layers that have not been detected yet are “nulled out” (equalized) according to the ZF or MMSE approach. Error propagation can be a problem because incorrect data decisions actually increase the interference when detecting subsequent layers. Thus, the order in which the layers are detected strongly influences the performance of NC.

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