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0 If we consider the maximum likelihood criterion for the optimum decoder, then the ML metric is defined as m(r, s) = InpN(rls, a), when CSI is available, and m(r, s) = In PN(rls), if it is not. Note that for memoryless channels the above defined metrics have the additive property. Assume that s is transmitted and r is received. Between the two codewords sand s the optimum decoder incorrectly decides s if and only ir m(r, s) 2: m(r, s), 3 We drop subscripts i and k and use sand § instead of Si and the pairwise error probability is independent of subscripts i and k.

As an alternative, the demodulator may make Q-ary decision, where Q > q. In this case it is said to make soft decision. In its extreme case, Q ---+ 00, no quantization is performed. Based on the quantized or un quantized information furnished by the demodulator, the decoder attempts to reconstruct the original transmitted message from the knowledge of the code used by the encoder and the redundancy contained in the received data. 2. 2: Block diagram of a modulator. 1). 2. The orthogonalization procedure provides us with a tool to represent the waveforms {Si(t)} as the points of an N-dimensional signal space formed by the orthonormal basis, {cPi(t)}.

A procedure for evaluating these factors for general two-dimensional signal sets is included in Appendix A and the results are summarized in the following paragraphs. 6. 11: Cut-off rates for the Rayleigh fading channel with channel state information. Fading Channel with CSI Assuming that the channel state information is available at the receiver, the Chernoff factor of signals sand s for a Rician fading channel iR derived as (see Appendix A) C(s, s) = C(S,S,Aopt) I+K 1 + K + _I_Is _ 4No sl2 exp ( 4No K Is - s'12 1 + K + _I_Is 4No ) sl2 .

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