Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

Radio Channel Characteristics 27The coherence time of the channel (t) c is the duration over which the channel characteristicscan be considered as time-invariant and can be approximated by(t) c ≈12 f D max. (1.26)If the duration of the transmitted symbol is larger than the coherence time, the channel istime-selective. On the other hand, if the symbol duration is smaller than (t) c , the channelis time-nonselective during one symbol duration. The coherence time of the channel is ofimportance for evaluating the performance of coding and interleaving techniques that tryto exploit the inherent time diversity D t of the mobile radio channel. Time diversity canbe exploited if the separation between time slots carrying the same information exceedsthe coherence time. A number of N s successive time slots create a time frame of durationT fr . The maximum time diversity D t achievable in one time frame is given by the ratiobetween the duration of a time frame and the coherence time,D t =T fr(t) c. (1.27)A system exploiting frequency and time diversity can achieve the overall diversityD O = D f D t . (1.28)The system design should allow one to optimally exploit the available diversity D O .For instance, in systems with multi-carrier transmission the same information should betransmitted on different sub-carriers and in different time slots, achieving uncorrelatedfaded replicas of the information in both dimensions.Uncoded multi-carrier systems with flat fading per sub-channel and time-invarianceduring one symbol cannot exploit diversity and have a poor performance in time- andfrequency-selective fading channels. Additional methods have to be applied to exploitdiversity. One approach is the use of data spreading where each data symbol is spreadby a spreading code of length L. This, in combination with interleaving, can achieve theperformance results that are given for D O ≥ L by the closed-form solution for the BERfor diversity reception in Rayleigh fading channels according to [45][ 1 − γP b =2( )nwhere represents the combinatory function,k] L L−1 ∑( )[ ]L − 1 + l 1 + γl, (1.29)l 2l=0γ =√11 + σ 2 , (1.30)and σ 2 is the variance of the noise. As soon as the interleaving is not perfect orthe diversity offered by the channel is smaller than the spreading code length L, or