台湾中华大学-数字通信系统与WLAN课程-调制与编码.pptVIP

Modulation and Coding Trade-Offs Tung-Chou Chen Shannon Capacity Theorem System Capacity Shannon showed that the system capacity C of a channel perturbed by AWGN is a function of the average received signal power S, the average noise power N, and the bandwidth W. The capacity relationship (Shannon-Hartley theorem) can be stated as It is theoretically possible to transmit information over such a channel at any rate R, R ≤ C, with an arbitrarily small error probability by using a sufficiently complicated coding scheme. For the information rate R C, it is not possible to find a code that can achieve an arbitrarily small error probability. Shannon Capacity Theorem Normalized Channel Capacity Shannon Capacity Theorem Normalized Channel Bandwidth Shannon Capacity Theorem Channel Capacity For the case where transmission bit rate is equal to channel capacity, R = C, then Shannon Capacity Theorem Shannon Limit Shannon Capacity Theorem Conclusions Shannon’s work provided a theoretical proof for the existence of codes that could improve the PB performance, or reduce the Eb/N0 required, from the levels of the uncoded binary modulation schemes to levels approaching the limiting curve. Example: For a bit error probability PB = 10–5, BPSK modulation requires an Eb/N0 of 9.6 dB (the optimum uncoded binary modulation). Therefore, for this case, Shannon’s work promised the existence of a theoretical performance improvement of 11.2 dB over the performance of optimum uncoded binary modulation, through the use of coding techniques. Today, most of that promised improvement (as much as 10 dB) is realizable with turbo codes. Bandwidth-Efficiency Plane Bandwidth Efficiency M-ary PSK The bandwidth efficiency is R/W = log2M. M-ary FSK The bandwidth efficiency is R/W = (log2M)/M. M-ary QAM The bandwidth efficiency is R/W = log2M. Bandwidth-Efficiency Plane Bandwidth-Efficiency Plane Power-limited Bandwidth-Limited Systems The two primary communications resources are the transmitted power a