Tham khảo tài liệu 'anatomy of a robot part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 226 CHAPTER NINE Physical Layer All that said digital communication comes down to one thing sending data over a channel. Another fundamental theorem came out of Shannon s work first mentioned in Chapter 8 . It comes down to an equation that is the fundamental limiting case for the transmission of data through a channel C B X log2 1 S N C is the capacity of the channel in bits per second B is the bandwidth of the channel in cycles per second and S N is the signal-to-noise ratio in the channel. Intuitively this says that if the S N ratio is 1 the signal is the same size as the noise we can put almost 1 bit per sine wave through the channel. This is just about baseband signaling which we ll discuss shortly. If the channel has low enough noise and supports an S N ratio of about 3 then we can put almost 2 bits per sine wave through the channel. The truth is Shannon s capacity limit has been difficult for engineers to even approach. Until lately much of the available bandwidth in communication channels has been wasted. It is only in the last couple of years that engineers have come up with methods of packing data into sine waves tight enough to approach Shannon s limit. Shannon s Capacity Theorem plots out to the curve in Figure 9-1. There is a S N limit below which there canot be error free transmission. C is the capacity of the channel in bits per second B is the bandwidth of the channel in cycles FIGURE 9-1 Shannon s capacity limit COMMUNICATIONS 227 per second S is the average signal power N is the average noise power No is the noise power density in the channel and Eb is the energy per bit. Here s how we determine the S N limit S C Eb N No X B C B X log2 1 S N C B log2 1 S No X B Since S Eb X C C B log2 1 Eb X C No X B Raising to the power of 2 2c b 1 Eb X C No X B Eb No B C X 2c b - 1 Eb X C No X B 2c b - 1 If we make the substitution of the variable x Eb X C No X B we can use a mathematical identity. The limit as x goes to 0 of x 1 1 x e. We want the lower limit .
