Defined bandwidth efficiency
In digital communication systems, the frequency band utilization is defined as the bandwidth of the transmission rate (per hertz), i.e.
\ [η = \ dfrac {R_B } {B} (Baud / Hz) \ tag {1} \] or \ [η = \ dfrac {R_b} {B} (b / (s * Hz)) \ tag {2} \] where \ (R_B \) represents a symbol transmission rate, and \ (R_B = \ dfrac {1 } { } T_B \) , \ (T_B \) for each symbol length (s). \ (R_b \) is the bit transmission rate, B is the bandwidth.
Seen from Formula 1 or Formula 2 at a certain bandwidth, bandwidth efficiency is determined by the symbol transmission rate or bit transmission rate. A maximum transmission rate of the channel and the Shannon Theorem and the Nyquist theorem decisions. To avoid confusion, in the description later herein uniform transmission rate in bits represent the channel transmission rate.
Shannon's theorem
When channel transmitting a data signal with a random thermal noise, channel capacity channel (i.e., channel the maximum transmission rate) \ (C_ {max} \) is calculated as
\ [C_ {max} = W * log_2 (1+ \ dfrac { S} {N}) \ Tag {3} \] \ (C_ {max} \) in units of (b / s), the formula 3 wherein W is the bandwidth, S is the average power of the signal being transmitted within the channel, N the channel noise power. That is according to formula 3, the bandwidth of the bandwidth efficiency in certain circumstances (by the SNR \ (\ dfrac} S {N} {\) ) determined, and increase bandwidth efficiency as infinite SNR also It will grow indefinitely, but will not actually the case, the maximum transmission rate is also limited by the Nyquist criterion.
Nyquist criterion
For noise-free low-pass channel a bandwidth W (Hz), the maximum symbol transmission rate Bmax of: \ [B_ {max} = 2 * W is \ Tag {. 4} \]
or if the symbol state coding method atoms M, obtained bit transmission rate limit information (channel capacity) a Cmax: \ [C_ {} = max * 2 * W is log_2M \ Tag. 5} {\]