Multicarrier modulation, cont.
Discrete multi tone (DMT)
Multicarrier modulation, cont. • • • •
• For baseband communication, FFT-based multicarrier modulation is called DMT. • Bit-loading is often incorporated in DMT.
Discrete multi tone (DMT) On Shannon’s channel capacity Bit-loading & SNR-gap Water-filling
• Baseband communication requires a real valued signal. • For N subcarriers (QAM-modulated) a 2N-size FFT is used. xn
(
µ ¶ X 2 N−1 j2πkn = Re √ Xk exp 2N 2N k=0
)
µ ¶ µ ¶ N 2N −1 X 1 X j2πkn j2πkn ∗ = √ Xk exp + X2N−k exp 2N 2N 2N k=0 k=N+1
• With special pre-processing of the data Xk a N-size FFT can be used to generate the 2N real-valued time-signal.
Shannon’s Channel Capacity • • • •
•
Shannon’s Channel Capacity
Claude Elwood Shannon, the father of information theory. ”A Mathematical Theory of Communications”, 1948. Shannon derived the fundamental limits for transmission of information (communication). Theorem: ”Let a discrete channel have the capacity C and a discrete source the entropy per second H . If H
Multicarrier modulation, cont. • • • •
• For baseband communication, FFT-based multicarrier modulation is called DMT. • Bit-loading is often incorporated in DMT.
Discrete multi tone (DMT) On Shannon’s channel capacity Bit-loading & SNR-gap Water-filling
• Baseband communication requires a real valued signal. • For N subcarriers (QAM-modulated) a 2N-size FFT is used. xn
(
µ ¶ X 2 N−1 j2πkn = Re √ Xk exp 2N 2N k=0
)
µ ¶ µ ¶ N 2N −1 X 1 X j2πkn j2πkn ∗ = √ Xk exp + X2N−k exp 2N 2N 2N k=0 k=N+1
• With special pre-processing of the data Xk a N-size FFT can be used to generate the 2N real-valued time-signal.
Shannon’s Channel Capacity • • • •
•
Shannon’s Channel Capacity
Claude Elwood Shannon, the father of information theory. ”A Mathematical Theory of Communications”, 1948. Shannon derived the fundamental limits for transmission of information (communication). Theorem: ”Let a discrete channel have the capacity C and a discrete source the entropy per second H . If H
