DCStradeoff docx

: Modulation and Coding Tradeoff and Digital Communications Design Goals in designing a DCS  Goals:  Maximizing the transmission bit rate  Minimizing probability of bit error  Minimizing the required power  Minimizing required system bandwidth  Maximizing system utilization  Minimize system complexity Error probability plane (example for coherent MPSK and MFSK) [dB] / 0 NE b [dB] / 0 NE b Bit error probability M-PSK M-FSK k=1,2 k=3 k=4 k=5 k=5 k=4 k=2 k=1 bandwidth-efficient power-efficient Design on the Error probability plane Bit error probability M-PSK M-FSK k=1,2 k=3 k=4 k=5 k=5 k=4 k=2 k=1 bandwidth-efficient power-efficient Selection of parameters - M in MP vs. MF - Eb/No for Pb requirement Limitations in designing a DCS  Limitations:  The Nyquist theoretical minimum bandwidth requirement  The Shannon-Hartley capacity theorem (and the Shannon limit)  Government regulations  Technological limitations  Other system requirements (e.g satellite orbits) Nyquist minimum bandwidth requirement  The theoretical minimum bandwidth needed for baseband transmission of R s symbols per second is R s /2 hertz. T2 1 T2 1− T )( fH f t )/sinc()( Ttth = 1 0 T T2 T− T2 − 0 Shannon limit  Channel capacity: The maximum data rate at which error-free communication over the channel is performed.  Channel capacity of AWGV channel (Shannon- Hartley capacity theorem): ][bits/s1log 2       += N S WC power noise Average :[Watt] power signal received Average :]Watt[ Bandwidth :]Hz[ 0 WNN CES W b = = Shannon limit …  The Shannon theorem puts a limit on the transmission data rate, not on the error probability:  Theoretically possible to transmit information at any rate , with an arbitrary small error probability by using a sufficiently complicated coding scheme  For an information rate , it is not possible to find a code that can achieve an arbitrary small error probability. CR b ≤ b R CR b > Shannon limit … C/W [bits/s/Hz] SNR [bits/s/Hz] Practical region Unattainable region Shannon limit …  There exists a limiting value of below which there can be no error-free communication at any information rate.  By increasing the bandwidth alone, the capacity can not be increased to any desired value.         += W C N E W C b 0 2 1log    = =       += WNN CES N S WC b 0 2 1log [dB] 6.1693.0 log 1 :get we,0or As 20 −≈=→ →∞→ eN E W C W b 0 / NE b Shannon limit