Comparison of Modulation Schemes Saravanan Vijayakumaran - PowerPoint PPT Presentation

Comparison of Modulation Schemes Saravanan Vijayakumaran sarva@ee.iitb.ac.in Department of Electrical Engineering Indian Institute of Technology Bombay October 15, 2013 1 / 10

Metrics for Comparing Modulation Schemes Metrics Qualitative Quantitative Power Spectral Complexity Robustness Efficiency Efficiency 2 / 10

Power Efficiency • For an M -ary signaling scheme � d min � ¯ P e ≈ N d min Q 2 σ     � � d 2 d 2 � E b ¯  = ¯ min min = N d min Q N d min Q    2 N 0 E b 2 N 0 • The power efficiency of a modulation scheme is defined as η p = d 2 min E b • The nearest neighbors approximation can be expressed as �� � η p E b P e ≈ ¯ N d min Q 2 N 0 3 / 10

Power Efficiency of Some Modulation Schemes Modulation Scheme η p On-off keying 2 Orthogonal signaling 2 Antipodal signaling 4 BPSK 4 QPSK 4 16-QAM 1.6 4 / 10

Spectral Efficiency Definition (Spectral Efficiency) The number of bits that can be transmitted using the modulation scheme per second per Hertz of bandwidth. Remarks • If a modulation scheme transmits N bits every T seconds using W N Hertz of bandwidth, the spectral efficiency is WT bits/s/Hz • We will use null-to-null bandwidth to calculate spectral efficiency 5 / 10

Spectral Efficiency of BPSK • Let S p ( f ) be the PSD of BPSK and let S ( f ) be the PSD of its complex envelope. S p ( f ) = S ( f − f c ) + S ( − f − f c ) 2 (Section 2.3.1 of Madhow’s book) • The complex envelope is given by ∞ � s ( t ) = b n p ( t − nT ) n = −∞ where p ( t ) is a rectangular pulse of duration T and b n ∈ {− A , A } . k = −∞ R b [ k ] z − k , PSD of the complex envelope is • Given S b ( z ) = � ∞ e j 2 π fT � | P ( f ) | 2 � = A 2 T sinc 2 ( fT ) S ( f ) = S b T 6 / 10

Power Spectral Density of BPSK PSD of BPSK Complex Envelope − f c − 1 1 f c f T T PSD of BPSK − f c f c f Null-to-null bandwidth of BPSK = 2 T (only +ve frequencies) Spectral Efficiency of BPSK = 0.5 7 / 10

Spectral Efficiency of Some Modulation Schemes Modulation Scheme Spectral Efficiency BPSK 0.5 BPAM 1 QPSK 1 16-QAM 2 8 / 10

Spectral Efficiency vs Relative Power Efficiency 16-QAM Spectral Efficiency (bits/s/Hz) 2 1 . 5 QPSK 1 BPSK 0 . 5 0 − 5 − 4 − 3 − 2 − 1 0 1 2 Relative Power Efficiency (dB) η p Relative Power Efficiency = 10 log 10 η p , BPSK 9 / 10

Thanks for your attention 10 / 10