University:
Boston University
Course:
CAS PY 211 | General Physics I
Academic year:

2024
Views:

152

Pages:

18
Author:

Hanusia3lug

Pulse Shaping in Unipolar OFDMbased Modulation Schemes OFDM-based Communication System  Discrete time-domain samples need to be mapped to continuous time-domain pulse shapes in order to obtain an analog signal suitable for modulation of a device such as a LED. Bit Stream Bit Stream M-QAM Modulator OFDM Modulator Channel Pulse Shaping M-QAM Demodulator AWGN + Match Filter & Sample OFDM Demodulator Optical Wireless Communication Based on OFDM  Real unipolar signals are required for IM/DD systems.  Real Signals through Hermitian symmetry in frequency: S(f) = S*(-f)  Unipolar signals are obtained in a variety of ways: DCO-OFDM, ACO-OFDM, PAM-DMT, U-OFDM, Flip OFDM, etc. lighting interference Unipolar OFDM (U-OFDM) / Flip OFDM  Frames are sent in two streams. In the second stream with reversed signs.  Therefore, sp[n] = -sn[n] (Tsonev et al., 2012, Fernando et al., 2011) ● sp[n] = Stream with positive samples ● sn[n] = Stream with negative samples sp[n] cyclic prefix sn[n] sp[n] cyclic prefix cyclic prefix sn[n] cyclic prefix U-OFDM/ Flip OFDM Theory  In U-OFDM, by design: sp[n] = -sn[n]  Original signal is obtained as so[n] = sp[n] - sn[n]  CLIP( s[n] ) = ( s[n] + |s[n]| ) / 2 !!! This representation is important !!!  sp[n] = - sn[n] => |sp[n]| = |sn[n]|  Therefore, distortion from clipping is completely removed by the subtraction operation. Going from Digital to Analog Domain  Samples are represented by pulse shapes  Different pulse shapes have different time and frequency characteristics cyclic prefix cyclic prefix Unipolar vs. Bipolar Pulse Shapes  Unipolar digital signals combined with unipolar pulse shapes produce unipolar analog signals.  Unipolar digital signals combined with bipolar pulse shapes produce bipolar analog signals. cyclic prefix cyclic prefix ! Negative ! Adding a Bias to a Bipolar Signal  Bipolar analog signals can be made unipolar by introducing a bias as presented below.  Bias increases power dissipation. bias Clipping Negative Values  Most of the analog signal is positive, so the negative values could be ignored (clipped).  This, however, introduces distortion and out-of-band interference. What if Pulse Shaping is Done Before Clipping?  Discrete bipolar signals are shaped with bipolar pulse shapes and clipping is performed afterwards. cyclic prefix cyclic prefix What if Pulse Shaping is Done Before Clipping?  Discrete bipolar signals are shaped with bipolar pulse shapes and clipping is performed afterwards cyclic prefix cyclic prefix Clipping the Negative Values  The useful signal is kept in the required band.  Only the distortion term is attenuated by limited channel response.  The necessary symmetry of the distortion term is kept after pulse shaping and after the channel effects for all three modulations.  Some distortion is still present. The non-causal response of the pulse-shaping filter disrupts the noise symmetry. Guard Interval at the End  A physical communication channel has a causal impulse response, which makes a cyclic prefix sufficient to maintain orthogonality.  A band-limited pulse shape like the raised cosine filter has a noncausal impulse response.  Non-causal pulse shapes disrupt the symmetry of the distortion terms. A second guard interval (cyclic suffix) can mitigate this. cyclic prefix cyclic suffix Effect of the Cyclic Suffix  Root-raised cosine filter with rolloff factor of 0.5, 16-QAM, Nfft=16 No suffix With suffix Effect of the Cyclic Suffix  Root-raised cosine filter with rolloff factor of 0.1, 16-QAM, Nfft=16 No suffix With suffix Effect of the Cyclic Suffix  Root-raised cosine filter with rolloff of 0.1, Nfft=32, 256-QAM Effect of the Cyclic Suffix in Numbers  S k  = signal in frequency domain  S k  = distorted signal in frequency domain  Signal-to-Distortion Ratio (SDR) = SDR in Different Scenarios * Nfft 32 64 256 ACO-OFDM SDR [dB] Prefix Only Prefix & Suffix 27.33 39.19 30.5 42.26 36.6 48.33 PAM-DMT SDR [dB] Prefix Only Prefix & Suffix 29.15 41.61 32.46 44.76 38.2 50.19 U-OFDM SDR [dB] Prefix Only Prefix & suffix 28.7 40.69 31.01 43 36.72 48.38 ! Cyclic suffix provides 12 dB improvement in SDR ! *Root-raised cosine filter with rolloff factor of 0.1 has been used in these calculations. The QAM constellation size is 256. Conclusions  Discrete unipolar signals require unipolar pulse shapes  Bipolar pulse shaping can be applied as long as pulse shaping is applied before clipping the negative values.  After pulse shaping, distortion terms still retain required symmetry to stay orthogonal to the useful information.  Non-causal pulse shapes disrupt the symmetry of the distortion terms. A second guard interval (cyclic suffix) can mitigate this.