Comparison of MultiCarrier Modulation Techniques

1
Comparison of Multi-Carrier Modulation Techniques
Center for Wireless COMMUNICATIONS

• Andrew S. Ling, Graduate Student
  (asling_at_ucsd.edu)
• Laurence B. Milstein, Professor
  (milstein_at_ece.ucsd.edu)

Abstract
Scenario 2
Scenario 2 MC-CDMA

• Same equations as for MC-DS-CDMA in Scenario 1
  (perfect and imperfect CSI), but with R1 replaced
  by R2 and (K-1)/N replaced by (K-1).

Much research has been done on systems, such as
multi-carrier CDMA, which transmit data over
several carrier frequencies to achieve frequency
diversity. While most of the existing research
focuses on only one system at a time, this work
performs a side-by-side comparison between two
multi-carrier schemes which have equal bandwidth,
information rate, and transmit power. One system
uses many narrow sub-bands, while the other uses
fewer relatively-wide sub-bands. Closed-form
expressions for the average bit error probability
(BEP) are derived for both systems under two
different cases for the coherence bandwidth of
the channel, assuming the availability of perfect
channel state information (CSI) at the receiver.
The same analysis is repeated for the case of
imperfect CSI, where channel estimates are
obtained via pilot symbols embedded within the
data. The trade-offs between the two systems are
investigated under different values for the
information rate, number of users in the system,
and number of pilot symbols used in the estimate.

• MC-CDMA Frequency non-selective (flat) fading
  in each sub-band independent fading between
  different sub-bands
• MC-DS-CDMA Frequency selective fading in each
  sub-band
• ( of resolvable paths L N)

Overview
Frequency Diversity
Scenario 2 MC-DS-CDMA vs. MC-CDMA
Scenario 1 MC-DS-CDMA

• Perfect CSI

• MC-CDMA potentially has greater frequency
  diversity
• MC-CDMA can be more susceptible to channel
  estimation errors and Doppler effects
• MC-CDMA will also have a higher peak-to-average
  power ratio

We would like to find closed-form expressions for
the average bit error probability of each of the
two systems, assuming the following

• Equal information rate, bandwidth, and transmit
  power
• Maximal-ratio combining
• Waveform shaping (raised-cosine filter),
  resulting in non-overlapping sub-bands
• Rayleigh fading
• Long spreading sequences (spreading sequences of
  the interfering users are modeled as independent,
  random binary sequences)
• No narrow-band interference
• Ignore Doppler effects for now
• No error-correction coding (aside from repetition
  coding)

• Imperfect CSI

The analysis will be repeated for two cases

• The receiver has perfect knowledge of the channel
  state information (CSI)
• The receiver has to estimate the channel via
  pilot symbols sent along with the data

Scenario 1 MC-DS-CDMA vs. MC-CDMA
Parameters
Scenario 2 MC-DS-CDMA

• MC-DS-CDMA
• M of bits transmitted in parallel per use
  of the channel
• R1 of repetitions per bit
• N processing gain per sub-band
• K of users
• MC-CDMA
• M of bits transmitted in parallel per use
  of the channel
• R2 of repetitions per bit
• K of users

• Rectangular MIP

Same equations and results as for MC-CDMA in
Scenario 2 (perfect and imperfect CSI).

• Exponential MIP

• Perfect CSI

It can be shown that R2 NR1.

• Channel estimation (sample average)
• Q of time slots per frame
• Qe of pilot symbols per frame

Partial-fraction expansion
For now, assume that the channel remains constant
over the duration of a frame.
Conclusions
Scenario 1

• The effects of channel estimation errors dominate
  at lower values of (Eb/h0), while the effects of
  diversity dominate at higher values of (Eb/h0).
• Scenario 1
• For M gt 1, we have R1 lt MR2/N. MC-DS-CDMA
  outperforms MC-CDMA at lower (Eb/h0) values,
  while MC-CDMA fares better at higher (Eb/h0)
  values.
• For M 1, we have R1 MR2/N, and MC-DS-CDMA
  outperforms MC-CDMA at all values of (Eb/h0).
• Scenario 2
• Rectangular MIP Both systems have equivalent
  performance.
• Exponential MIP MC-CDMA performs better at all
  values of (Eb/h0).

• Imperfect CSI

Scenario 1 MC-CDMA

• Perfect CSI

Future Work

• Imperfect CSI

• MC-DS-CDMA Frequency non-selective (flat)
  fading in each sub-band independent fading
  between different sub-bands
• MC-CDMA Correlated block fading (perfect
  correlation within each block)

• Use a more realistic channel that varies from bit
  to bit, instead of from frame to frame.
• Incorporate Doppler effects into the channel
  model. This will lead to inter-carrier
  interference, and we expect this to have a
  greater impact on MC-CDMA because of its narrower
  sub-bands.

Partial-fraction expansions
Acknowledgments
This project is partially funded by the Center
for Wireless Communications (CWC) at UCSD and by
the UC Discovery Program.