Simone Morosi and Tiziano Bianchi

1
Università degli Studi di Firenze Dipartimento di
Elettronica e Telecomunicazioni
12 MCM of the COST 289 October 30-31 Firenze,
Italy
Pulse Repetition and Cyclic Prefix Communication
Techniques in Impulse Radio UWB Systems

• Simone Morosi and Tiziano Bianchi
• Electronics and Telecommunications Department,
  University of Florence
• Via di Santa Marta 3, 50139 Firenze, ITALY
• Tel [phone] Fax [phone]
• e-mail morosi, bianchi_at_lenst.det.unifi.it

This work has been supported by Italian Research
Program (PRIN 2005) Situation and location aware
design solutions over heterogeneous wireless
networks.
LENST
Laboratorio di Elaborazione Numerica dei Segnali
e Telematica
2
Outline

• Motivation
• System model
• Frequency Domain Detection
• Comparison Criteria
• Simulation Results
• Conclusions

3
Motivation

• Our goal
• The comparison of two techniques for Impulse
  Radio UWB systems which are based on the pulse
  repetition according to the spreading factor
  value and the Cyclic Prefix insertion.
• Both techniques cause a throughput loss and have
  to be compared both in terms of performance and
  capacity, i.e. the maximum data rate which is
  afforded.
• The redundancy due to the CP approach is not
  considered as an overhead, but as an alternative
  to the processing gain Nf .
• Our tool Frequency Domain Detection (FDD)
• FDD has been proposed for UWB single user systems
  in Bia04 and Ishi04 and extended to high
  data-rate multiuser systems in Mor05
• This approach is based on both the introduction
  of the cyclic prefix and the use of a frequency
  domain detector. This approach is well suited for
  the applications which are based on data-rate
  scalability and rely on data gathering.

Bia04 T. Bianchi and S. Morosi, Frequency
domain detection for ultra-wideband
communications in the indoor environment,
in Proc. of the IEEE Eighth International
Symposium on Spread Spectrum Techniques and
Applications, 2004, Aug.-Sept 2004. Ishi04 Y.
Ishiyama and T. Ohtsuki, Performance evaluation
of UWB-IR and DS-UWB with MMSE-frequency domain
equalization (FDE), in Proc. of the IEEE
GLOBECOM 04, vol. 5, Nov.-Dec. 2004. Mor05 S.
Morosi and T. Bianchi, Frequency Domain
Multiuser Detectors for Ultra-Wideband
Short-Range Communications, in Proc. of ICASSP
2005, Philadelphia, PA, USA, Mar. 2005.
4
Signal Structure (I)

• tl indicates the delay of the l-th user with
  respect to the access point time reference
• t(b) indicates the pulse shift that implements
  binary PPM
• Tf and Tc are the frame and the chip periods
• bl(i) 1 is the i-th binary symbol transmitted
  to the l-th user. The same bit is transmitted
  over Nf consecutive frame periods (TbNfTf ).
• Nc chips fit exactly in one frame period (Tf
  NcTc ).
• Each active user is associated with a
  time-hopping pseudo-random periodic pattern cl(m)

0
1
2
3
TH code 0,1,2,3
5
Signal Structure (II)

• The transmitted signal can be represented more
  conveniently as

The discrete sequences pl(k) and ql(k) are
periodic with period Nw 2Nc Nf .
6
Downlink Model (I)

• We consider a base station transmitting Nu
  signals synchronously to a set of Nu users Iu
  1, 2, . . . , Nu

• The Received Signal can be expressed as

• The function f(t) takes into account the effects
  of the channel, of the antennas, and of the
  matched filters of both transmitter and receiver.
  
• The signal x(k) represents the digital
  counterpart of the UWB-IR TH-SS signal
• The signal h(t) models thermal noise.

7
Downlink Model (II)

• By assuming that channel characteristics are
  constant over the entire block of samples and by
  sampling r(t) with period Tw , the following
  digital transmission model is obtained

• h(n) f (nTw) represents the equivalent
  discrete channel impulse response of the UWB-IR
  system.
• e(n) h(nTw) represents a discrete time noise
  process.

8
Block Representation

• The discrete signal xl(n) is divided in blocks of
  M samples
• Low Data Rate scenario
• MNM Nw , we need exactly NM blocks to transmit
  a single bit
• High Data Rate scenario
• M NbNw a group of Nb bits is transmitted over a
  block of M samples

• Each block is extended by means of a cyclic
  prefix of length K.
• If K Lc (Delay Spread), the channel does not
  cause any interference between adjacent blocks.

9
Frequency Domain Detection (I)

• Any circulant matrix can be diagonalized by using
  a DFT.
• We can express the channel matrix as

• WM is an MM Fourier transform matrix and ?H is a
  MM diagonal matrix whose entries represent the
  channel frequency response.

• The received vector after cyclic prefix removal
  can be expressed as a function of the bits of all
  active users, the TH sequences, and the channel
  frequency responses.

10
Frequency Domain Detection (II)

• The decision variables can be expressed as
• Low Data Rate
• High Data Rate

• Minimum Mean Square Error (MMSE) detection has
  been considered, due its good tradeoff between
  performance and complexity.

where s2e is the noise variance and s2b
indicates the power of transmitted symbols. This
solution avoids noise amplification at the
detector when the SNR is low.
11
How to compare the systems

• If we assume that the CP size K has been fixed,
  the minimum block size required by FDD is M K.
• Since UWB allows for redundancy in terms of pulse
  repetition, we set the block size as small as
  possible and compensate for the loss of
  throughput by shortening the pulse repetition
  factor Nf.
• The block size is set to M K. In order to have
  the same rate of the original system, the
  repetition factor of the FD system is set to NCPf
  Nf/2.

• This choice does not impose any relationship
  between M and the number of samples NCPw
  2Nc NCPf that are associated with a single bit.

12
Complexity considerations

• Choosing K Lc - 1 (classical FD receiver) gives
  optimum performance at a cost of a high
  complexity, i.e., too long CP.
• Also the rake has to face an analogous
  inconvenient with suboptimum implementation
  (partial RAKE, selective Rake, ..)
• We proposed also a reduced complexity FD
  receiver, in which only a subset of the total
  channel paths is taken into account in this
  system K (and hence M) is reduced.
• This solution is the FD counterpart of the
  partial RAKE and permits a smaller length of the
  CP and, therefore, a smaller size FFT. The
  drawback of this solution is the introduction of
  an increased ISI term (due to the last replicas
  of the channel which are no more contained into a
  single block of samples).
• Nonetheless the MMSE detector can be redisegned
  by considering the increased ISI this solution
  is defined partial-FD (P-FD) receiver.

13
Channel Model

• The channel model has been simulated relying on
  the model proposed by Cassioli et al in
• Dajana Cassioli, Moe Z.Win, and Andreas
  F.Molisch,The ultra-wide bandwidth indoor
  channel From statistical model to simulations,
  IEEE J. Select. Areas Commun., vol. 20, no. 6,
  pp. 12471257, Aug. 2002.
• A slow fading scenario has been assumed, so that
  the channel coefficients could be approximated as
  constant over a single block of samples.
• Only the small scale fading statistics have been
  considered, assuming no shadowing and a reference
  pathloss of 0 dB.
• A constant power delay profile has been assumed,
  setting the power ratio between the line-of-sight
  replica and the reflected ones as 0.4 and
  choosing a decaying constant corresponding to a
  rms delay spread of about 50 ns, a typical value
  for indoor environments.

14
Working Conditions

• The considered an UWB-IR scenario consists of an
  Access Point (AP) transmitting to a variable
  number of Mobile Terminals (MTs).
• All the communications from the AP have been
  assumed synchronous.
• The information bits are modulated (2-PPM) with
  Tw 2 ns pulse duration
• High Data-Rate (HR) system
• Nf 4, Nc 4 15.6 Mbit/s.
• Medium Data-Rate (HR) system
• Nf 16, Nc 4 3.9 Mbit/s.
• Low Data-Rate (LR) system
• Nf 128, Nc 32 243.6 kbit/s.
• The digital channel model has LRAKE 100
  sample-spaced resolvable replicas.

15
LR Single User
Both receivers achieve good performance unless a
very low number of fingers or a very short CP is
considered.
Nf 64, Nc 16, single data flow
16
LR 100 load
It is important to consider an enough long CP in
order to prevent from ISI detrimental effects.
In particular, for high values of Eb/N0 the
MMSE is not able to suppress the effects of the
ISI caused by short CP and its performance tend
to converge to the values of the RAKE receiver
error floor.
Nf 64, Nc 16, 16 data flows
17
MR 50 load
Nf 16, Nc 4, Eb/N0 15 dB
Nf 16, Nc 4, 2 data flows
The same trend can be seen for a half loaded high
rate system. Note that the PFDMMSE Equalizer has
interesting results the definition of the new
equalization law permits to avoid the degradation
caused by the ISI.
18
HR Single User
Nf 4, Nc 4, single data flow
If an enough long CP is used the FD MMSE
equalizer greatly overcomes the system based on
the pulse repetition and the use of the RAKE
receiver.
19
Conclusions

• We compared UWB-IR systems based on the pulse
  repetition according to the spreading Factor
  value and the use of the RAKE receiver and on the
  Cyclic Prefix insertion and Frequency Domain MMSE
  Equalization.
• Both systems admit sub-optimal implementation.
• Both systems have been considered in different
  scenarios characterized by services with
  different rate and system with variable load.
• The simulation results show that the system which
  is based on the Cyclic Prefix insertion and the
  adoption of the Frequency Domain MMSE is more
  suitable for high data rate highly loaded systems.