Title: Simone Morosi and Tiziano Bianchi
1Università 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 39 055 4796485 Fax 39 055 472858
- 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
2Outline
- Motivation
- System model
- Frequency Domain Detection
- Comparison Criteria
- Simulation Results
- Conclusions
3Motivation
- 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.
4Signal 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
5Signal 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 .
6Downlink 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.
7Downlink 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.
8Block 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.
9Frequency 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.
10Frequency 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.
11How 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.
12Complexity 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.
13Channel 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.
14Working 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.
15LR 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
16LR 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
17MR 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.
18HR 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.
19Conclusions
- 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.