A multicode approach for high data rate UWB system design

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 57, NO. 2, FEBRUARY 2009

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A Multicode Approach for High Data Rate UWB System Design Mohamed Kamoun, Laurent Mazet, Marc de Courville, Member, IEEE, and Pierre Duhamel, Fellow, IEEE Abstract—This contribution provides a very high data rate UWB system design based on direct sequence spreading. In order to attain > 500Mbps for short range communication, two classical solutions are feasible: either use very short spreading sequences or very large bandwidth. These classical strategies increase intersymbol interference. In contrast, our approach consists in allocating multiple long codes to each user. Long codes allow to cope with channel impairments while the use of multiple codes maintains very high bit rates. With such high data rates the receiver obviously has to be simple by requiring a low complexity digital processing. This paper shows that the proposed strategy is compatible with simple receivers. In fact, even if the amount of interference increases, joint usage of very long codes and simple linear receiver can result in high data rate, high performance UWB system. This assertion is substantiated through comparisons with existing UWB solutions. Index Terms—Multicode spreading, spread spectrum, ultrawideband (UWB), wireless personal area network (WPAN).

of very high rate sequences. In the existing proposal, the difficulty comes with the increase of the data rate, which imposes to shorten the spreading sequences. As a consequence there is an increase of the interference which results either in performance degradation or in receiver complexity increase. This paper provides means of solving this problem while maintaining a scalable complexity at the receiver. Section II provides a brief overview of UWB systems. Section III presents the motivations for using spread spectrum techniques in UWB system design while Section IV depicts the transmitter architecture based on multicode approach and Section V describes several possible receivers. In Section VI, the parameters that drive the system performance are optimized in order to derive the best modes. Section VIII compares the chosen system design with MBOFDM and DSUWB existing proposals. II. UWB S PECIFICITIES W ITH R ESPECT TO THE C HANNEL

I. I NTRODUCTION

U

WB technology is a serious candidate for the new emerging Wireless Personal Area Network (WPAN). In this context UWB is expected to provide very high data rates ≥ 500Mbps for short range communication. Many physical layer schemes have been proposed to address such rates on the wireless medium. Historically pulse based systems have been first proposed as the main modulation technique for UWB. The pulse based modulations inherently occupies a very large bandwidth (several GHz), which is required due to the very low emitting power[1]. This technique is currently considered for low data rate in the sensor network context, but seems to be discarded for high data rate transmissions. Another physical layer, Multi Band Orthogonal Frequency Division Modulation (MB-OFDM), has been proposed within the IEEE802.15.3a task group. This technique is based on the well known OFDM scheme which allows good immunity towards multipath channels. In this proposal, only a 500MHz band is used at a given time, and a frequency hopping technique spreads the signal over several GHz (see [2], [3]). Finally, Direct Sequence Spreading (DSS) has also been proposed in the UWB framework (DSUWB). In this scheme, the data are spread over few GHz of bandwidth by means Paper approved by S. A. Jafar, the Editor for Wireless Communication Theory and CDMA of the IEEE Communications Society. Manuscript received April 28, 2006; revised January 10, 2007 and January 1, 2008. M. Kamoun and P. Duhamel are with LSS SupElec, 3 Rue Joliot-Curie, 91192 Gif sur Yvette Cedex, France (e-mail: [email protected]; [email protected]). L. Mazet and M. de Courville are with Motorola Labs Paris, Parc Les Algorithmes, Saint Aubin, 91193 Gif sur Yvette Cedex, France (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TCOMM.2009.02.060265

A. UWB Spectrum Ultra Wide Band is defined as any system which operates with a bandwidth greater than one fourth the central frequency or larger than 500MHz. In UWB some parameters like propagation attenuation and penetration through obstacles are not constant on the whole bandwidth. This makes the channel much different from the narrow band case, mostly due to the fact that the central frequency in UWB signals cannot be considered as the carrier frequency. This increases the channel response length, and largely impacts the overall system performance. From a regulatory point of view since UWB systems overlap with existing ones, they must be limited by a spectral mask which defines the maximum power density spectrum of the transmitted UWB signal. More specifically, in the USA, the FCC limits the spectrum of UWB signals as described in the so called ‘part 15 rule’ document which is concerned with intentional radiators. The main allocated bandwidth lies between 3.1GHz and 10.5GHz, with an upper power spectral limit of −41dBm/MHz. Other frequency ranges are allowed in FCC part 15 but are not considered in our design. B. UWB Channels It is well known that wideband systems are impaired by intersymbol interference due to multipaths. In such systems (typically a bandwidth of 5-20MHz), the receiver distinguishes some groups of paths, each group being described by an attenuation coefficient ck (t). The channel is thus identified by a finite length vector [c0 . . . cN−1 ]. These paths (or group of paths) correspond to spatial details which size is about few meters.

c 2009 IEEE 0090-6778/09$25.00 

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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 57, NO. 2, FEBRUARY 2009

TABLE I R AY A RRIVAL R ATE IN ns−1 λ in ns−1 channel length in ns

CM1 2.5 17

CM2 0.5 13

CM3 2.5 33

CM4 2.5 60

When increasing the bandwidth the receiver is able to resolve more paths. In fact, in Ultra Wide Band systems the bandwidth is so large that spatial details of few centimeters are seen on the channel at the receiver side. These channels are very long with respect to the considered symbol duration, as is evidenced by the Saleh Valenzuella (SV) model. The IEEE802.15.3a task group has adopted a modified version [4] of SV model initially detailed in [5]. More precisely, a delay spread of 50ns covers only 1 sample with a 20MHz wideband systems like 802.11 however with a sampling rate of 1GHz the channel covers dozens of samples. This is the main difficulty encountered when trying to use DSUWB with very high data rates as will be shown below. III. D IRECT S EQUENCE S PREADING M OTIVATION A. Motivation for Spreading The channel length seen by UWB signals makes the direct sequence spreading a serious candidate for the choice of UWB modulation. Assuming a correlation based receiver, best performance will be obtained by collecting individually the multipath rays through the spreading sequence. Thus the chip frequency must be of the same order of magnitude as the arriving process rate λ, which expresses the average number of rays per time unit. As an example, Table I provides the values of λ as given in [4]. This gives an order of magnitude of the sampling frequency (1GHz) and of the channel length (from 17 to 60 samples). These very long channel responses also have consequences on the choice of the sequence length which must be chosen in such a way as to limit the intersymbol interference. Define the channel length as the time duration when the cluster energy falls 10dB below the first one. Corresponding channel lengths for IEEE802.15.3a task group are given in Table I. In such a situation, the use of short spreading sequences would require complex equalization schemes. Since our intent is to use very simple receivers (linear), we avoid this solution. In contrast, we choose spreading sequences longer than the channel duration. Thus, if the chip frequency is set to 1.3GHz, the maximal symbol rate would be 58Ms/s for CM1, 77Ms/s for CM2, 30Ms/s for CM3 and 16Ms/s for CM4. Obviously, this is not compatible with the target high data rates since with a CM1 channel an non-coded data rate of 400Mbps requires a QAM256 modulation. We propose to recover the high data rate while keeping long spreading sequence by superimposing synchronously multiple codes. By doing so each code can be modulated with a lower order modulation. We denote this strategy as the ‘multicode approach’. This technique has already been used with CDMA systems in order to increase the data rate for a given user. In [6] the authors describe the basis of a multicode CDMA system and focus mainly on the code assignement. However the considered multipath channel correspond to wideband

personal communication context which is limited to few MHzof bandwidth. In [7] a code design is proposed for UWB which shows better performance than m-sequence in a UWB channel context. However this study is limited to a correlator receiver without forward error correction. The design which is proposed here is based on random codes, takes into account the inter-symbol interference introduced by multipath channel. As an example, an non-coded data rate of 400Mbps is achievable in CM1 context with 4 codes modulated by a QPSK constellation. This strategy relies on the assumption that increasing the code length makes the system more immune to intersymbol interference and makes the equalization easier. This is demonstrated in Section VI. A given data rate can be obtained by various combinations of modulation order, number of codes and sequence lengths. The available data rate depends on five quantities: 1) The bandwidth which depends on the chip duration and the transmitting pulse shape. In the sequel, we consider that is given by Bw = T1c 2) The code length Lc 3) The number of available codes Nc 4) The modulation order M 5) The channel capacity per information symbol C (SINR) where SINR is the Signal to Noise and Interference Ratio at the output of the receiver. Given these quantities, the maximal achievable bit rate writes as: Nc CM (SINR) (1) Rmax = Lc Tc where CM (SINR) is the mutual information between the emitted symbols and the received outputs for the considered modulation order. Equation (1) involves inter-dependent quantities, since the SINR also relies on Lc and Nc . Thus, one has to look for a good trade-off between all these parameters (see Section VI). B. Impact of Multicode on System Range In a first step we evaluate by simulation the impact of multicode increase on the available rates in a very simple situation. More specifically, we analyse the impact of the processing gain and the modulation order on the achievable capacity at a given range. This ideal context consists in i) a random code set ii) a Gaussian channel iii) a free space attenuation model. vi) a linear mmse receiver with perfect channel knowledge. We assume very long sequences which allows to use asymptotic derivations. According to [8], the asymptotic (Lc → ∞) signal to noise and interference ratio (SINR) for each code depends on the SNRand the processing gain β = NLcc SNR 1 SINR∞ (SNR) = (β−1) − + 2 2



(β−1)2

SNR 1 SNR2 +(β+1) + 4 2 4 (2)

For finite values of Lc the SINR behaves (in distribution) as a gaussian random variable with mean SINR∞ (SNR) and variance σSINR given by 1 σ2SINR = 1 correspondacen

2SINR∞ (1 + SINR∞)2 β(1+SINR∞ )2 SNR

beta alpha

+ β1

− 2SINR2∞

(3)

KAMOUN et al.: A MULTICODE APPROACH FOR HIGH DATA RATE UWB SYSTEM DESIGN I

Available data rate in Gbps with different processing gains 0.7

555

PG 4 QPSK PG 8 QAM16 PG 12 QAM64

f2

f1

0.6

90

Available data rate in Gbps

0

0.5

Q 0.4

f2 − f1 = f0 0.3

Fig. 2.

Method for I/Q imbalance workaround.

0.2

0.1

0

0

5

10

15

20

25 Distance in m

30

35

40

45

50

Fig. 1. Available data rates with 1.3GHz of band and a maximal rate of 650Mbps.

The ergodic maximal rate can thus be written as: Rmax = Bw A

E [CM (SINR)] log2 (M)

(4)

where the expectation is over a gaussian random variable with mean SINR∞ and variance σSINR , A = log 2(M)/β. Rmax is driven by the raw bit rate Bw A. When increasing the range, the SNR obviously decreases and the quantity E [CM (SINR)] / log2 (M) (which is always < 1) also decreases. However, this term decreases rapidly with high constellation order. Thus, for a fixed value of raw bit rate Bw A, a good choice for increasing the range is to select constellations with the lowest possible order. Fig. 1 depicts the available bit rate versus the range for Bw A = 650Mbps and various configurations of processing gains and constellation orders. One can see that for short range all options are equivalent. However the available capacity decreases more slowly when increasing the range in the case of small processing gains and small constellation orders. For the very long ranges, which is equivalent to very low SNR, almost all options are also equivalent. This corresponds to the wideband regime detailed by Verdu in [9] where the · · system capacity is given by Bw SNR C (0) where C (0) is the derivative of the mutual information (w.r.t. SNR) of the considered modulation at SNR=0. This value is the same for all QAM constellations and it is equal to 1/ log(2). However, typical useful distances in wireless PAN applications lie between 5m and 30m. This corresponds to cases where the parameters of interest have an influence. In what follows, we investigate the best tuning of all parameters in a realistic context. IV. D IRECT S EQUENCE M ULTICODE T RANSMITTER A RCHITECTURE The transmitter architecture is depicted in Fig. 3. The data bits are convolutionally encoded. The coded bits go through an interleaver in order to ensure that successive encoded bits meet independent channels. The encoded interleaved bits are mapped on a QAM constellation. An special care need to be considered when using very large bandwidth (∼ 1GHz) I/Q modulation. Current I/Q modulators

can tolerate a base-band bandwidth in the order to 500MHz [10]. With higher bandwidth (> 1GHz) we propose to shift the signal of I and Q branches to a high intermediate frequency f1 (see Fig. 2) and perform 0/90 phasing with another high carrier frequency f2 such that f2 − f1 = f0 . With this apparatus we can limit the I/Q imbalance by ensuring a fractional bandwidth fB2 less than 30% which corresponds to acceptable values for I/Q modulators. For the choice of intermediate frequencies, since we need a central frequency of f0 = 3.9GHz we can take f1 = 12GHz and f2 = 8.1GHz. This method leads to an additional cost and power consumption of the UWB device. However current OFDM based solution [10] faces similar problems since it requires very accurate oscillator (because of the use of OFDM modulation) with very large bandwidth 500MHz. The same constellation is used for all codes. The mapped symbols are grouped into set of Nc symbols represented by a vector d(k) = [d1 (k) · · · dNc (k)]T . Each symbol di (k) is spread with a code ci . Denoting C the matrix of all codes, the baseband transmitted signal can be written in vector form as y(k) = [y0 (k) · · · yLc −1 (k)]T = Cd(k)

(5)

where y(k) is a Lc length vector and C is an Lc × Nc matrix. Since the codes are assigned to the same user, a fair comparison requires to use the same power independently of the number of codes. Hence the elements of matrix C are  normalized to ± √1N so that E |yi (k)|2 = 1 ∀i ∈ [ 0 .. Lc − 1 ]. c The multicode modulator is followed by a frequency upconverter which shifts the transmitted signal to the central frequency assigned to the user. The complex envelope of the transmitted signal is thus given by s(t) =

∞ Lc −1

∑∑

yi (k)ψ(t − (kLc + i)Tc ) exp( j2π fc t)

(6)

k=0 i=0

where ψ is the shaping transmit filter assumed here to be a rectangle impulse. ψ(t) = 1 for 0 ≤ t ≤ Tc and 0 otherwise. This ensures that s(t) is a zero mean normalized random variable. fc is the signal central frequency.   E |s(t)|2 = 1 (7) After going through a multipath channel h(t), one Lc length slice of the received signal is expressed as: ⎤ ⎡ r(kLc ) ∞ ⎥ ⎢ .. r(k) = ⎣ (8) ⎦ = ∑ Hi y(k − i) . r((k + 1)Lc − 1)

i=0

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Encoder

Interleaver

QAM Mapper

Code Mapper

bk

Σ

dk

c1 Fig. 3.

ci

yk

cNc

DS UWB multicode modulator.

where Hi are the Toeplitz matrices defined below. ⎤ ⎡ hiLc hiLc −1 · · · hiLc −Lc +1 ⎥ ⎢ .. .. .. .. ⎥ ⎢ . . . . ⎥ ⎢ (9) Hi = ⎢ ⎥ .. . . ⎣ . . hiLc −1 ⎦ hiLc +Lc −1 ··· ··· hiLc  T h = h0 · · · h(Lh −1) is the vector containing the samples of the channel h(t) at the chip rate frequency. Coefficients h j are null for j < 0 and j ≥ Lh . Equation (9) shows the connection between the channel length and the intersymbol interference that impairs the received signal. Equation (8) always involves at least two terms except when the channel is reduced to a single coefficient h0 . The first term H0 y(k) corresponds to the contribution of the symbol of interest to vector rk while the remaining terms represent intersymbol interference. In our design the sequence lengths are chosen in such a way that the intersymbol interference beyond the second term is negligible. By doing so, the intersymbol interference reduces to H1 yk−1 i.e. Lc ≥ Lh . With a bandwidth of 1.2GHz this condition is ensured for all channels with Lc = 72. V. D IRECT S EQUENCE L INEAR R ECEIVERS A. Receiver Architecture As explained in the motivation part of the paper, our intent is to tune the system parameters for the most efficient use of linear receivers, which are known for their reduced complexity. In the resulting combination of very long codes assigned to a single user, the linear receiver must altogether separate the data from the superimposed codes and equalize the channel. A general multicode linear receiver is depicted in Fig. 4. After a low noise amplifier (LNA) and a downconverting stage the base-band signal is correlated by a bank of filters which delivers the received symbols. Three options have to be considered for the correlation: • Pure analog correlation: With pure analog correlation, the filters are generated in analog domain. Each correlator is followed by a sampler and an ADC which converts the correlation value in digital domain. The ADCs operate at the symbol rate which is much lower than the chip frequency. We can also consider only one ADC switching between the different samplers and operating at Nc times the symbol rate. Analog option is limited because the filter coefficients cannot be easily modified. • Pure digital correlation: With pure digital correlators, the base band signal is sampled at the chip frequency. Then,

•

an ADC operating at the chip rate converts these samples in digital domain where the correlation is achieved. Clearly this option is very demanding in terms of ADC and signal processing, which is the price to be paid for flexibility. Semidigital correlation: With semidigital correlation, filter coefficients are stored digitally. Digital to analog converters deliver the coefficients to an analog multiplyintegrate device fed by samples of the baseband signal. Note that the samples of the baseband signal are not Ato-D converted, and that a zero order hold ensures that the resulting signal shares the same bandwith as the filters. The correlation result is A-to-D converted at the symbol rate. This option relaxes the constraint on ADC operating frequency and has almost the same flexibility as the pure digital solution.

In our context we assume that the receiver architecture uses either the second or the third option to ensure that the filter coefficients can be adapted to the channel within the receiver. In what follows we study the performance of a set of possible linear receivers. The complexity of the each receiver depends on two main parameters: 1) The filter length which corresponds to the time window considered to demodulate one symbol. 2) The complexity of filter calculation. Each filter is represented by a vector fi , i ∈ 1..Nc of length L f . Note that they do not necessarily have the same length as the spreading sequence. The correlator outputs are the estimated symbols, which are made of four contributions (see Fig. 5): 1) A signal term which results from the correlation of the filter fi with its corresponding code ci 2) An intercode interference which results from the correlation of the filter fi with the other codes of the same symbol. 3) An intersymbol interference which results from the correlation of the filter fi with all the sequences corresponding to the previous symbol. 4) Finally, a Gaussian noise which results from the correlation of the filter fi with the Gaussian noise. The three last terms impair the received signal. The main measure of the system performance is thus given by the signal to noise and interference ratio (SINR) which is the ratio between the signal and undesired terms.

KAMOUN et al.: A MULTICODE APPROACH FOR HIGH DATA RATE UWB SYSTEM DESIGN

557

Metrics computation

c3

LNA

ISI

c2 c1

downconverting

c3

ICI

c2 f1

exp( j2π fct)

fi

c1

fNc

f1

Fig. 4.

DS multicode linear receiver architecture.

symbol k-1

symbol k

time

B. Considered Linear Receivers

Fig. 5.

Since several codes address the same user, one could attempt to equalize and detect the streams carried by all parallel codes jointly. Joint detection would significantly increase the complexity of the receiver compared to separate processing of each stream without noticeable performance improvement, especially for very long codes which is our context. The reason is that random long codes, most of the time have very low intercorrelation. These assertions have been verified by simulations, and this paper only addresses the separate case. First we derive the equalizers involved in three types of linear receivers. The receiver complexity increases with the length of the corresponding filters, hence we assume that the equalizer degree does not exceed twice the sequence length. We further assume that the channel coefficients are perfectly known at the receiver. 1) Multicode Rake Receiver: The multicode rake receiver involves Nc parallel rake computations. Each filter is matched to a single code filtered by the channel. The receiver equalizes the first Lc coefficients of the channel by means of filters of length 2Lc . The equalizer corresponding to code ci is given by  H H H H0 f i = ci (10) H1

both solutions. The equalizer matrix has size 2Lc × Nc and is given by:  rk  dk = FH rk+1 (12)  dk 2 F = argmaxE dk − 

2) Basic Linear MMSE Receiver: The linear MMSE receiver allows to better separate signals carried by different codes. It is known to maximize the signal to noise and interference ratio[11], [12]. This equalizer is provided here as an inner product of a slice of Lc chips with a set of Lc coefficients. It can be written for an individual code or for the whole set of codes. Both approaches turn out to be equivalent. For the ith code, the corresponding filter fi is:

The resulting MMSE receiver for the ith code is:

fi = where

A=

Lh Lc

A−1 H0 ci H 1 + ci H0 H A−1 H0 ci

(11)



∑

i=0

Hi CCH Hi H + σ2 I − H0 ci ci H H0 H

3) Double Window Linear MMSE Receiver: The basic MMSE linear receiver does not take into account the interference between two successive slices of length Lc . We provide here a double window MMSE receiver which capitalizes on two successive frames (kth and (k + 1)th) in order to estimate the kth symbol. Obviously the improvement brought by this receiver is potentially more substantial with strong intersymbol interference, but can be counterbalanced by the fact that the filter captures more noise samples. Simulations below compare

Intercode interference and intersymbol interference.

As a result, F writes as:

 −1 F = B + XXH X

where

 B=

and B00

=

B01 B10

= =

B11

=

B00 B10



B01 B11

(13)

+ σ2 I

(14)

 L i= Lhc ∑i=1  Hi CCH Hi H L i= Lhc ∑i=1 Hi CCH Hi+1 H B01 H  L i= Lhc Hi CCH Hi H ∑ i=0 i=1

and

 X=

fi = 

H0 H1

(15)

C

(16)

K−1 xi 1 + xiH K−1 xi

(17)

H0 ci and K = B + XXH − xi xi H . Note that H1 this receiver has the same form as in the single window case. 4) Variable Linear Length MMSE Receiver: Depending on the channel length and the processing capabilities of the receiver we can also use a variable length MMSE receiver which takes into account only a subset of the received samples. By adding zero channel coefficients we can always assume that the channel length is a multiple of the sequence length i.e Lh = mLc . An L f length linear MMSE receiver can be written as ⎤ ⎡ rk ⎥ .. k = FH S ⎢ d (18) ⎦ ⎣ . where xi =

rk+m−1 where F is a L f × Nc matrix, S is a L f × mLc matrix whose c elements are in {0, 1} and ∑mL j=1 Si j = 1 ∀i ∈ [ 1 .. L f ] ⎡ ⎤ 1 0 0 ··· 0 ⎢ 0 ··· 1 0 · · ·⎥ ⎢ ⎥ S=⎢ . (19) ⎥ . . . ⎣ . ⎦ . 0···

0

···

1

0

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The linear filter F is given by −1  H H F = SH0 CCH H0 SH + SH1 CCH H1 SH SH0 Cm where2

⎡ ⎢ ⎢

H0 = ⎢ ⎢ ⎣

(20)

⎡

⎤ C ⎢ ⎥ C = Im C and Cm = ⎣ 0 ⎦ .. . h0 .. . .. .

hmLc −1

⎡ ⎤ ⎤ 0 hmLc −1 · · · 0 ··· 0 h1 .⎥ .. ⎥ ⎢ .. .. .. .. .. ⎢ . . . .. ⎥ . . ⎥ ⎥ ⎥ and H1 = ⎢ . ⎢ ⎥ ⎥ . .. .. ⎣ .. . 0⎦ . hmLc −1 ⎦ · · · · · · h0 0 ··· ··· 0

The variable linear MMSE receiver can be used to select only significant paths for reduced complexity receivers or to get better performance with very long channels. For the sake of simplicity we will only consider simple and double window receivers in the remaining. VI. M ODE S ELECTION A mode is defined by the parameters cited in Section III which are the bandwidth Bw = T1c , the sequence length Lc , the number of codes Nc and the modulation order M in addition to the forward error code (FEC) rate. Modes are chosen with the following target data rates 110Mbps, 400Mbps, 800Mbps and 1.6Gbps. Notice that a given data rate can be obtained by many possible parameter combinations. These parameters can be chosen according to various criteria such as: 1) Range maximization with predetermined FEC rate and maximal bit error rate. 2) Range maximization for a given capacity. Being based on a fully specified receiver, the first criterion is more realistic while the second one evaluates the distance to the maximal achievable data rate. Only the first criterion is considered in this paper. A. Design Approach With Realistic Encoding Assuming that the remaining noise after the linear receiver is Gaussian, the main parameter that drives the system performance is the SINR. The range prediction needs to link the SNR at the receiver antenna (which depends on the distance to the transmitter) to the SINR at the output of the linear receiver. Since the range computation only depends on the SINR, this quantity has to be evaluated for the three receivers of interest.

Bw S 0 NF L (δ)kB T Bw

(21)

where Bw is the occupied bandwidth (the inverse of the chip rate), and S0 is the constraint on the power density spectrum at the transmitter. It is determined by the FCC mask which states that S0 ≤ −41dBm/MHz. kB T is the Gaussian noise power density spectrum, NF is the noise figure chosen as 7dB 2

stands for the Kronecker product

where c is the light speed and fc is the geometric mean of the √ maximal and the minimum frequency: fc = fmin × fmax . This model is generally considered as being more accurate than the simple free space one, and has been chosen in the 802.15.3a standard proposals[4]. However, corresponding performance evaluation are not available in the open literature, therefore, for comparison purposes, we also provide ranges with free space model. C. SINR Calculation In order to evaluate the receivers performance the SINR is compared to its maximal value corresponding to the channelless context with perfectly orthogonal codes: SINRmax = βSNR

(24)

1) Rake Receiver: The rake receiver known as the matched filter receiver maximises the signal to noise ratio at its output. Hence it is suitable when the interference noise can be neglected compared to the Gaussian noise. The signal term at the output of the rake receiver is given by   H H xxH = cH i H 0 H 0 + H 1 H 1 ci The individual SINR at the output of the ith rake filter fi writes: xH i xi (25) SINRrake (SNR) = xH 1 i Mxi + H SNR xx i i

where M = B + XXH − σ2 I − xi H xi . Matrices B and X have been already defined in equations (15) and (16). 2) Basic Linear MMSE Receiver: The SINR seen by the stream transmitted on on the ith code is given by SINRmmse = ci H H0 H A−1 H0 ci

(26)

3) Double Window Linear MMSE Receiver: The SINR seen by the stream transmitted on the ith code given by

B. Propagation Model The SNR at the receiver is given by SNR =

in our case. L (δ) is the attenuation due to propagation over the distance δ. We consider a two slopes propagation model, characterized by a path loss exponent of 2 (free space) for distances between 1m and δ0 = 4m followed by a path loss of 3 for longer distances.   4π fc δ 2 L (δ) = for δ ≤ δ0 (22) c   4π fc δ 2 δ L (δ) = for δ ≥ δ0 (23) c δ0

SINRmmse2 = xi H Pxi

(27)

where P = B + XH X − σ2I D. SINR Comparison of the Various Receivers This comparison is based on the average SINR (denoted SINR) at the output of the receiver. The averaging is performed over all channel realizations in a random spreading context.

KAMOUN et al.: A MULTICODE APPROACH FOR HIGH DATA RATE UWB SYSTEM DESIGN

F. Average Bit Error Performance

Average SNIR vs SNR with Lc=24 Nc=4 for different receivers 20

By assuming that the resulting noise after the linear receiver is Gaussian, the BER can be evaluated from the SINR by considering the error performance of the Forward Error Correction (FEC) scheme. For example in non-coded case combined with a BPSK modulation, the average bit error rate BER is given by  √  1 BER = E erfc SINR (28) 2

Average SNIR in dB

15

10

5

0

-5 -10

Rake Double window MMSE Single window MMSE Maximal SNIR value -5

0

5

10

15

SNR in dB

Fig. 6.

559

Average SINR vs SNR with Lc = 24 and Nc = 4.

1) Why Random Spreading: We assume that the channel remains constant during the frame length (L symbols). A single code set is used during this period of time. Code sets are chosen randomly. Obviously this scheme does not ensure any code orthogonality. This is not a problem since orthogonal codes are efficient in a channel-less system or with a very short channel which is not the case in this paper. Moreover, considering random sets simplifies the analysis and relaxes the constraints on system design. 2) Receiver Performance Evaluation: Equation (25) shows that the SINR for the rake receiver saturates when increasing the SNR as illustrated on Fig. 6. For very low SNRs, the rake receiver is equivalent to the double window MMSE receiver since the major unwanted signals provide from the Gaussian noise rather than the intersymbol and intercode interference. The MMSE receivers do not show any saturation for the considered SNR range (from -10 to 12dB) and for 24 length codes in CM1 context. However saturation is expected with much higher SNRs or with very long channels like CM4. For both MMSE receivers the SINR varies linearly as a function of the SNR. However the double window MMSE exceeds the single window one by about 3dB (in this case). This is mainly due to the extra signal energy captured by using two successive sequences kth and (k + 1)th as an input to decode the kth symbol. The double window MMSE is very close to the channel-less, orthogonal codes performance in terms of average SINR (in dB, SINR = SNR + 10 log10 (β)). Obviously, for longer codes, all gaps between basic MMSE, double window MMSE and the channel-less orthogonal code case decrease.

The expectation is taken over all codes and channel realizations. In a coded case, denote by Fc the function providing the performance of the FEC scheme with Gaussian noise, BER is thus given by BER = E [Fc (SINR)] (29) VII. S ELECTED M ODES A. Context In this section we provide a system design example with two bandwidths: 1.3GHz and 2.6GHz. The considered receiver is based on double window linear MMSE equalizer. The considered code lengths are 24 and 48 which correspond to the typical channel length of CM1 model with a 2.6GHz bandwidth. The considered encoding schemes are based on a 1/3 convolutional encoder ([133, 145, 171]8) with different puncturing patterns so that the following coding rates are obtained: 1/3,1/2, 2/3 and 3/4. The modulation can be either a BPSK, a QPSK, a 16QAM or a 64QAM constellation. B. Selection Method The target bit rates are 108Mbps, 433Mbps, 866Mbps, 1300Mbps and 1625Mbps. They are considered with a ±5% accuracy. Fig. 7 depicts the corresponding bit rate for all parameter combinations (with a bandwidth of 1.3GHz). Each vertical line corresponds to the raw bit rate achieved by a fixed number of codes. Each point represents the bit rate corresponding to a single combination of constellation order and coding rate.

E. Code Length and Number of Codes Trade-Off

C. Channel Estimation Overhead In order to take into account the channel estimation cost we evaluate the minimum number of chips which are required to have an channel estimate error which is lower than working noise by 10 dBs. This corresponds to a training sequence which are 10 times longer than the spreading code. According to the channel length given in Table I and since the coherence time of UWB channel is about 200μs, the channel estimation overhead is less than 1%.

As seen in Section VIII, the best averaged SINR is linear with the SNR and this linearity can be obtained only with long sequences (longer than channel impulse response). We aim at tuning the system in this linear region while avoiding to superimpose too many codes for the same user. Indeed beyond this linear region, SINR saturates, and too many codes would also impact SINR and increases receiver complexity. Our choice is to use the shortest codes allowing linear SINR and, as a result, the trade-off is between the communication robustness and the data rate.

D. Selected Modes Among all parameter combinations that attain the target bit rates with a precision of ±5%, we select those achieving the maximal range. Table II provides the ranges corresponding to the selected modes. It illustrates the benefit of longer codes. As an example, the best mode for 433Mbps involves 8 codes of length 48 (achievable range 20m) while the best combination of modulation order and code length for two codes situation provides a range of 14m.

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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 57, NO. 2, FEBRUARY 2009

TABLE III R ANGES OF E XISTING UWB P ROPOSALS W ITH F REE S PACE ATTENUATION

Modes for Bandwidth=1.3GHz with Code length=48 for various number of codes Nc=2 Nc=4 Nc=6 Nc=8 Nc=10

1600

Mode MB OFDM range DS UWB range DS Multicode DS Multicode 3bit quantization

Data rate in Mbps

866

433

108

modes

Fig. 7.

• •

Available data rates for 24 and 48 length codes. TABLE II A S ELECTION OF M ODES

Range 1 corresponds to two slopes attenuation model Range2 corresponds to a free space attenuation Rate Mbps

Band

Lc

108 108 108 108 108

2.6 2.6 2.6 2.6 1.3

48 48 48 24 48

433 433 433 433 433 433

2.6 2.6 2.6 2.6 2.6 1.3

48 48 24 48 24 48

867 867 867 867 867

2.6 2.6 2.6 2.6 2.6

48 48 24 24 24

1300 1300 1300 1300 1300

2.6 2.6 2.6 2.6 2.6

48 24 48 24 24

1625 1625 1625 1625 1625

2.6 2.6 2.6 1.3 1.3

48 48 24 24 24

Nc

ORDER

Mode 108 Mb/s 2 qpsk 6 bpsk 4 bpsk 2 bpsk 6 qpsk Mode 433 Mb/s 8 qpsk 6 qpsk 4 qpsk 6 qam16 6 qpsk 8 qam16 Mode 866 Mb/s 8 qam16 6 qam16 6 qpsk 4 qam16 6 qam16 Mode 1300 Mb/s 8 qam16 6 qam16 8 qam64 8 qpsk 4 qam16 Mode 1600 Mb/s 10 qam16 10 qam64 10 qpsk 10 qam16 10 qam64

Code

Range1

Range2

1/2 1/3 1/2 1/2 1/3

20.3 20.2 19.5 17.9 13.6

45.7 45.4 42.9 38.0 25.0

1/2 2/3 1/2 1/3 1/3 1/2

11.8 11.3 10.6 10.4 10.0 6.4

20.4 18.9 17.1 16.8 15.9 8.1

1/2 2/3 2/3 1/2 1/3

7.6 6.9 6.7 6.6 6.5

10.5 9.0 8.7 8.4 8.2

3/4 1/2 1/2 3/4 3/4

5.6 5.1 5.1 4.9 4.8

6.5 5.8 5.8 5.5 5.3

3/4 1/2 3/4 3/4 1/2

4.8 4.4 3.7 1.1 1.0

5.2 4.7 3.7 1.1 1.0

model

VIII. C OMPARISON W ITH C URRENT P ROPOSALS This section compares the proposed approach to the two main system proposals for WPAN standardization in the IEEE 802.15.3a task group. The first proposal named MBOA (Multi Band OFDM Alliance) is based on an OFDM modulation with a bandwidth of 500MHz and 100 data carriers among a total of 128. A frequency hopping pattern is applied in order to occupy a 1.5GHz bandwidth. This allows a time gating processing gain of 4.5dB. Two possible redundancy modes are used to increase the SNR: i) a repetition of factor 2 within each OFDM symbol which ensures a real FFT output, ii) a repetition of factor 2 of whole OFDM symbols allowing an SNR gain of 3dB. In

110Mbps 10m 10m 45m 35 m

480Mbps 2.5m 2m 10m3 5m4

addition to this redundancy, the data stream is convolutionally encoded with 4 possible coding rates: 11/32, 1/2, 5/8, 3/4 obtained (by puncturing) from a 1/3 rate convolutional code ([133, 145, 175]8). The second proposal in the IEEE 802.15.3a task group is based on direct sequence spreading with possible MBOK modulation[13] and is denoted as DSUWB (Direct Sequence UWB). There are two possible bands of operation: a lower band from 3.1GHz to 4.85GHz and an upper band from 6.2GHz to 9.7GHz. A 1/2 rate convolutional code ([57, 65]8) is used with possible puncturing allowing to obtain 1/2 and 3/4 rates. The sequence lengths can be either 1, 2, 4, 6, 12 or 24. In this proposal some modes use the MBOK modulation which are not considered in this comparison. The criterion used for comparison is the allowed range of operation for the various systems at similar data rates. This range corresponds to a packet error rate of 8.10−2 with 1024 Bytes packets which is equivalent to a bit error rate of 10−5 . Unless otherwise stated we assume one slope free space attenuation model and CM1 channel model. The first point of comparison is the mode at 110Mbps. This mode exists in the MBOA. For DSUWB we chose a single code of length 12, 2.6GHz bandwidth and a 1/2 coding rate. Finally, our corresponding mode involves 6 sequences of length 48, QPSK constellation and a 1/3 forward error convolutional encoder (Table II column Range2). According to Batra[3], the 110Mbps mode of MBOA proposal has a range of 10m. The DSUWB 110Mbps mode has also a range of 10m (according to our own simulations). The proposed architecture range (45m) is more than four times that of the current proposals. The second point of comparison is the mode of 480Mbps. This mode exists in MBOA. For DSUWB we chose a single code of length 4, 2.6GHz bandwidth and 3/4 coding rate. This is compared to the mode involving 8 codes of length 48, 16QAM and 1/2 coding rate which has a data rate of 866Mbps. The MBOA 480Mbps mode has a range of 2.5m[3] while the equivalent mode in DSUWB (500Mbps) has a range of 2m. Our mode of comparison has a range of 10m for almost twice the bit rate. By introducing a channel quantization over 3 bits per real coefficient, the range of DS-multicode is reduced from 45m to 10m for 108Mbps mode and 12m for 433Mbps one. We assume that the channel estimation error is driven by the quantization noise. IX. C ONCLUSIONS This contribution proposed a physical layer UWB system design based on multicode direct sequence spread spectrum allowing an efficient use of linear receivers. This choice allows

KAMOUN et al.: A MULTICODE APPROACH FOR HIGH DATA RATE UWB SYSTEM DESIGN

to obtain altogether high data rates and reduced complexity. We showed that many parameters need to be optimized in this context in such a way to reduce the intersymbol and the intercode interference. The data rate increase is not obtained by shortening the spreading sequences but by increasing the number of superimposed codes assigned to the same user. At the same time, the code length are kept long to obtain good performance of the linear receivers. Compared to existing proposals, our system design allows to enlarge the system range by quite large quantities (up to 4) especially for high bit rates. R EFERENCES [1] M. Z. Win and R. A. Scholtz, “Impulse radio: how it works,” IEEE Commun. Lett., vol. 2, no. 2, Feb. 1998. [2] A. Batra, et al., “Multi-band OFDM physical layer proposal for IEEE 802.15 task group 3a - IEEE P802.15-03/268r3,” draft technical specification, IEEE, Mar. 2004. [3] A. Batra, J. Balakrishnan, G. R. Aiello, J. R. Foerster, and A. Dabak, “ Design of a multiband OFDM system for realistic UWB channel environments,” IEEE Trans. Microwave Theory Technol., vol. 52, Sept. 2004. [4] J. Foerster, “Channel modeling sub-committee report final,” Tech. Rep., IEEE, Dec. 2002. [5] A. A. M. Saleh and R. A. Valenzuela, “A statistical model for indoor multipath propagation,” IEEE J. Select. Areas Commun., pp. 128–137, Feb. 1987. [6] C.-L. I and R. D. Giltin, “Performance of multi-code CDMA wireless personal communications networks,” in Proc. IEEE Veh. Technol. Conf., July 1995, pp. 1060–1064. [7] P. Spasojevic and I. Seskar, “Ternay zero correlation zone sequences for multiple code UWB,” in Proc. Conf. Inform. Sciences Syst., Mar. 2004, pp. 939–943. [8] D. N. C. Tse and O. Zeitouni, “Linear multiuser receivers in random environments,” IEEE Trans. Inform. Theory, vol. 46, no. 1, pp. 171–188, Jan. 2000. [9] S. Verdú, “Spectral efficiency in the wideband regime,” IEEE Trans. Inform. Theory, vol. 48, no. 6, June 2002. [10] ECMA, “High rate ultra wideband PHY and MAC standard,” Tech. Rep., ECMA International, 2005. [11] R. Lupas and S. Verdu, “Linear multiuser detectors for synchronous code-division multiple-access-channels,” IEEE Trans. Inform. Theory, vol. 35, Jan. 1989. [12] D. N. C Tse and S. Hanly, “Linear multi-user receiver: effective interference, effective bandwidth and user capacity,” IEEE Trans. Inform. Theory, vol. 45, no. 2, pp. 641–657, Mar. 1999. [13] R. Fisher, R. Kohno, M. McLaughlin, and M. Welborn, “DS-UWB physical layer submission to 802.15 task group 3a,” Tech. Rep., IEEE, July 2004. Mohamed Kamoun was born in Sfax Tunisia in 1978. He received the engineering degree from Ecole National Supérieure de Techniques Avancées, Paris, France in 2001, a master degree in semiconductor physics from the Université Paris Sud, Orsay, France, in 2001, a master degree in digital communication from Ecole Nationale Supérieure des Télécommunications in 2002, and the Ph.D. degree from the Université Paris sud, Orsay, France in 2006. Since 2002 he has been working for Motorola Laboratories, Paris, France, where he is now a research engineer. His research interests include digital signal processing and cooperative wireless communication.

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Laurent Mazet received his Engineering degree in Electrical Engineering and M.Sc degree in signal processing from Ecole Nationale Supérieure des Télécommunications (Paris, France) in 1996 and he received his PhD degree in digital signal processing from the University of Marnes la Vallée (France) in 1999. In 2000, he joined the Motorola European Communications Research Lab (Saclay, France) as a research engineer in the Broadband Systems and Technologies Lab. Since then, he focuses his studies on advanced baseband algorithms design for Wireless Local Area Networks. Marc de Courville (M’96) was born in Paris, France, on April 21, 1969. He graduated from the Ecole Nationale Supérieure des Télécommunications (ENST, “Engineering University”), Paris, France, in 1993 and received the Ph.D. degree, from the ENST, also in 1996. Since 1996, he has been working for Motorola Laboratories, Paris, France, and is now a Research Team Manager involved in projects dealing with multicarrier and ultra-wideband systems for current and future generations of wireless local and personal area networks (IEEE 802.11a/b/g/n, IEEE 802.15.3a, and beyond). His research interests include digital communications and digital signal processing. Pierre Duhamel (M’87-SM’87-F’98) was born in France in 1953. He received the Eng. degree in electrical engineering from the National Institute for Applied Sciences (INSA) Rennes, France, in 1975 and the Dr.Eng. degree and the Doctoratés Sciences degree, both from Orsay University, Orsay, France, in 1978 and in 1986, respectively. From 1975 to 1980, he was with Thomson-CSF, Paris, France, where his research interests were in circuit theory and signal processing, including digital filtering and analog fault diagnosis. In 1980, he joined the National Research Center in Telecommunications (CNET), Issy les Moulineaux, France, where his research activities were first concerned with the design of recursive charge-coupled device filters. Later, he worked on fast algorithms for computing Fourier transforms and convolutions and applied similar techniques to adaptive filtering, spectral analysis, and wavelet transforms. From 1993 to September 2000, he was a Professor at Ecole Nationale Supérieure des Télécommunications (ENST), Paris, France, where his research activities focused on signal processing for communications. From 1997 to 2000, he was head of the Signal and Image Processing Department of ENST. He is currently with CNRS/LSS (Laboratoire de Signaux et Systemes/National Center of Scientific Research), Gif-sur-Yvette, France, where he is developing studies in signal processing for communications (including equalization, iterative decoding, and multicarrier systems) and signal/image processing for multimedia applications, including source coding, joint source/channel coding, watermarking, and audio processing. Dr. Duhamel was Chairman of the IEEE DSP committee from 1996 to 1998 and a member of the SP for the IEEE comm. committee until 2001. He was Co-General Chair of the 2001 International Workshop on Multimedia Signal Processing, Cannes, France, and Co-technical Chair of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 2006, Toulouse, France. He was the IEEE Distiguished Lecturer for 1999. A paper he coauthored on subspace-based methods for blind equalization received the "Best Paper Award" from the IEEE T RANSACTIONS ON S IGNAL P ROCESSING in 1998. He was also awarded the “Grand Prix France Telecom” by the French Science Academy in 2000. He was an Associate Editor of the IEEE T RANSACTIONS ON S IGNAL P ROCESSING from 1989 to 1991, an Associate Editor for the IEEE S IGNAL P ROCESSING L ETTERS , and a Guest Editor for the Special Issue on Wavelets of the IEEE T RANSACTIONS ON S IGNAL P ROCESSING.