Design of STBC- Multiband Ultra-Wideband (UWB) System by Using DWT with Three Transmit Antennas

20 JOURNAL OF TELECOMMUNICATIONS, VOLUME 25, ISSUE 1, MAY 2014

Design of STBC- Multiband Ultra-Wideband (UWB) System by Using DWT with Three

Transmit Antennas

Abstract - In this paper Outage performance is investigated for space-time block coded multiband orthogonal frequency division multiplexing ultra-wideband systems STBC MB-OFDM UWB. The design of STBC MB-OFDM UWB systems, with three transmit and single receive antennas, with the goal of achieving 1 Gbps data rate. We study the performance of these systems with different channel models schemes. The new proposed structures for the STBC-MB-UWB system based on wavelet transform (DWT) depends on the transmitted signal that generated by space time block coding matrix (G3)at the transmitter side, and the inverse of STBC matrix(G3) at the receiver side. The results extracted by a computer simulation for a single user. These STBC-MB-UWB systems were modeled using MATLAB V7.10 for the two types of the transform FFT and DWT (Wavelet Transform) are considered to allow various parameters of the system to be varied and tested. The simulations results, and evaluation tests of these proposed systems (Bit Error Rate (BERs)) and the operating range of these systems are obtained using frequency domain baseband simulations as well as more realistic full-system simulations. The results of all systems in the four types of channels (CM1, CM2.CM4) will be examined and compared. Finally, Simulation results show that the STBC MB-OFDM UWB systems with Discrete Wavelets Transform DWT provide significant gains for 1 Gbps transmission over MB-OFDM UWB systems using conventional method with Fast Fourier transform FFT. The simulation results are presented to support the theoretical analysis..

Index Terms: UWB, CM1.. CM4, multiband, OFDM, .

1. INTRODUCTION After the FCC allowed the use of UWB transmitters in the 3.1 to 10.6 GHz (requiring that the transmitters limit their EIRP to -41.25 dBm/MHz [1]), the industry has moved from the impulse radio paradigm towards other physical layer options. Although the impulse radio techniques have many advantages for the low rate and/or military applications, for commercial high data rate Wireless Personal Area Networks (WPANs) other modulation/transmission schemes have proved to be more attractive. One of the most popular approaches to UWB system design is the Multi-Band Orthogonal Frequency Division Multiplexing (MB-OFDM) [2][3]. This approach has received wide industry support and has been adopted by many industry alliances such as [4][5] and standardized by ECMA in December 2005 as a high-rate UWB PHY and MAC standard [6]. The highest physical layer (PHY) data rate in the current MB-OFDM specification [3] is only 480Mbps. This data rate cannot meet the requirements of future wireless applications, such as wireless High Definition (HD) video streaming. Thus, the next generation MB-OFDM UWB systems target more than 1Gbps PHY data rates. In order to achieve such high data rates, new modulation and coding techniques are needed. The Multiple Input Multiple Output (MIMO) technique is a promising solution, since it can increase channel capacity greatly under rich scattering scenarios. The MIMO technique has been adopted in many wireless systems such as the IEEE 802.11n Wireless Local Area Networks (WLANs) [7]. It is likely that the next generation UWB systems will employ the MIMO technique as well as precoding techniques. The MIMO technique is used to increase the data rate, while the precoding techniques are used to achieve frequency domain diversity which leads to improved system performance [11]. Outage probability is an important performance measure in wireless communication systems, and is usually defined as the probability of unsatisfactory signal reception. The outage analysis for multiple-antenna systems is always performed under assumptions of Rayleigh, Rice or Nakagami fading channels [12, 13]. However, for the IEEE 802.15.3a UWB channel model [11], which further considers the log-normal shadowing effect, few results have ever appeared according to our best knowledge. In this paper, recent advances in high

speed electronics and novel UWB antenna designs have resulted in a fresh look of UWB systems. The first generation of commercial UWB systems will be based on -UWB and multiband OFDM. On the other hand, the application of the wavelet packets to wireless systems has been studied in a wide variety of forms [4]. Those studies have shown to provide good performance against time-varying fading channels and narrowband interference rejection as wavelet waveforms have low sidelobes [15]. Those properties make WPs a very attractive design alternative for UWB applications. Hence, we propose a novel multi-channel modulation scheme for UWB transmissions based on the Fast Fourier transform (FFT) and discrete wavelet transform DWT combined with spread spectrum and multiband approaches, as analogous to multicarrier CDMA and multiband OFDM. Thus, two possible structures are studied, namely multiband DWT multiplexing and DWT-CDMA multiplexing [16-18]. Indeed, the proposed techniques divide UWB channels into a set of parallel channels. Exploiting the properties of wavelet packets in time and frequency, a set of multi-channel basis functions can be formed such that the corresponding channel-output functions remain nearly orthogonal for any UWB channel. Multiple accesses are introduced in the form of a time-frequency hopping code (similar to multiband OFDM) [19-21]. The remaining of this paper is organized as follows. Section 2, briefly describes the MB-OFDM UWB system. Section 3, Provides the details of the system model and modulation schemes used to achieve 528 Mbps data rate and signal model. Section 4 presents the simulation results obtained using different simulation settings, and the conclusions are drawn in Section 5.

2. MULTI-BAND UWB SYSTEM A multiband OFDM system devides the spectrum between 3.1 to 10.6 GHz into several non-overlapping subbands each one occupying approximately 500 MHZ of bandwidth [2]. Information is transmitted using OFDM modulation over one of the subbands in a particular time-slot. The transmitter architecture for the multiband OFDM system is very similar to that of a conventional wireless OFDM system. The main difference is that multiband OFDM system uses a time-frequency code (TFC) to select the center

Murad O. Abed Helo


frequency of different subbands which is used not only to provide frequency diversity but also to distinguish between multiple users (see figure 1 a). Different puncturing patterns of a 1/3 convolutional mother code combined with time and/or frequency repetition, generate ten data rates from 55 Mbps to 480 Mbps. One OFDM symbol has duration of 312.5 ns and a bandwidth of 528 MHz. A 128 point IFFT or IDWT is used along with a cyclic prefix (CP) length of 60.6 ns to modulate 122 subcarriers among which 100 subcarriers are allocated to data, 64 subcarriers are used for frame synchronization and 10 subcarriers provide 9.5 ns of guard interval for switching between subbands. Here, we consider multiband OFDM in its mandatory mode ie. employing 3 first subbands. More details about multiband OFDM system parameters and its advantages for UWB transmission can be found in [2] [4]. This preamble is used for time and frequency synchronization. After the time domain preamble, a frequency domain training sequence is transmitted. This sequence, which is repeated 6 times, is employed for channel estimation. This means that in the TFI mode two copies of the frequency domain sequence are available for the channel estimation in each band. The frequency domain training sequence as well as the header and the data that follows it are generated using an OFDM modulation scheme with N = 128 sub-carriers. Instead of a more traditional cyclic prefix, each symbol (including the preamble and training sequences) is padded with NZP = 33 zeros. Within each OFDM symbol, 61 sub-carriers are used for data transmission and 64 are used for pilot symbols. Also, 10 sub-carriers (five on each edge) are used as guard sub-carriers. The data from the adjacent sub-carriers is copied on these sub-carriers. On each data sub-carrier, the data is modulated either using QPSK.

2.1. UWB Channel Model We have modeled the multipath channel using the model provided in [1]. This is the channel model adopted for use in the IEEE 802.15.3a standardization Task Group. This model is similar to the Saleh-Valenzuela (S-V) multi-cluster model [8]. Each cluster has an exponential decay profile. The overall power of each of the clusters also exponentially decays with time. The difference between this adopted model and the SV model is that instead of a Rayleigh distribution for the coefficient of each path, a log-normal distribution is used. To model the shadowing effects, the overall gain of each channel realization is also modulated by another log-normal shadowing coefficient. As given in [11], four different sets of parameters (referred to as CM1 through CM4) are available. These models (parameter sets) are chosen to represent different channel conditions in typical usage scenarios. CM1 describes a LOS (line-of sight) scenario with a separation between transmitter and receiver of less than 4m. CM2 describes the same range, but for a non-LOS situation. CM3 describes a non-LOS scenario for distances between TX and RX 4-10m. Scenario 4 finally describes an environment with strong delay dispersion, resulting in a delay spread of 25ns. Note that, when using the model, the total average received power of the multipath realizations is typically normalized to unity in order to provide a fair comparison with other wideband and narrowband systems. The channel characteristics and corresponding parameter matching results in Table 1 correspond to a time resolution of 167 psec, although the output of the model described in the appendix yields

continuous time samples (i.e., based upon an infinite bandwidth). How this model matches measurements with bandwidths greater than 6 GHz is unknown due to the lack of measurement data at this bandwidth.

Table 1: Multipath channel target characteristics and model parameters.[11]

Target Channel Characteristics CM 1 CM 2 CM 3 CM 4

m [ns] (Mean excess delay) 5.05 10.38 14.18 rms [ns] (rms delay spread) 5.28 8.03 14.28 25 NP10dB (number of paths within 10 dB of the strongest path)

35

NP (85%) (number of paths that capture 85% of channel energy)

24 36.1 61.54

Model Parameters [1/nsec] (cluster arrival rate) 0.0233 0.4 0.067 0.067 [1/nsec] (ray arrival rate) 2.5 0.5 2.1 2.1 (cluster decay factor) 7.1 5.5 14.00 24.00 (ray decay factor) 4.3 6.7 7.9 12 1 [dB] (stand. dev. of cluster lognormal fading term in dB)

3.4 3.4 3.4 3.4

2 [dB] (stand. dev. of ray lognormal fading term in dB)

3.4 3.4 3.4 3.4

x [dB] (stand. dev. of lognormal fading term for total multipath realizations in dB)

3 3 3 3

Model Characteristics

m 5.0 9.9 15.9 30.1 rms 5 8 15 25 NP10dB 12.5 15.3 24.9 41.2 NP (85%) 20.8 33.9 64.7 123.3 Channel energy mean [dB] -0.4 -0.5 0.0 0.3 Channel energy std dev. [dB] 2.9 3.1 3.1 2.7

In [1], Snow et al provided some information-theoretic performance measures of MB-OFDM for UWB communications from the aspect of outage capacity and cutoff rates. To estimate the performance of MB-UWB systems with multiple antennas, we also use the calculation of outage capacity of UWB channels and get a rough picture of the data rates that can be achieved. We assume that the multipath channels for different antenna pairs are statistically independent. For the multipath block fading channels, the outage capacity is the theoretical limit which shows the highest achievable data rate at certain outage error rate. For the multi-band OFDM systems, because of the frequency-hopping feature, there are a total of 300 data sub-carriers that must be averaged to calculate the average capacity:

).det(log180

12180

1

iiti

Nrav HHNSNRIC (1)

where Cav is the average capacity, Hi is the channel matrix on the i-th subcarrier, and Nt and Nr are the number of transmit and receive antennas, respectively. The outage probability Pout associated with a target rate R is defined as Pout = Pr (Cav < R). For example, if we set the outage probability to 0.1, we can determine the target rate R corresponding to this channel outage. The maximum data rate theoretically attainable at PER = 0.1 can be estimated as Rdata = R W Rc, where R is the outage capacity (in bits/s/Hz), W is the bandwidth, and Rc is the code rate. Using independent realizations of the CM2 channel model [1], we have calculated outage capacity at PER = 0.1 for all possible antenna formations. We can see that at medium SNR, (Tx and Rx) system can provide double the data rate that can be achieved by the (Tx and Rx) system with the same bandwidth. Also, (Tx and Rx) system has certain


advantage over the (Tx and Rx) system from the capacity point of view. Therefore, UWB system with multiple antennas is a good candidate to increase the date rate up to 1 Gbps with the fixed 1 Gbps bandwidth.

2.2. Simulation Environment To simulate the behavior of the above systems in multipath environment, we have generated the UWB channel using independent realizations of the models provided in [12], which can be re-sampled and converted to the baseband frequency domain channel coefficients. This assumes that the channels are independent, i.e. sufficient multipath exists and antennas are separated in space by at least one wavelength. Furthermore, the power of the channel coefficients is normalized, i.e., it has been assumed that shadowing does not exist. Also, the effect of increased path loss at higher frequency band has not been taken into account. These simple simulations have been used to compare different modulation options. A full system-level simulation model, including real world impairments, has also been set-up to evaluate the performance of the most promising systems in this paper. The transmitter includes a Digital to Analog Converter (DAC) operating at 1GHz, an analog filter to remove signal images, and a mixer to up-convert the signal to the desired frequency at each transmit antenna. For each receive antenna, the analog front-end in the receiver includes a mixer to bring the signal down to baseband, a filter to reduce out-of-band signal and an AGC-ADC (Automatic Gain Control - Analog to Digital Converter) loop to adjust gain and to digitize the signal. The base-band module processes the ADC output data to detect the burst and to correct for frequency and timing errors. It then processes the frequency domain preamble to estimate the channel, which is used to equalize the header and payload symbols. The equalized data is then demapped to generate to the header symbols. The payload symbols are processed based on the parameters decoded from the Header symbols. In all simulations, the Packet Error Rate (PER) performance is calculated using the average PER for all channel realizations. The performance is measured at PER = 0.1 [21].

3. SYSTEM DESIGN The block diagrams of the proposed systems for MB-UWB are depicted in Figure (1) and (2).These Figures illustrates a typical MB-UWB system used for Multicarrier modulation. In the conceptual block diagram of a MB-UWB, suppose the data packet dn generated at a rate of Rs, is a stream of serial data to be transmitted using this scheme of modulation. The receiver is based upon a square-law detector followed by a low-pass filter and an analog-to-digital converter (ADC) with built-in track and hold circuit. Figure (2) shows the block schematic diagram of this UWB receiver. A low-pass filter with 1 GHz cut-off frequency (rise time 350 ps) performs averaging of the square-law detector output signal. After 20 dB of amplification, the signal with a track and hold circuit with 1 GHz bandwidth is required. The amplified detector signals of 20 mV (10 LSB) will ensure reliable detection. Each data packet convert the data streams from serial to parallel form to construct a one dimensional vector contains the data symbols to be transmitted as shown:

TLddddd ).......( 1210 (2)

Where, L is the packet length. Each serial-to-parallel converted data symbols. As a result each data symbol becomes a vector with L bits. So, a matrix D of size L by L is obtained. Then each column of the matrix D converts to serial data using parallel-to-serial converter. The same procedure illustrated in [14] will be used with each converted serial data. The transmitted baseband signal of user k is written as:

M

m n

N

ucmmkck uTnTtfndEtS

1 0 1, )()()( (3)

where k=1, ..., K, K is the active user number; dk(n) corresponding to the BPSK complex signal denotes the nth data symbol of the kth user, and {dk(n)} are assumed to be independent, identically distributed (i.i.d) with equal probability, and Tb is the symbols period. The chip period Tc, corresponds to the minimum orthogonal shifting defined in complex wavelet packet; Ec is the mean energy over a chip. So the sub-carrier symbol period T=MTc,,M, is the number of sub-carriers [13]. The OFDM based on DWT will be used, from OFDM encoder throughout generation and insertion of Pilot carriers [12], the OFDM modulation using IDWT and the addition of the cyclic prefix. This is followed by sequences insertion, parallel to serial conversion for transmitter and then the channel effect for transmitted sequence is added. The received additive sequences in receiver antenna are passed through serial to parallel conversion and sequence separation. After this step each sequence discarded the cyclic prefix and inter to OFDM demodulator that use the DWT where after, the zero padding is removed from each sequence and the training sequence will be used to estimate the channel transfer function, h(t) using :

)()(

)(kHkY

kXe

pe k=0,1,.,N-1 (4)

For each received sequence [13].

We assume that the wireless channel from transmitter antenna to receive antenna experience independent, slow time-varying frequency selective Rayleigh fading, whereas every sub-carrier channel is considered to be flat and slow fading [15]. So the impulse response of mth subcarrier channel from transmit antenna to the receive antenna for user k can be repressed as

)()exp()( ,,,, kmkmkkmkmk tjth (5) Where mk , and mkj , denote the amplitude and phase of

mk , respectively are i.i.d uniform variables in the interval [0,2] for different k, m. So at the receiver, after down converting to baseband, the received signal from receive antenna can be written can be written by:

Kk

mkkk tnthttStr1

, )()()()(

K

k

M

m n

N

umkc ndE

1 1 0 1, )( (6)

)()( , tntuTnTtf mkkkcm Where n(t) is AWGN noise terms with double sided power spectrum density N/2 and zero mean. Single-path delay k is i.i.d. for different k and uniforms in [0,Tc],and tk is the


time misalignment of user k with respect to the reference user at the receiver which is i.i.d for different k and uniforms in [0, Ts.].

Nv Tc

lcc

llli dtvTiTtfvctrY1

, )()()(

K

k

M

m n

N

u Tckkcmmkc tuTnTtfndE

1 1 0 1, )()(

dtvctuTnTtf kmklkccl )()( , (7)

Since cross-correlation functions of the optimized Multiwavelets packets satisfy equation

)()()( nlmnTR clmf therefore the interference from same

sub-carrier and same user k=1, interference from other sub-carrier and same user will equal zero. The desired output is

Nv Tc

lcn

llilici dtvTiTtftniNdEY1

,, })()()({ (8)

3-1 A FAST COMPUTATION METHOD OF DWT ALGORITHMS Under the reconstruction condition 0 dtt , the continuously labeled basis functions (wavelets), tkj , behave in the wavelet analysis and synthesis just like an orthonormal basis. By appropriately discretizing the time-scale parameters, , s, and choosing the right mother wavelet, t , it is possible to obtain a true orthonormal basis. The natural way is to discretize the scaling variable s in a logarithmic manner jss 0 and to use Nyguist sampling rule, based on the spectrum of function x (t), to

discretize at any given scale Tsk j 0 . The resultant wavelet functions are then as follows:

0020, ktsst jjkj (1) If s0 is close enough to one and if T is small enough, then the wavelet functions are over-complete and signal reconstruction takes place within non-restrictive conditions on t . On the other hand, if the sampling is sparse, e.g., the computation is done octave by octave (s0 = 0), a true orthonormal basis will be obtained only for very special choices of t . Based on the assumption that wavelet functions are orthonormal:

Figure (1): (b) UWB transmitter and Receiver[10]

Fig.(1) (a) Block Diagram of a STBC-MB-UWB system


otherwise

nkandmjifdttt nmkj 0

1,, (2)

For discrete time cases, (2.8) is generally used with s0 = 2, the computation is done octave by octave. In this case, the basis for a wavelet expansion system is generated from simple scaling and translation. The generating wavelet or mother wavelet, represented by t , results in the following two-dimensional parameterization of tkj, .

22 2, ktt jjkj (3) The 22 j factor in (2.9) normalizes each wavelet to maintain a constant norm independent of scale j. In this case, the discretizing period in is normalized to one and is assumed that it is the same as the sampling period of the discrete signal -j2 k . All useful wavelet systems satisfy the multiresolution conditions. In this case, the lower resolution coefficients can be calculated from the higher resolution coefficients by a tree-structured algorithm called filter-bank [30]. In wavelet transform literatures; this approach is referred to as discrete wavelet transform (DWT).

3.1.1 The Scaling Function The multiresolution idea is better understood by using

a function represented by t and referred to as scaling function. A two-dimensional family of functions is generated, similar to (3), from the basic scaling function by [30]:

ktt jjkj 2 2 2, (4) Any continuous function, f(t), can be represented, at a given resolution or scale j0, by a sequence of coefficients given by the expansion:

k

kjjj tkftf ,000 (5)

In other words, the sequence kx j0 is the set of samples of the continuous function x(t) at resolution j0 . Higher values of j correspond to higher resolution. Discrete signals are assumed samples of continuous signals at known scales or resolutions. In this case, it is not possible to obtain information about higher resolution components of that signal. It is however, desired to use the given samples to obtain the lower resolution representation of the same signal. This can be achieved by imposing some properties on the scaling functions. The main required property is the nesting of the spanned spaces by the scaling functions. In other words, for any integer j, the functional space spanned by [31]:

,2,1 ; , kfortkj (6) Should be a subspace of the functional space spanned by:

,2,1 ; ,1 kfortkj (7) The nesting of the space spanned by ktj 2 is achieved by requiring that t be represented by the space spanned by t2 . In this case, the lower resolution function, t , can be expressed by a weighted sum of shifted version of the same scaling function at the next higher resolution, t2 , as follows: 2 2 ktkht

k

(8)

The set of coefficients kh being the scaling function coefficients and 2 maintains the norm of the scaling function with scale of two. t being the scaling function which satisfies this equation which is sometimes called the refinement equation, the dilation equation, or the multiresolution analysis equation (MRA) [29-31].

3.1.2 The Wavelet Functions The important features of a signal can better be described or parameterized, not by using tkj , and increasing j to increase the size of the subspace spanned by the scaling functions, but by defining a slightly different set of functions tkj, that span the differences between the spaces spanned by the various scales of the scaling function.

It is shown that these functions are the same wavelet functions discussed earlier. Since it is assumed that these wavelets reside in the space spanned by the next narrower scaling function, they can be represented by a weighted sum of shifted version of the scaling function t2 as follows:

2 2 ktkgtk

(9) The set of coefficients kg s is called the wavelet function coefficients (or the wavelet filter). It is shown that the wavelet coefficients are required by orthogonality to be related to the scaling function coefficients by [29,31]: khkg n 11 (10)

One example for a finite even length-N kh kNhkg k 11 (11)

The function generated by (9) gives the prototype or mother wavelet t for a class of expansion functions of the form shown in (3).

For example the Haar scaling function is the simple unit-width, unit-height pulse function t shown in Fig. (2.) [30] and it is obvious that t2 can be used to construct t by: 122 ttt (12)

which means (8) is satisfied for coefficients 210 h , 211 h .

The Haar wavelet function that is associated with the scaling function in Fig. (2a) are shown in Fig. (2.b). For Haar wavelet, the coefficients in (12) are 210 g , 211 g .

Fig. (2): (a) Haar Scaling Function, (b) Haar wavelet function.


Any function tf could be written as a series expansion in terms of the scaling function and wavelets by [31]:

000 ,,

jj kkjj

kkjj tkbtkatf (13)

In this expansion, the first summation gives a function that is a low resolution or coarse approximation of f(t) at scale j0 . For each increasing j in the second summation, a higher or finer resolution function is added, which adds increasing details. The choice of j0 sets the coarsest scale whose space is spanned by tkj .0 . The rest of the function is spanned by the wavelets providing the high-resolution details of the function. The set of coefficients in the wavelet expansion represented by (13) is called the discrete wavelet transform (DWT) of the function f(t). These wavelet coefficients, under certain conditions, can completely describe the original function, and in a way similar to Fourier series coefficients, can be used for analysis, description, approximation, and filtering. If the scaling function is well behaved, then at a high scale, samples of the signal are very close to the scaling coefficients. In order to work directly with the wavelet transform coefficients, one should present the relationship between the expansion coefficients at a given scale in terms of those at one scale higher. This relationship is especially practical by noting the fact that the original signal is usually unknown and only a sampled version of the signal at a given resolution is available. As mentioned before, for well-behaved scaling or wavelet functions, the samples of a discrete signal can approximate the highest achievable scaling coefficients. It is shown that the scaling and wavelet coefficients at scale j are related to the scaling coefficients at scale (j + 1) by the following two relations.

m

jj makmhka 1 2 (14)

m

jj mbkmgkb 1 2 (15)

The implementation of equations (14) and (15) is illustrated in Fig.(3). In this figure, two levels of decomposition are depicted. h and g are low-pass and high-pass filters corresponding to the coefficients nh and ng respectively. The down-pointing arrows denote a decimation or down-sampling by two. This splitting, filtering and decimation can be repeated on the scaling coefficients to give the two-scale structure. The first stage of two banks divides the spectrum of kja ,1 into a low-pass and high-pass band, resulting in the scaling coefficients and wavelet coefficients at lower scale kja , and kjb , . The second stage then divides that low-pass band into another lower low-pass band and a band-pass band.

For computing fast discrete wavelet transform (FDWT) consider the following transformation matrix for length-2:

100000

10000010

100000

10000010

gg

gggg

hh

hhhh

T

(16)

and the following transformation matrix for length-4:

10000000323210000000

0000321000000032101000000032

00003210000000003210

gggggggg

gggggggg

hhhh

hhhhhhhh

T

(17)

Here blank entries signify zeros. By examining the transform matrices of the scalar wavelet as shown in equations (16) and (17) respectively, one can see that, the first row generates one component of the data convolved with the low-pass filter coefficients ( 0h , 1h , ). Likewise the second, third, and other upper half rows. The lower half rows perform a different convolution, with high pass filter coefficients ( 0g , 1g , ). The action of the matrix, is thus to perform two related convolutions, then to decimate each of them by half (throw away half the values), and interleave the remaining halves.

By using (11), the transform matrices become:

010000

01000001

100000

10000010

hh

hhhh

hh

hhhh

T

(18)

23000000010123000000

0000012300000001231000000032

00003210000000003210

hhhhhhhh

hhhhhhhh

hhhh

hhhhhhhh

T

(19)

It is useful to think of the filter ( 0h , 1h , 2h , 3h ) as being a smoothing filter, H, something like a moving average of four points. Then, because of the minus signs, the filter ( 3h , 2h , 1h , 0h , ), G, is not a smoothing filter. In signal processing contexts, H and G are called Quadrature mirror filters. In fact, the nh s are chosen so as to make G yield, insofar as possible, a zero response to a sufficiently smooth data vector. This results in the output of H, decimated by half accurately representing the datas smooth information. The output of G, also decimated, is referred to as the datas detail information.

Fig. (3): The filter bank for calculating the wavelet coefficients.


For such characterization to be useful, it must be possible to reconstruct the original data vector of length N from its N/2 smooth and its N/2 detail. That is affected by requiring the matrices to be orthogonal, so that its inverse is just the transposed matrix:

0000100010000000

0000000010010000000001001000

2

hhhh

hhhh

hhhh

T

(20)

2013000031020000

02100300000

000000300001000200002000130003100020000200013000310002

000023001100032000

2

hhhhhhhh

hhhh

hhhhhhhh

hhhhhhhh

hhhhhhhh

hhhh

T

(21)

For a length-2 nh , there are no degrees of freedom left after satisfying the following requirements [89,140]:

110

21 0 22 hh

hh (22)

which are uniquely satisfied be:

21 ,

211 , 02 hhhD (23)

These are the Haar scaling function coefficients, which are also the length-2 Daubechies coefficients. For the length-4 coefficients sequence, there is one degree of freedom or one parameter which gives all the coefficients that satisfies the required conditions [74-78]:

03 1 2 0 13210

23 2 1 0 2222

hhhhhhhh

hhhh

(24)

Letting the parameter be the angle , the coefficients become

22sincos13

22sincos12

22sincos11

22sincos10

h

h

h

h

(25)

These equations give length-2 Haar coefficients of equation (21) for 23,2,0 and length-4 Daubechies coefficients for 3 . These Daubechies-4 coefficients have a particularly clean form:

2431,

2433,

2433,

2431

4Dh (26)

The structure of a one-dimensional DWT is shown in Fig. (4). nX is the 1-D input signal. nh and ng are the analysis lowpass and highpass filters which, split the input signal into two subbands: lowpass and highpass. The

lowpass and highpass subbands are then downsampled generating nX L and nX H respectively.

The up sampled signals are filtered by the

corresponding synthesis lowpass nh~ and highpass ng~ filters and then added to reconstruct the original signal. Note that the filters in the synthesis stage, are not necessary the same as those in the analysis stage. For an orthogonal filter bank, nh~ and ng~ are just the time reversals of nh and ng respectively [33].

To compute a single level FDWT for 1-D signal the next step should be followed: 1. Checking input dimensions: Input vector should be of length N, where N must be power of two. 2. Construct a transformation matrix: using transformation matrices given in (18) and (19). 3. Transformations of input vector, which can be done by apply matrix multiplication to the NN constructed transformation matrix by the N1 input vector.

3.1.3- Computation of IFDWT for 1-D Signal: To compute a single level IFDWT for 1-D signal the next step should be followed: 1. Let X be the Nx1 wavelet transformed vector. 2. Construct NxN reconstruction matrix, T2, using

transformation matrices given in (20) and (21). 3. Reconstruction of input vector, which can be done by

apply matrix multiplication to the NxN reconstruction matrix, T2, by the Nx1 wavelet transformed vector.

3.2 Signal model of Three Transmit and One Receive Antenna At a given symbol period, three signals are transmitted simultaneously from three transmit antennas. The signal transmitted from antenna one (Tx1) is denoted by S1, the signal from antenna two (Tx2) by S2 and the signal from antenna three (Tx3) by S3. This process will go on in the same manner until transmitting the last row of the G3 transmission matrix as given in equation (27). This matrix has a rate of half (1/2) and is used as STBC encoder to transmit any complex signal constellations. The encoding, mapping and transmission of the STBC can be summarized in Table 2.

Fig. (4): Analysis and Synthesis stages of a 1-D single level DWT.


Table 2: Encoding and mapping of STBC for three transmit antennas using complex signals

For the four transmit and one receive antenna system, the channel coefficients are modeled by a complex multiplicative distortions, h1 for the first transmit antenna, h2 for the second transmit antenna and h3 for the third transmit antenna. The channel coefficients explained above are summarized in Table 3.

(27)

Table 3: Three transmit and one receive channel coefficients

Assuming the fading is constant over the four consecutive symbols and then channel coefficients can be represented as

(28)

The receiver in this case will receive eight different signals in eight different time slots. The received signals can be represented as

(29)

The combiner in Figure (1) builds the following three combined signals

(30)

4. SIMULATION RESULTS OF THE PROPOSED MB-UWB SYSTEMS: In this section the simulation of the proposed MB-UWB Systems in MATLAB R2010a are achieved. In this part, we used Rayleigh's distribution method to simulate the effect of antenna selection for ultra-wide band system. Under CM1-CM4 channel model, we suppose that the transmitting completely understood the channel condition information. And system used DWT STBC-MB-UWB, exploited BPSK map, an OFDM symbol had 180 subcarriers. Table (2) shows the parameters of the system that are used in the simulation; the bandwidth used was 1GHz and carrier frequency 4.2 GHz using Daubechies-4 coefficients for Discrete Wavelet DWT with level two.

Table 2: Simulation Parameters

DWT-MB- UWB DFT-MB- UWB DWT FFT Multicarrier Types QPSK QPSK Modulation Types 1GHz 1GHz Bandwidth 128 128 Number of sub-carriers 128 128 Size of packet

Db4 with 1 and 2 level Wavelet type CM1 CM1

Channel model CM2 CM2 CM3 CM3 CM4 CM4

4.1. Performance of MB-UWB in CM1 Channel model: Simulations are done utilizing the IEEE 802.15.3a multi-path channel [11] to obtain a detection probability over SNR. The probability of detection becomes about 0.5 when SNR is 27dB in the IEEE 802.15.3a CM1 and CM4. The channel models consist of AWGN, IEEE 802.15.3a CM1 (Residential LOS) with a parameter shown table (1). In this section, the channel is modeled as CM1 for wide range of SNR from 0dB to 40dB. Simulation result of the proposed STBC-MB-UWB Systems is simulated as shown in Figure (1) which gives the BER performance of STBC-MB-UWB Systems in CM1 channel model. It is shown clearly that the STBC-MB-UWB Based on DWT is much better than STBC-MB-UWB systems based on FFT. This is a reflection to the fact that the orthogonal bases of the wavelets is much significant than the orthogonal bases used in FFT. From Figure (5) it can be seen that for BER=10-4 the SNR required for STBC-MB-UWB Based on DWT about 6.5dB,8dB and 12dB for 1,2 and 3 antennas and for STBC-MB-UWB Based on FFT have 26.5dB, 30dB and 33.5dB respectively, therefore a gain of 20dB for the DWT against FFT. As shown in Figure (5) it was found that the DWT- STBC-MB-UWB is outperform significantly other than other systems for this channel model.

1

2

1 1 1 1

2 2 2 2

33 3 3 3

( ) ( )

( ) ( )

( ) ( )

j

j

j

h t h t T h h e

h t h t T h h e

h t h t T h h e

1 1 1 2 2 3 3 1

2 1 2 2 1 3 4 2

3 1 3 2 4 3 1 3

4 1 4 2 3 3 2 4

5 1 1 2 2 3 3 5

6 1 2 2 1 3 4 6

7 1 3 2 4 3 1 7

8 1 4 2 3 3 2 8

* * ** * ** * ** * *

r h s h s h s nr h s h s h s nr h s h s h s nr h s h s h s nr h s h s h s nr h s h s h s nr h s h s h s nr h s h s h s n

1 1 1 2 2 3 3 1 5 2 6 3 7

2 2 1 1 2 3 4 2 5 1 6 3 8

3 3 1 1 3 2 4 3 5 1 7 2 8

* * * * * *

* * * * * *

* * * * * *

s h r h r h r h r h r h r



1 1 1 2 2 3 3 1 5 2 6 3 7

2 2 1 1 2 3 4 2 5 1 6 3 8

3 3 1 1 3 2 4 3 5 1 7 2 8

* * * * * *

* * * * * *

* * * * * *

s h r h r h r hr h r h r

s h r h r h r h r hr h r

s h r h r h r h r hr h r


4.2. Performance of MB-UWB in CM2 Channel model: In this type of channel, the signal affected by the flat fading with addition to AWGN; in this case all the frequency components in the signal will be effect by a constant attenuation and linear phase distortion of the channel, which has been chosen to have a Rayleigh's distribution of IEEE 802.15.3a CM2 with a parameter shown table (1). From Figure (6) it can be seen that for BER=10-4 the SNR required for STBC-MB-UWB Based on DWT about 8dB,9dB and 12dB for STBC-MB-UWB Based on DWT with using 1,2 and 3 antennas and FFT have 30dB,33dB and 37dB respectively, therefore a gain of 21.5dB for the DWT against STBC-MB-UWB Based on FFT. As shown in Figure (5) it was found that the DWT- STBC-MB-UWB is outperform significantly than other systems for this channel model.

4.3. Performance of MB-UWB in CM3 Channel model: In this section, the channel model is assumed to be IEEE 802.15.3a CM3, where the parameters of the channel in this case as shown in table (1). That BER performance of MB-UWB Based on DWT, DWT and FFT are shown in Figure (7). It was clearly that BER performance of MB-UWB Based on DWT is better than STBC-MB-UWB Based on DWT and FFT. The STBC-MB-UWB Based on DWT has BER

performance 10-4 at SNR=9.5dB, 12dB and 15dB for STBC-MB-UWB DWT and STBC-MB-UWB Based on FFT have the same BER performance at 33.5dB. From the above results it can be concluded that the MB-UWB Based on DWT is most significant than the conventional systems (FFT based STBC-MB-UWB) and DWT based STBC-MB-UWB in this channel model CM3 that have been assumed.

4.4 Performance of MB-UWB in CM4 Channel model In this section, the channel model is assumed to be selective fading channel of IEEE 802.15.3a CM4, where the parameters of the channel shown in table (1). The BER performance of proposed system and conventional systems was shown in Figure (8). From this figure, it is clearly that proposed system (STBC-MB-UWB Based on DWT) is better than STBC-MB-UWB Based on FFT. The MB-UWB Based on DWT has BER performance 10-4 at SNR=13dB,15dB and 19dB for STBC-MB-UWB based on DWT for 1,2 and 3 antennas and the same BER performance at 35.5dB,38.5dB and 45dB for STBC-MB-UWB Based on FFT.

From the above results it can be concluded that the MB-UWB Based on DWT was most significant than the conventional systems (FFT based MB-UWB) in the different channel models that have been assumed in these simulations.

Figure 5: BER performance of STBC-MB-UWB System in CM1 channel model





5. CONCLUSIONS In this paper, we investigate the performance of the STBC-MB-UWB based on DWT systems under IEEE 802.15.3a UWB channel models CM1-CM4, in which the multipath effect is considered. Based on the obtained results, we can see that the STBC-MB-UWB system with based on DWT with three antennas provides the best performance compare with the same systems designed using FFT in the different channel models that have been assumed in this paper. The Simulations results proved that the proposed design achieved much lower bit error rates and better performance than FFT- STBC-MB-UWB and assuming reasonable choice of the bases function and method of computations and the use of multiple antennas at the transmitter enhances the system spectral efficiency and supports better error rate and these benefits come at no extra cost of bandwidth. The improvements are about 20dB over FFT systems in all type UWB channel. In terms of performance, this method using DWT and STBC cans double the data rate while keeping the same transmission range in a new STBC-MB-UWB system. REFERENCES

[1] Snow C., Lampe L., and Schober R. 2009. "Interference Mitigation for Coded MB-OFDM UWB", IEEE Trans. on Broadcasting, Vol.48, No.3, pp 223-229, September 2009.

[2] Batra 2004 Multiband OFDM physical layer proposal for IEEE 802.15 Task Group 3a. IEEE P802.15-03/142r2-TG3a;.

[3] Stphane van Roy, Claude Oestges, Franois Horlin, and Philippe De Doncker A Comprehensive Channel Model for UWB Multisensor Multiantenna Body Area Networks IEEE Transactions On Antennas And Propagation, Vol. 58, No. 1, January 2010.

[4] A.H. Muqaibel Directional modeling of ultra wideband communication channels, IET Commun., 2010, Vol. 4, Iss. 1, pp. 5162.

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[7] Ghorashi S.A, Said F, Aghvami AH. 2006 Transmit diversity for multiband OFDM UWB systems IEE Proc Communications; vol. 153:pp5739.

[8] Koga H., N. Kodama, and T. Konishi, 2003"High-speed power line communication system based on wavelet OFDM," in Proc. IEEE ISPLC 2003, Kyoto, Japan, May 2003, pp. 226-231.

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[15] G.C.H.Chuang, P.A. Ting, J. Y. Hsu, J. Y.Lai, S.C. Lo,Y.C.Hsiao, and T. D. Chiueh, A MIMO WiMAX SoC in 90 nm CMOS for 300 km/h mobility, in IEEE Int. Solid-State Circuits Conf. (ISSCC) Dig.Tech. Papers, 2011, pp. 134136.

[16] Mohammed Z.J., VIDEO Image Compression based on Multiwavelets Transform, PhD Thesis, University of Baghdad, June 2004.

[17] S. Maki, E. Okamoto, Y. Iwanami, Performance Improvement of Haar based Wavelet Packet Modulation in Multipath Fading Environment, ISCIT 2007, October 2007, Sidney, Australia.

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Murad O. Abed Helo (Member IEEE) was born in Babylon-1962, Iraq. He received the B.Sc. degree in Electrical Engineering from the University of Baghdad (1984)-Iraq, M.Sc. degrees in Electronics Engineering from the University of Technology-Iraq in 2002. Since 2004, he has been with the University of Babylon-Iraq, where he is lecturer in Electrical Engineering Department. His research interests include, Image processing, wireless communications and intelligent system.

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Design of STBC- Multiband Ultra-Wideband (UWB) System by Using DWT with Three Transmit Antennas