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The increasing needs for high data rates, better performance in various types of channels and relatively simple systems are the motivation for different proposed schemes. The combination of a Polynomial Cancellation Coding with OFDM will gain a lower ICI. Using Space-Time Block Codes increases data rate makes the system more immune against the selectivity of the channel. As well as introducing novel types of mappings to enhance the performance more and more.
In this chapter, the Discrete Slantlet is inserted and treated in various ways with OFDM system. This emerging fields promise of much enhancement for those systems that use them, in comparison with the conventional types.
3.1 SLANTLET TRANSFORM BASED OFDM SCHEME
Wireless digital communication is rapidly expanding resulting in a demand for systems that are reliable and have a high spectral efficiency, to fulfill these demands OFDM technology has drawn a lot of attention.
In this a new technique is proposed to improve the performance of OFDM. The new technique is use the Slantlet transform (SLT) instead Fast Fourier transform (FFT) in order to reduce the level of interference, this also will remove the need for Guard interval (GI) in the case of the FFT-OFDM and therefore improve the bandwidth efficiency of the OFDM. And also the SLT-OFDM is better than wavelet packet (WP)-OFDM in the selective channel because the slantlet filter bank is less frequency selective than the traditional DWT filter bank, due to the shorter length of the filters and SLT algorithm is faster than WP algorithm. The main results were obtained are that the performance of SLT-OFDM is better on average by 18dB in comparison with that of FFT-OFDM flat fading channels. For frequency selective fading channel the SLT-OFDM performs better than the FFT-OFDM on the lower SNR region, while the situation will reverse with increase SNR values.
3.2 System for FFT-Based OFDM
The block diagram of the given system for OFDM is depicted in figure (3, 1). First of all, the input serial data stream is formatted into the word size required for transmission e.g. 2 bit/word for QPSK and 4 bit/word for 16-QAM, and shift into a parallel format. The data is then transmitted in parallel by assigning each word to one sub-carrier in the transmission. After that , the data to be transmitted on each sub-carrier is then mapped into one of M-ary PSK or M-ary QAM constellation format, as determined [in addition, differential-PSK (DPSK) and differential -QAM (DQAM) are available]. This process will convert data to corresponding value of M-ary constellation which is complex word, i.e. real and imaginary part. The training frame (pilot sub-carriers frame) will be inserted and sent prior to information frame. This pilot frame will use to make channel estimation that's used to compensate the channel effects on the signal. After that, the complex words frame and pilots frame will pass to IFFT to generate an OFDM symbol. Zeros will be inserted in some bins of the IFFT in order to make the transmitted spectrum compacts and reduce the adjacent carrier's interference.
Fig. (3,1): Block Diagram of OFDM System
The OFDM modulator and demodulator of FFT-based OFDM is shown in figure (3, 2).
(a) OFDM Modulator
(b) OFDM Demodulator
Fig. (3, 2): The OFDM modem system
3.3 Proposed System for Slantlet transforms -OFDM (SLT-OFDM)
The overall system of OFDM is the same as in figure (3,3). The only difference is the OFDM modulator and demodulator. The slantlet transform SLT-OFDM modulator and demodulator that used is shown in the figure below:
(a) SLT-OFDM modulator
Fig. (3, 3) SLT-OFDM modem system
The processes of the S/P converter, the signal demapper and the insertion of training sequence are the same as in the system of FFT-OFDM. Also the zeros will be added as in the FFT based case and for the same reasons. After that the inverse slantlet transform (ISLT) will be applied to the signal.
The main and important difference between FFT based OFDM and SLT based OFDM is that the SLT based OFDM will not add a cyclic prefix to OFDM symbol. Therefore the data rates in SLT based OFDM can surpass those of the FFT implementation. After that the P/S converter will convert the OFDM symbol to its serial version and will be sent through the channel.
At the receiver, also assuming synchronization conditions are satisfied, first S/P converts the OFDM symbol to parallel version. After that the SLT will be done. Also the zero pads will remove and the other operations of the channel estimation, channel compensation, signal demapper and P/S will be performed in a similar manner to that of the FFT based OFDM.
3.3.1 Performance of the OFDM Systems in the Flat Fading Channel
In this type of channel, the signal will be affected by the flat fading with addition to AWGN (Additive White Gaussian Noise), in this case all the frequency components in the signal will be affected by a constant attenuation and linear phase distortion of the channel, which has been chosen to have a Rayleigh's distribution. A Doppler frequency (Doppler Shift) of 50 & 100 Hz is used in this simulation and the table (3, 1) explains the simulation parameters. Figure (3, 4) shows the BER performance of SLT-OFDM and FFT-OFDM in flat fading channel for QPSK modulation type.
Table (3, 1) Simulation Parameters
Number of sub-carriers
Number of SLT points
Number of FFT points
Frequency selective fading+AWGN.
Fig. (3, 4) BER performance of SLT and FFT- OFDM for QPSK modulation in flat fading channel.
3.3.2 The Performance of OFDM Systems in Frequency Selective Fading Channel (multipaths-channel)
The BER performance of SLT and FFT-OFDM systems in frequency selective fading channel are shown in figure (3, 5). This case corresponding to multipaths where two paths are chosen and the attenuation and delay of the second path are -8dB and 8 samples respectively. From the figure (3,5), it is clear that the BER performance of SLT-OFDM will become constant after a certain SNR. From the same figure, one can see that the BER curves of FFT-OFDM will decrease with the increase of the SNR. In the frequency selective fading the SLT-OFDM is not better than the FFT-OFDM for all the SNR.
Fig. (3, 5): BER performance of SLT and FFT-OFDM for QPSK modulation in selective fading channel.
The above results can be interpreted as follows. The FFT-OFDM has a guard interval(cyclic prefix) of 25% this mean that a cyclic prefix is equivalent to 16-samples, therefore no ISI will effect on the FFT-OFDM until the delay of the second path exceed 16 samples. Since the delay of the second path is equal to 8-samples as assumed above, no ISI will effect on it, while in SLT-OFDM there's no cyclic prefix this mean that ISI will occur in SLT-OFDM. Also due to high spectral containment between the sub-channels in SLT,SLT-OFDM will robust again ISI and ICI until a certain SNR value, after this value , the SLT-OFDM performance will be constant approximately with the increasing of SNR and the FFT-OFDM performance will become better than it.
In flat fading channel, it was found that the SLT-OFDM performance was better than that of the FFT-OFDM. A gain of about 18dB was obtained in SLT-OFDM over that for the FFT-OFDM and also the effect of Doppler Shift is very slightly in SLT-OFDM. But in frequency selective fading channel (multipaths case), the situation will be changed. Since the Cyclic Prefix (CP) which is already exists in the FFT-OFDM will eliminate the ISI, therefore no ISI will occurred in FFT-OFDM if the CP is greater than the delay spread of multipaths (in this case we considered that this condition is satisfied ). In the case of WP-OFDM there's no CP therefore ISI will occurred. Therefore the BER performance of SLT-OFDM was better than the FFT-OFDM case until a certain value of SNR. After this value the FFT-OFDM was better than SLT-OFDM. It was noticed that the BER curves of SLT-OFDM will become flat (constant with the increase of SNR).
The concept of diversity is significant in wireless communications. The wireless channel is not only affected by noise, but also it suffers from attenuation due to destructive addition of multipath in the propagation media and due to interference from other users. It is difficult to determine the transmitted signal if secure attenuation occurs. Unless some replicas of transmitted signal which is less-attenuated is provided to the receiver. This resource is called diversity, and it can make the wireless channel more reliable and to increase the error-rate performance. In most wireless communication systems, a number of diversity methods are used in order to get the required performance. According to the domain where diversity is introduced, diversity techniques are classified into temporal, frequency and space diversity .
Temporal diversity: Replicas of the information bearing signal are transmitted in different time slots, where the separation between the time slots is greater than the coherence time of the channel.
Frequency diversity: In this case, replicas of the information bearing signal are transmitted in different frequency bands, where the separation between the frequency bands is greater than the coherence bandwidth of the channel. The signal is spread over frequency, examples can be found in spread-spectrum technologies like CDMA.
Antenna (spatial) diversity: It has been observed that antennas with a spacing of more than half a wavelength lead to spatially uncorrelated channels. The transmission of replicas of the information bearing signal over these uncorrelated spatial channels leads to spatial diversity.
Note that not all kinds of diversity are always feasible. For example a slowly fading channel (with a long coherence time) cannot support temporal diversity with practical interleaving depths. Similarly, frequency diversity is not feasible when the coherence bandwidth of the channel is comparable to the bandwidth of the signal employed. However, irrespective of the channel characteristics, antenna diversity can always be exploited as long as there is sufficient spacing between the antennas. It becomes very important to utilize spatial diversity at both the transmitter and the receiver especially when other forms of diversity are not feasible due to the nature of the channel available as well as the nature of the signaling used in the system. In a practical communication system, the base-station is usually equipped with multiple antennas to exploit spatial diversity. It is not possible to provide the handset with many antennas due to size and cost constraints. It is common practice to use the multiple base-station antennas for receiver diversity in a reverse link (handset to base-station) transmission. Hence, the problem of using multiple antennas at the receiver is very well studied. In particular, techniques such as maximum likelihood combining, equal gain combining and selection of antennas are used depending on the extent of channel information available at the receiver.
Smart antenna technology provides a wide variety of options, ranging from single-input, multiple-output (SIMO) architectures that collect more energy to improve the signal to noise ratio (SNR) at the receiver, to multiple-input, multiple-output (MIMO) architectures that open up multiple data pipes over a link. The number of inputs and outputs here refers to the number of antennas used at the transmitter and receiver, respectively.
Different smart antenna architectures provide different benefits which can be broadly classified as array gain, diversity gain, multiplexing gain and interference reduction. The signaling strategy at the transmitter and the corresponding processing at the receiver are designed based on link requirements (data rate, range, reliability etc.). For example, in order to increase the point to point spectral efficiency (in bits/sec/Hz) between a transmitter and receiver, multiplexing gain is required which is provided by the MIMO architecture. The signaling strategy also depends on the availability of channel information at the transmitter. For example, MIMO does not require channel knowledge at the transmitter, although it enjoys improved performance if channel information is available. On the other hand, spatial division multiple access (SDMA) does require channel information at the transmitter which is used to increase the network throughput at the media access (MAC) layer. The advantage of point-to-multipoint SDMA over point-to-point MIMO is that SDMA deploys multiple antennas only at the cellular base station or wireless local area network (LAN) access point, thus reducing cost of the cell phone or network interface card (NIC) .
3.5.1 Space Time Block Code
Spatial diversity can be leveraged to combat severe attenuation in wireless communications. To reduce the receiver complexity while maintaining satisfactory performance with spatial diversity, space-time block codes with simple encoding and decoding structures were proposed and extensively studied for the last several years . Space-Time Codes give good performance in that they provide the system with transmits diversity. Diversity is obtained by transmitting a signal on several antennas simultaneously (space) and several symbol periods (time), which leads to an increase in diversity without loss of bandwidth. In addition to the spatial diversity, some of the schemes also provide additional coding gain. Many of the practical Space-Time Code schemes that achieve these high capacities, such as spatial multiplexing  and Space-Time Block Coded (STBC) systems are designed so as to allow simple symbol detection at the receiver because they map the symbols linearly to the transmitter antennas.
3.5.2 Alamouti Code
A simple Space-Time Block Code scheme is the famous Alamouti code . Figure (3.6) shows the baseband representation of the classical two-branch Maximal-Ratio Receive Combining (MRRC). At a given time, a signal s0 is sent from the transmitter. The channel including the effects of the transmit chain, the airlink, and the receive chain may be modeled by a complex multiplicative distortion composed of a magnitude response and a phase response. The channel between the transmit antenna and the receive antenna zero is denoted by h0 and between the transmit antenna and the receive antenna one is denoted by h1 where
Noise and interference are added at the two receivers. The resulting received baseband signals are
Where n0 and n1 represent complex noise and interference. Assuming n0 and n1 are Gaussian distributed, the maximum likelihood decision rule at the receiver for these received signals is to choose signal si if and only if (iff)
Where is the squared Euclidean distance between signals x and y calculated by the following expression:
The receiver combining scheme for two-branch is as follows:
From equation (3.5) it can be seen that the desired signal so is amplified by gain which it was attenuation factor. Expanding (3.8) and using (3.4) and (3.5) it get choose si iff
or equivalently choose si iff
For PSK signals (equal energy constellations)
Where Es is the energy of the signal. Therefore, for PSK signals, the decision rule in (3.7) may be simplified to choose si iff
The maximal-ratio combiner may then construct the signal , as shown in Figure (3.6), so that the maximum likelihood detector may produce , which is a maximum likelihood estimate of s0.
Figure (3.6) Two-branch MRRC
Figure (3.7) Two-branch transmit diversity with one receiver
Figure (3.8) Two-branch transmit diversity scheme with two receivers.
22.214.171.124 Two-Branch Transmit Diversity with One Receiver
Figure (3.7) shows the baseband representation of the two branch transmit diversity scheme.
The scheme uses two transmit antennas and one receive antenna and may be defined by the following four functions:
â€¢ The encoding and transmission sequence of information symbols at the transmitter;
â€¢ The channel estimation scheme at the receiver;
â€¢ The combining scheme at the receiver;
â€¢ The decision rule for maximum likelihood detection.
1- The Encoding and Transmission Sequence: At a given symbol period, two signals are simultaneously transmitted from the two antennas. The signal transmitted from antenna zero is denoted by s0 and from antenna one by s1. During the next symbol period signal (-s1*) is transmitted from antenna zero, and signal s0* is transmitted from antenna one where * is the complex conjugate operation. This sequence is shown in Table (3.2).
In Table (3.1), the encoding is done in space and time (space-time coding). The encoding, however, may also be done in space and frequency. Instead of two adjacent symbol periods, two adjacent carriers may be used (space-frequency coding).
Table (3.2) The Encoding and Transmission Sequence For the Two-Branch Transmit Diversity Scheme
The corresponding codeword can be written as:
The channel at time t may be modeled by a complex multiplicative distortion h0(t) for transmit antenna zero and h1(t) for transmit antenna one. Assuming that fading is constant across two consecutive symbols, can be write
Where T is the symbol duration. The received signals can then be expressed as:
Where and are the received signals at time t and T and n0 and n1 are complex random variables representing receiver noise and interference.
2- The channel estimation scheme is done by the following
a- At the transmitter
â€¢ At time t the training symbol Tr which transmitted with data is the same for both signals s0 and s1
â€¢ At time t+T the training symbol Tr is transmitted with signal s0 and -Tr is transmitted with signal s1
b- At the receiver
â€¢ At time t the received signal can be expressed as:
r0=s0h0 + s1h1 +Trh0+Trh1+n0
In the estimator the data is discarded so that the received signal r0 can be rewritten as
â€¢ At the time t+T the received signal without data can be expressed as
To estimate h0 is done by follow
To estimate h1 is done by follow
3- The Combining Scheme: The combiner shown in Figure (3.7) builds the following two combined signals that are sent to the maximum likelihood detector:
It is important to note that this combining scheme is different from the MRRC in (3.5). Substituting (3.10) and (3.11) into (3.12) it get
4) The Maximum Likelihood Decision Rule: These combined signals are then sent to the maximum likelihood detector which, for each of the signals s0 and s1, uses the decision rule expressed in (3.7) or (3.9) for PSK signals.
The resulting combined signals in (3.13) are equivalent to that obtained from two-branch MRRC in (3.5). The only difference is phase rotations on the noise components which do not degrade the effective SNR. Therefore, the resulting diversity order from the two-branch transmit diversity scheme with one receiver is equal to that of two-branch MRRC.
126.96.36.199 Two-Branch Transmit Diversity with Two Receivers
There may be applications where a higher order of diversity is needed and multiple receive antennas at the remote units are feasible. In such cases, it is possible to provide a diversity order of 2*2 with 2 transmit and 2 receive antennas. The generalization to 2 receive antennas is trivial.
Table (3.3) The Definition of Channels between the Transmit and Receive Antenna
Table (3.4) The Notation for the Received Signals at the Two Receive Antennas
Figure (3.8) shows the baseband representation of the scheme with two transmits and two receive antennas. The encoding and transmission sequence of the information symbols for this configuration is identical to the case of a single receiver, shown in Table (3.1). Table (3.2) defines the channels between the transmit and receive antennas, and Table (3.3) defines the notation for the received signal at the two receive antennas.
no,n1,n2 and n3 are complex random variables representing receiver thermal noise and interference. The combiner in figure (3.3) builds the following two signals that are sent to the maximum likelihood detector:
Substituting the appropriate equations it have
These combined signals are then sent to the maximum likelihood decoder which for signal s0 uses the decision criteria expressed in (3.17) or (3.18) for PSK signals. Choose si iff
Choose si iff
Similarly, for s1 using the decision rule is to choose si signal iff
or, for PSK signals, choose si iff
3.5.3 Orthogonal Space-Time Block Codes
The Alamouti code is one example of Space-Time Block Codes with orthogonal design. The designed codeword has either row and/or column orthogonality independent from the encoded symbols. For instance, codes designed for three and four transmit antennas are given by
3.6 Advantages and Disadvantages of MIMO
â€¢ Advantages of MIMO
In wireless communications, the objectives are to increase throughput and transmission quality. MIMO systems can take advantage of the shortcoming of a wireless channel - the multipath- and turn it into an advantage. In MIMO systems, random fading  and multipath delay spread can be used to increase throughput. MIMO systems offer an increase in capacity without the need to increase bandwidth and/or power. Spatial Multiplexing (SM) is a technology that exploits this feature of MIMO systems in order to achieve the theoretical capacity limit in practice. Spatial Multiplexing uses different transmit antennas which send different signals. The signals are multiplexed in the channel and in the receive antennas, and then demultiplexed in the receiver.
Apart from improving throughput, MIMO systems can also improve transmission quality. Diversity  is a technology used in MIMO for this purpose. Multiple antennas can be used to minimize the effect of fading caused by multi-path propagation. When the antennas at the receive side are adequately spaced, then several copies of the transmitted signal are received through different channels and with different fading. The probability, that all received copies of the transmitted signal is in deep fading, can be regarded as small. Therefore can deduce that diversity should improve the quality of the wireless link.
â€¢ Disadvantages and limitations of MIMO
One obvious disadvantage of MIMO is that they contain more antennas: MIMO increases complexity, volume, and hardware costs of the system compared to SISO.
In the presence of frequency selectivity, since the orthogonal frequency division multiplexing (OFDM) technique can significantly reduce the receiver complexity, a combined system of STBC with OFDM called a MIMO-OFDM or in this work called STBC-OFDM system. Due to incorporating both the advantages of space-time coding and OFDM , MIMO-OFDM seems to be an attractive solution for future broadband wireless communication systems. This combine coding and modulation. Space time codes were recently proposed ; these codes have high spectral efficiency and operate at very low SNR.
For example a space-time coding on two adjacent blocks of data symbols, i.e., X(n) and X(n+1) as shown in figure (3.9) which combine
Figure (3.9): (2TX-1RX) Space-Time Block-Coded OFDM
Space-time blocks code with OFDM to achieve spatial diversity gain over frequency-selective fading channels. In effect, apply space-time coding on blocks of data symbols instead of individual symbols. Space-time encoder takes two data vectors X(n) and X(n+1) and transmits
Antenna #1: X(n) -X*(n+1)
Antenna #2: X(n+1) X*(n)
The demodulated vectors are
Where h1 and h2 are channel response, N1 and N2 are complex random variables representing receiver noise and interference.
X^(n)=(|h1|2+|h2|2) X(n)+h1* N1+h2N2*
X^(n+1)=(|h1|2+|h2|2) X(n+1)+h2* N1-h1N2
3.7 Channel Estimation of OFDM Systems
Since the radio channel is frequency selective and time varying for wide band mobile communication systems, a dynamic estimation of channel is necessary for OFDM signal .
To estimate the channel transfer function and the inverse of the channel transfer function is applied to every OFDM frame to compensate for the channel effects, much like equalization . There are two types of channel estimations, block type and comb-type pilot channel estimation.
3.7.1 Block-Type Pilot Channel Estimation
In block-type, channel estimation can be performed by inserting pilots carriers into all of sub-carriers of OFDM symbols .OFDM channel estimation symbols are transmitted periodically. Block- type pilot channel estimation has been developed under the assumption of slow fading channels.
The estimation of the channel can be performed by using either Least Square (LS) or Minimum Mean Square Estimation (MMSE) algorithms.
For least square (LS), the estimate channel frequency response is given by
and it is used to find the estimated transmitted signal Xe(k)
Xe (k) =Y (k)/He (k) , k=0,1,â€¦â€¦.,N-1 (3.22)
When the channel is slow fading, the channel estimation inside the block can be update using the decision feed back equalizer at each sub- carrier .To understand the OFDM system see Appendix A.
3.7.2 Comb-Type Pilot Channel Estimation
The comb-type pilot channel estimation has been introduced to satisfy the need for equalization when the channel changes fast, even in one OFDM block. This type consists of algorithm to estimate the channel at pilot frequency, and to interpolate the channel. The Np pilot signals are uniformly inserted into X(k) according to the following equation:
Where L=number of carriers/NP and Xp(m) is the mth pilot carrier.HP (k) is the channel frequency response at the pilot sub-carriers.
The estimation of the channel at pilot sub-carriers based on LS estimation is given by:
, k=0, 1,â€¦,NP-1 (3.24) Where YP(k) and XP(k) are the received and transmitted signals at kth pilot sub-carrier respectively.
An efficient interpolation is necessary in order to estimate channel at data sub-carriers by using the channel information at pilot sub-carriers. The interpolation of the channel can depend on linear interpolation, 2nd order interpolation, low pass interpolation, spline cubic interpolation .
3.8 A Proposed System for STBC-OFDM Based IFFT/ISLT with
Two-Transmitters and Two-Receiver
The s block diagram presented in figure (3, 10) can be used to present a communication system uses conjunction with PCC or MC-CDMA to enhance the performance.
General block diagram of STBC-OFDM is proposed in figure (3, 10). The diagram is general enough to describe the STBC-OFDM, PCC-STBC-OFDM and MC-CDMA-STBC-OFDM where in the case of STBC-OFDM removing the block of "mapping data onto sub carriers from the transmitter and the block of "weight and add sub carriers at the receiver. The figure also represents two cases on is Alamouti case and the other is classical MRRC.
(if PCC or MC-CDMA used)
RAYLEIGH FADING CHANNEL
RAYLEIGH FADING CHANNEL
(if PCC or MC-CDMA used)