WO2008116167A1

WO2008116167A1 - Synchronization method and communication system implementing such method

Info

Publication number: WO2008116167A1
Application number: PCT/US2008/057855
Authority: WO
Inventors: Nizar Al-Aawar
Original assignee: D & H Global Enterprise, Llc
Priority date: 2007-03-22
Filing date: 2008-03-21
Publication date: 2008-09-25

Abstract

A multi-user resource allocation and power-minimizing method for synchronization within a communications system is provided. A communications system that uses this synchronization method is also provided, the system comprising at least one transmitter and at least one receiver, the transmitter and the receiver being connected by a channel wherein information transmitted by the transmitter passes through the channel and then reaches the receiver, and the channel comprises a number of sub-channels in frequency domain and a number of slots in time domain and each sub-channel is comprised of a combination of sub-carriers, wherein sub-carrier allocation is obtained.

Description

PATENT COOPERATION TREATY APPLICATION

SPECIFICATION

SYNCHRONIZATION METHOD AND COMMUNICATION SYSTEM IMPLEMENTING SUCH METHOD

This application claims the benefit and priority of United States Provisional Patent

Application No. 60/896,391 filed March 22, 2007. FIELD OF THE INVENTION

The present invention relates generally to communications and communication systems. More particularly, it relates to a method for providing a high synchronization to a broad-band wireless access Wide Area Network (WAN), including a cellular phone

network as well as other communication networks. It also relates to a system that uses such method. BACKGROUND OF THE INVENTION

The broad-band wireless access industry, which provides high-rate network

connections to stationary sites, has matured to the point at which it now has a standard

for second-generation wireless area networks. The Worldwide Interoperability for Microwave Access (referred to as "the standard" or "WiMAX" in accordance with the standard known as "IEEE 802.16," the subsections of which will be referred to herein as

"802.16x") provides specifications for both fixed Line-of-Sight (LOS) communication in the range of 10-66 GHz (802.16c), and fixed, portable, Non-LOS communication in the

range of 2-11 GHz (802.16a and 802.16d). In addition, the standard defines wireless communication for mobiles, moving at a speed of 125 KMPH, in the range of 2-6 GHz (802.16e). Support for both Time Division Duplex (TDD) and Frequency Division Duplex (FDD) Spread Spectrum (SS) is provided, both using a burst transmission format whose framing mechanism supports adaptive burst profiling in which transmission parameters, including the modulation and coding schemes, may be adjusted individually to each SS on a frame-by-frame basis, thus providing high data rates.

802.16e represents a standard for Non-LOS communications in the frequency range of 2-6 GHz. It is well implemented by using scalable Orthogonal Frequency Division Multiplex Access (OFDMA) as its physical layer scheme. OFDMA is a multiuser version of Orthogonal Frequency Division Multiplexing (OFDM) modulation scheme. OFDM is based upon the principle of frequency-division multiplexing, but is implemented as a digital modulation scheme. The bit stream to be transmitted is effectively split into multiple parallel streams, typically hundreds or thousands. The available frequency spectrum is divided into several sub-channels, and each low-rate bit stream is transmitted over one sub-channel by modulating a sub-carrier using a standard modulation scheme. The sub-carrier frequencies are selected so that the modulated data streams are orthogonal to each other, meaning that cross-talk between the sub-channels is eliminated. This orthogonality occurs when sub-carriers are equally spaced by the symbol rate of a sub-carrier.

Multiple access is achieved in OFDMA by assigning subsets of sub-carriers to individual users. This allows simultaneous low data rate transmission from several users. OFDMA can also be considered as an alternative to combining OFDM with Time Division Multiple Access (TDMA) or time domain multiplexing. Low data rate users can send continuously with low transmission power instead of using a pulsed high power carrier. Constant delay, and shorter delay, can be achieved.

The OFDMA symbol time (T₈) is selected depending on the channel conditions and available bandwidth, and simulations provide a means of selecting right values of T₈ in different channel conditions. Additionally, it has been shown that certain values of 7_S out-perform others in all conditions, thus invalidating their use. The primary advantage of OFDMA is the ability to cope with severe channel conditions, including multi-path and narrowband interference without complex equalization filters. That is, channel equalization is simplified by using many slowly modulated narrowband signals instead of one rapidly modulated wideband signal.

One of the major requirements of OFDMA, however, is high synchronization. That is, the access controller of the WiMAX standard uses a scheduling algorithm for which the subscriber user, such as a new mobile user, need compete for entry into the network. After that, it is allocated an access slot by the Base Station (BS). The time slot can enlarge and contract, but remains assigned to the user. This scheduling algorithm is stable under overload and over-subscription conditions. It also allows the BS to control the quality of service parameters by balancing time-slot assignments to users. Detecting the timing offset of a new mobile user entering the network, which is not time-aligned using cross-correlation and "auto-correlation" in the time domain and cross-correlation in the frequency domain at the BS, has been simulated. Results indicate that the processing load can be significantly reduced by using frequency domain correlation of the received data or by using "auto-correlation" followed by cross- correlation of localized data.

The use of an Adaptive Antenna System (AAS) in 802.16e improves the system performance, where beam-forming is implemented in the direction of a desired user. 802.16e specifications are provided such that mobility of the SS at 125 KMPH is allowed. OFDMA is used as the physical layer scheme. Channel coding (CC) is provided by use of mandatory CC and optional Block Turbo Coding (BTC), Channel Turbo Coding (CTC) and low density parity check codes (LDPC). Data is randomized and interleaved to avoid loss of carrier recovery and burst errors. In addition to AAS and Space Time Coding (STC), an optional Multi-Input Multi-Output (MIMO) scheme has been specified. Code Division Multiple Access (CDMA) codes are used along with the random window length based contention control algorithm for initial ranging, periodic ranging, bandwidth request and handoff. The inter BS communications have been defined, which will be used as a backbone network between the BS's to aid the inter-cell Mobile Subscriber Station (MSS) handoff. This ensures fast and accurate synchronization at the cost of slightly increased complexity. A variable Fast Fourier Transform (FFT) size and symbol time is provided which could be set depending on the environment and allocated bandwidth.

Put together, the 802.16 technology would enable the SS to get Broadband Wireless Access (BWA) at all times in all locations, either when stationary, or at pedestrian speed or when traveling at 125 KMPH. As previously mentioned, OFDMA is a multi-carrier transmission scheme where the information is transmitted on multiple sub-carriers, with a lower data rate, instead of one high data rate carrier and moreover, the sub-carriers are orthogonal to each other, leading to saving of bandwidth. See Fig. 2. The major disadvantage of an OFDMA system is its requirement of perfect synchronization in time and frequency. But the advantages of using OFDMA are far more and provide enough reasons for the popularity of the OFDMA systems. A typical channel fade will degrade only a few of the sub-carriers, which in most cases can be compensated by use of efficient interleaving and channel coding. OFDMA systems can be implemented very efficiently by using the Inverse Fast Fourier Transform (IFFT) at the transmitter and FFT at the receiver. The overall complexity and its increase with data rate in OFDMA systems is far less than the single-carrier systems, hence OFDMA is becoming a widely accepted technology and more prominent to be used in future mobile wireless communication standards.

For successful operation of the OFDMA system, it is required that the sub- carriers should never loose orthogonality between each other at any time. The advantage of an OFDMA system is lost when the sub-carriers are no longer orthogonal to each other. This imposes quite stringent requirements to be fulfilled by the transmitter and the receiver.

Ideally, to maintain orthogonality, it is required that the symbol duration be exactly inverse of the sub-carrier spacing and that the FFT be considered over symbol duration such that it covers an integer number of cycles. Moreover, the consecutive sub-carriers differ by one full cycle only. See Fig. 3. If the system is to operate in a multi-path environment, then each sub-carrier should experience a flat fading, hence the sub-carrier spacing should be less than the coherence bandwidth and each symbol should experience a time-invariant channel. Hence, the symbol time should be less than the coherence time or else the complexity of the receiver increases when overcoming the fading effect.

Reduction of inter-symbol interference, which would require that a bulky equalizer be constructed at the receiver in a single carrier system, is overcome by the use of "guard time" in an OFDMA system. A guard time is added in time domain between two OFDMA symbols and the FFT is considered over duration such that there is no component from the previous or next symbol (see Fig. 1), which nulls the Inter- Symbol Interference (ISI) and thus avoids the bulky equalizer. ISI is completely eliminated when the multi-path signal delay is within the guard time. When designing an OFDMA system, proper values are selected depending on the environment so as to satisfy the above condition. Multi-carrier systems have the problem of Inter-Carrier Interference (ICI), which results from loss of orthogonality between the sub-carriers. This happens when the FFT is considered over a duration where the sub-carrier is not present (non-integer number of cycles), which would be the case when multi-path is present and the guard time has amplitude zero. This is reduced by use of cyclic prefix, where a copy of the last part of the symbol, followed by the symbol itself, is transmitted. This ensures orthogonality over the FFT period in case of delayed multi-path. See Fig. 3. An unstable and non-synchronized local oscillator can cause frequency drift, resulting in FFT bins being placed such that it samples component from other sub- carriers along with the required, leading to ICI. Again, see Fig. 3. The phase noise from oscillator will cause the sub-carrier spectrum to change. Even though FFT bins are placed at the right place in the frequency domain, with phase noise, a non-zero component of other sub-carriers will be realized, which also results in ICI. Hence the stability of the oscillator is very much required.

In a mobile fading channel, where the channel varies fast, the performance is highly degraded and hence channel estimation is to be done to overcome the effect of fading. For this, an OFDMA system has pilot symbols (on pilot sub-carriers) embedded in between the data symbols (on data sub-carriers), each of which provides the channel information at the receiver. These channel estimation values at the receiver are interpolated over the data sub-carriers and the data symbols are decoded. Much depends on the pilot spacing in both time and frequency domain as the channel characteristics should not change significantly between pilot sub-carriers, or else the interpolation would not be accurate. SUMMARY OF THE INVENTION

The present invention is drawn to a multi-user resource allocation and power- minimizing method for synchronization within a communications system, and to a communications system that uses this synchronization method, the system comprising at least one transmitter and at least one receiver, the transmitter and the receiver being connected by a channel wherein information transmitted by the transmitter passes through the channel and then reaches the receiver, and the channel comprises a number of sub-channels in frequency domain and a number of slots in time domain and each sub-channel is comprised of a combination of sub-carriers, wherein sub-carrier allocation is obtained. The system also uses an adaptive antenna array to determine the transmitter's location upon initial ranging.

The foregoing and other features of the present invention will be apparent from the foregoing detailed description. DESCRIPTION OF THE DRAWINGS

Fig. 1 is a graphical representation of an orthogonal signal with a guard time in the frequency domain and for a given FFT duration.

Fig. 2 is a graphical frequency domain comparison of a signal generated in the FDMA spectrum and the same signal generated in the OFDM spectrum, illustrating the saving of bandwidth in the OFDM spectrum due to the modulation of data streams that are orthogonal to one another.

Fig. 3 is a graphical representation of signals generated in the OFDM spectrum and illustrating that the FFT be considered over symbol duration and that symbol duration be inverse of sub-carrier spacing to maintain signal orthogonality.

Fig. 4 is a graphical representation of a time plan showing one TDD time frame.

Fig. 5 is a graphical representation of a symbol illustrating exemplary sub-carrier mapping.

Fig. 6 is a block diagram graphical representation of a system model or the signal chain at a base frequency band. Fig. 7 is a graphical representation comparing the mobile subscriber station bit error rate as compared to the power per symbol when using the method of the present invention and when not. DETAILED DESCRIPTION

A general communication system consists of two blocks, a transmitter and receiver, connected by a channel. The information transmitted by the transmitter passes through the channel and then reaches the receiver. If the channel does not distort the transmitted signal, then the receiver can retrieve the transmitted information successfully. But, in practice, the channel typically alters the transmitted information making the task difficult for the receiver. The main aim of the designer is to reduce the number of errors made at the receiver. To achieve this, certain information is required at the receiver, such as to how the channel alters the information, so that the channel impairments can be mitigated.

The "uplink" transmissions (i.e., transmission from a Mobile Subscriber Station (MSS) to the Base Station (BS)) have definition in both frequency and time, i.e. the bandwidth allocated to a MSS is defined by a number of sub-channels in frequency domain and a number of slots in time domain. See Fig. 4. A sub-channel is a combination (i.e., non-sequential) of sub-carriers, and a slot in the OFDMA uplink is defined as three OFDMA symbols. Another way of representing a sub-channel is by using a combination of six different "tiles." Each tile (i.e., the smallest data unit, such as that shown in Fig. 5) spans three OFDMA symbols in time and four sub-carriers in the frequency domain. Six (or eight, in certain special case) of these tiles, form a sub- channel, which is the minimum allocated transmission region for any MSS, spanning at least a total of seventy-two sub-carriers (i.e., 6 x 4 subcarriers x 3 (at least) OFDMA symbols). The six tiles in a sub-channel are mapped far apart on the total spectrum (2,048 sub-carriers). For example, say tiles use sub-carriers numbered 448 to 451 ; 512 to 515; 984 to 987; 1189 to1192; 1505 to 1508; and 1753 to 1756. Moreover, the location of the tile structure changes for every three OFDMA symbols (which is due to a rotation scheme). Since the sub-carriers are far apart in both time and frequency domain, except for within a tile, the channel estimation is to be done on each tile separately and hence any knowledge or prior estimate about the channel response which could improve the system performance is not available.

The block diagram shown in Fig. 6 represents the whole system model or the signal chain at base band. The block system is divided into three main sections, namely, the transmitter, the receiver and the channel. The model has been tested with and without the channel coding, which is illustrated in the dotted box representing the channel coding and decoding. The Bit Error Rate (BER) plots have been obtained for at least 2,000 errors to obtain a good confidence limit.

The data is generated from a random source, and consists of a series of ones and zeros. Since the transmission is done block-wise, when Forward Error Correction (FEC) is used, the size of the data generated depends on the block size used, the modulation scheme used to map the bits to symbols (e.g., QPSK, 16QAM digital modulation), and whether FEC is used or not. The generated data is passed on to the next stage, either to the FEC block or directly to the symbol mapping if FEC is not used. In the event that case error correcting codes are used, the data generated is randomized so as to avoid long runs of zeros or ones, which results is ease in carrier recovery at the receiver. The randomized data is encoded using tail biting Convolutional Codes (CC) with a coding rate of !4 (puncturing of codes is provided in the standard, but not simulated here). Finally, interleaving is done by two-stage permutation, first to avoid mapping of adjacent coded bits on adjacent sub-carriers and the second permutation insures that adjacent coded bits are mapped alternately onto less or more significant bits of the constellation, thus avoiding long runs of lowly reliable bits.

The coded bits (uncoded, if FEC is not used) are then mapped to form symbols. The modulation scheme used is QPSK or 16QAM (QPSK unless otherwise specified) with gray coding in the constellation map. In any case, the symbol is normalized so that the average power is unity, irrespective of the modulation scheme used.

The sub-carrier allocation is mentioned above where the uplink transmission is configured to separate data into a set of four sub-carriers for three time symbols, named as the tile structure. Symbols are allocated indices representing the sub-carriers and OFDMA time symbol, and then passed onto the next stage, the IFFT, to convert into time domain. Total synchronization of an OFDMA system is a very important criterion which should be fulfilled to avoid any interference (ISI and ICI) leading to performance degradation. In OFDMA, it is required that all transmissions from various MSS should arrive at the BS at the same time. If one imagines a cell size of 20 km, we would then have a maximum Round Trip Delay (RTD) of around 133.3 μs. This means that, instead of arriving at expected time at the BS, data may arrive anytime within 0 to 133.3 μs as a result of this delay. If the symbol duration is 64 μs, the amount of error in detection of data at the BS is very high. The whole network should be synchronized to one reference and in WiMAX this reference is the BS clock. All data is expected to arrive at the same time at the BS receiver and all data addressed to the MSS is transmitted at same time. The MSS, which are distributed all over the cell, receive data at different instants in time and similarly transmit data at different instants in time, depending on their distance from the BS. A MSS at the cell boundary receives data quite late and transmits data very early when compared with a MSS that is close to the BS.

When a new MSS is seeking entry into the network, its distance, with reference to the BS, is not yet known and, hence, the RTD is not known. The MSS has no idea as to what time or power should be used for transmitting the initial signal back to the BS. This is the BS's job to detect this new MSS, to find the misalignment between the new MSS and the network, and then to send a response in order to correct it.

Reducing system complexity without compromising performance has been the major focus of this work. It has been shown that a better approach is to use frequency domain correlation by using IFFT, which is very simple and efficient in implementation.

The following starts with a brief description of this problem and how an 802.16e system handles this situation. Next, this application explains the calculation of timing, frequency and power offset. The major focus here is to reduce the complexity of the system, and still maintain the system performance at an acceptable level. Methods to estimate the timing offset, using both time and frequency domain correlation, have been explained and later corroborated with simulation results. It is shown that, in time domain, the complexity of implementing a full cross-correlation is very high and can be significantly reduced if the CDMA code at the receiver is quantized and represented using just 2 bits.

An OFDMA system performance highly depends on synchronization between the transmitter and the receiver. When a new SS or MSS is trying to enter a network, it is not synchronized. Hence, it tries to achieve coarse synchronization by listening to the transmissions from the BS, and then starts transmitting to achieve fine synchronization. The MSS starts transmission by the least possible power, each time increasing it by a level, if nothing is heard back from the BS. The BS is to detect the new MSS and calculate the time offset, frequency offset and power offset, then reply back to the MSS to correct its transmitting parameters before transmitting data. The process goes on (with a maximum of 16 times) until the MSS has achieved synchronization. This process of obtaining synchronization and logging onto the network is known as "initial ranging."

The BS requires that all the signals received at the BS be time synchronized, irrespective of the source location within the cell. During the start of initial ranging, the timing offset between MSS and BS can be more than the RTD, which is quite high. The sub-carriers carrying data from the new MSS might have frequency offset and are delayed (compared with signal from other MSS) thereby causing a loss of orthogonality over the FFT period, hence resulting in ICI. Moreover, if the new MSS uses more power, its probability of getting detected is more, but it leads to increased interference to the data on other sub-carriers. Hence, the requirement is to detect the new MSS at BS with the least possible power.

In the 802.16e OFDMA system, code division multiple access (CDMA) codes are used to improve the system efficiency in detecting the new user. A new MSS will transmit one of the pre-defined CDMA codes, which should be detected at the BS. The BS is not only to detect the new MSS but also to calculate its timing, frequency and power offset. Power offset can be detected by calculating the difference between the required power and the received power. The following section will describe in detail the process of recovering the timing and frequency offset information and the causes for performance degradation.

The phase of the correlation output in time domain is equal to the phase drift between samples that are "symbol time" per "FFT size" (or, symbol time/FFT size) seconds apart. Hence, frequency offset can be obtained by dividing correlation phase by 2τrT_s. When the MSS achieves coarse synchronization, it decodes the Uplink Channel Descriptor (UCD) message which contains information as to the maximum power that the BS can receive and the power which was transmitted by the BS. The MSS calculates the received signal strength and computes the losses in the channel and calculates the maximum power that it can use for transmitting the ranging request (CDMA code). After acquiring such information, it will transmit at a power level below the maximum level and start the ranging process. If it does not get a response back from the BS, then it transmits the CDMA code at a higher power level. If the MSS has achieved the coarse synchronization and is yet unable to decode the UCD message, it will start transmitting at the lowest possible power level and increasing it a level higher until it receives a response. Power offset at the BS is simply calculated as the difference between the required power at the BS and the received power.

The signal processing load depends on the method used and the accuracy dependent on the amplitude of the ranging subscriber. In the worst case, in terms of complexity, would be to run cross-correlation on the received data, the CDMA code can be represented by double precision or by 2 bits. In any case, the data length remains the same hence the first step is to calculate the worst case length of data to operate on. To get that, one must assume a symbol time of 64 μs, with an FFT size of 2,048. Consider a cell radius of 20Km, the maximum RTD can be 133 μs, data from the ranging subscriber can arrive anywhere within this delay, hence the processing should be done for 133 + 64 = 197 μs. This corresponds to 6,304 samples of complex data which is to be correlated with 2,048 samples of CDMA code (144 bits long in the frequency domain and 2,048 in the time domain). Correlation is performed by multiplying the two vectors followed by summation. This is repeated for the total data by shifting the window as shown in Fig. 3. Hence the total computations made are 2,048 complex multiplications and 2,048 complex additions repeated 4,256 times. This is repeated for 'n' possible codes out of a total of 255 codes. The previous value is obtained in the case where one performs full cross-correlation. If one quantizes the code into 2 bits and then cross-correlates the computations, this would reduce to 6,144 complex additions repeated 4,256 times per code. This is because multiplication with sign bits (2 bit quantized data; i.e. 1 real + 1 complex), is equivalent to sign change and additions. By using quantized code, one will require the ranging MSS to transmit at a higher power (which has "less effect" on data users, as the user probably gets detected when the amplitude is below 0.4, beyond 0.4 the degradation is seen) and one achieves a very high improvement in speed and reduced processing load. However, there are certain complex multipliers depending on the bandwidth or size of the FFT that are the result of the FFT of the convolution. These complex multipliers are obtained as follows: We start by defining a group in the 3 dimensional in Riemann complex plane where R³ consists of real 3-by-3 orthogonal matrices of determinant +1. Using the familiar Euler angle decomposition, we may express any such element g of R³ in terms of rotations about the z and y axes. Let

''

Thus, any function in this space can be written in terms of these two functions

We next let L² (R3 ) denote the space of square integrable functions on R . The inner product of two functions f and h on R³ is given as

To each g € R³ we can associate a linear operator Ω(g) which acts on a function f in L²(S²):

This is the left regular representation of R³ on L²(S²). The invariant subspaces, Vl, are indexed by the non-negative integers. The dimension of each is dim Vl = 21 + 1. The familiar spherical harmonics span these invariant subspaces. To be precise, for a given I, Vl is spanned by the spherical harmonics of degree I and orders

Thus

where D'ι_<m (g) is a Wigner d-function.

J,M ,M' integers

where d^J _MM'(β) denotes what we will refer to as the Wigner d-function. The Wigner-d functions are related to the Jacobi polynomials, and satisfy a three-term recurrence relation.

where

and

The d-functions satisfy the orthogonality condition

in addition to the following three-term recurrence:

To properly initialize the above recurrence, we have found the following special cases especially useful:

Back to the Fourier expansion of the rotated function f, by means of a matrix multiplication, the matrix in question is a semi-in_nite block diagonal matrix (i.e. along the diagonal), where the lth bloGk is of size (2I+1)_(2I+1), and each block is D'(g) = D¹ ^mn_(g)- Using all this, the Fourier expansion of the rotated function f is the matrix-vector product

By the Peter-Weyl Theorem

Hence, any function f € L²(R³ ) may be written as a sum of the Wigner d-functions:

where

Convolution of two functions f1 ; f2 2 € L 2 (/DR3 ) is defined to be

where h € R . Given the Fourier coefficients in the expansions of f1 and f2:

we found the Fourier coefficients of their convolution to be

One may obtain the Fourier coefficients of their convolution in a very elegant manner. Note that corresponding to each integer J is an irreducible representation of R³. We next arrange the coefficients of f1 as a block diagonal matrix, where the J-th block, of size (2J +1 )_(2J +1), contains the (suitably ordered) Fourier coefficients at that degree J. We next do the same for f2. The Fourier coefficients of the convolution are just the product of the two matrices. What is happening is that the J-th block in f1's matrix is multiplied with the J-th block in f2's matrix.

The Riemann surface technique mentioned above can be expanded to a multiple dimensional space and is validated by comparing to the regular convolution technique through an iterative approach as follows:

1. Choose a bandwidth B, and orders M, M':

2. Generate random Wigner d-coefficients where max(|M|,|M'| )≤ k≤ B-1 ,

uniformly distributed between -1 and 1.

3. Take the inverse DWT of the above coefficients, resulting in the 2 B-many function

samples

where

4. Take the forward DWT of the above sample values, resulting in a new set of d- coefficients,

5. Compute the error

If auto-correlation of length W is used on the received data (see Fig. 5), the required calculations would be 2,048 complex multiplications and 2,048 complex additions for one time, followed by 2 multiplications, 1 addition and 1 subtraction repeated 2,208 times. By doing so, one gets the "plateau," or the most probable location of the new user. Then, to get an accurate result, cross-correlation of 'n' CDMA codes is performed over this localized data (length 'm'). Further improvement is obtained when one of the codes is quantized using 2 bits before auto-correlation is performed.

This multi-user resource allocation method is known to be the best practical power-minimizer algorithm, i.e. the one that makes the system use the least amount of total power to transmit the desired user bit-rates. This nearly optimal method solves the optimization problem described above. As this problem is a combinatorial optimization problem, it is essential to relax the constraints of integer bits per sub-carrier and no sub- carrier sharing to allow the allocation coefficient a_u,n (energy/symbol) is a real number within the interval [0,1]. This value represents the fraction of each sub-carrier that each user takes. Also, the number of bits per sub-carrier b_u,_n is now a real number within the interval [0, a_u,_n

With these modifications, the new problem is the same as the original problem, but now the minimization of the cost function is done over a larger set. Besides, the objective function becomes convex over a convex set. Hence, standard convex optimization techniques can be used to solve the larger set and standard convex optimization techniques can be used to solve the following objective function.

sA.

^min (») = X^_* ^V« € {l,...,t/} fid

where Pj is the power of transmission which is calculated as an amount of energy over time which gives the total power required. The last equation is the communication standard, or constraint, imposed on the algorithm.

The solution proposed in this algorithm is derived after obtaining the Lagrangian L from the constrained objective function and differentiating L with respect to b_Uιn and a_u,n respectively. From here, the necessary conditions for the optimal solution are obtained and then it can be shown that, if H_Uln(l_q,u) are different for all /c, then

u'= mgmn{lϊ_u h )}

(3)

(4) With this, a fixed set of Lagrange multipliers Iu, u ε{1 ,...,U} can be used to determine u' for each n using equation (3) above. Although this leads to the optimal solution, the individual rate constraint b_min(u) may not be satisfied. To solve this cost function an iterative searching algorithm shown in the above equations (1) is proposed. Starting with some small values for all Iu, the iterative method increases one of the Iu until the data rate constraint for user u is fulfilled. Then, the process is repeated for the rest of the users, one at a time. The results obtained from this resource allocation algorithm cannot be used immediately in the original problem. This is because the resulting b_u,n may not be an integer and within the available set of bits per sub-carrier. Another mis-match may be a resulting a_u,n within (0,1) indicating a time-sharing solution. Simply quantizing b*_u,n and a_u,n does not satisfy the individual rate constraints. So, and in order to give a complete solution, the algorithm described above is used to obtain the basic sub-carrier allocation. Following, a single user bit-loading algorithm is applied to each user on the allocated sub-carriers. The short code displayed in Fig.1 can be used to eliminate the time-shared sub-carriers before single-user bit-loading is applied to each user.

It should also be mentioned here that the present demand in the field of wireless communication is not only to provide data communication when the user is mobile but also to provide high data rate by consuming less bandwidth (achieve good spectral efficiency). Moreover, the system complexity and its implementation are of major concern and sometimes limit the implementation of efficient techniques. Efficient channel coding schemes and diversity schemes are used to achieve high system capacity at less power. The WiMAX standard provides specifications for efficient forward error correction techniques and optional schemes like Adaptive Antenna Systems (AAS), Space Time Coding (STC) and multi-input multi- output (MIMO) systems. Of these, AAS achieves high system capacity with implementation cost that is mainly concentrated at the base station (BS), which can be easily tolerated. Hence, this is a good solution for increasing system capacity with least cost. Transmitting data from a single antenna to cover the entire cell (isotropic) is difficult and has many disadvantages which is why sectorized antennas are widely used in wireless communications, where the cell is divided into sectors, generally 3 or 6 such sectors. This provides many advantages such as reduced interference, increased range and reduced Signal to Noise Reduction (SNR), at the cost of some complexity at the transmitter (BS) which is usually acceptable. Beam-forming is the next step used to further improve the performance of the system, where the number of sectors are many more. Apart form the advantages gained by using sectorization, Space Division Multiple Access (SDMA) can be implemented, thus increasing the system capacity.

Beam-forming is nothing more than obtaining a radiation pattern in the desired way and in the desired direction. This can be achieved by using a single antenna element (directive antennas), but must be mechanically rotated in order to form a beam in another location. An example of this would be the well-known Radio Detection and Ranging (RADAR) methodology using a rotating antenna. There are many problems associated with such mechanical rotation which make a rotating antenna not suitable for commercial communication where the requirement is data transmission. The electronic version of this is to use an array of elements and to feed them (or "sample") such that the direction of radiation is maximized in one direction. The type of antenna element used and its arrangement in the array, affects the radiation pattern. Beam-forming is achieved by forcing the antenna array radiation pattern to point in one particular direction. This is obtained by using an array of antennas, fed with the same signal at different time instants or provided with phase shifts. Accordingly, a ranging MSS trying to enter an AAS system poses two problems to the BS. One is the unknown time offset and another is the unknown direction of arrival of signals. A simple solution to this problem is to use a single antenna output to detect the time and frequency offset information and to use this information to find to shape the Radio Frequency (RF) beam signal of the antenna.

There are mainly two approaches to beam-forming: switched beam-forming and adaptive beam-forming. Switched beam-forming is a simpler approach where the direction of arrival of the signal is detected and a corresponding beam is formed in that direction by multiplying a pre-computed complex vector (adding phase shift and scaling) called an array factor. When the user moves out of the beam, the next beam takes over, called switching. In practice, the data from antennas is stored and multiplied with different AF to obtain many beams and processing the data concurrently, thus increasing the capacity by SDMA. Adaptive beam-forming is more complex, but more efficient, where the radiation pattern is constructed dynamically such that interferers are blocked by placing nulls and beam is formed in the direction of users. By using a fully adaptive antenna array, the beam can be constantly steered in the direction of the user as it moves. Here, the direction of signal arrival is computed more frequently, followed by computation of array factor, i.e. complex weight for each antenna and the beam pattern formed by its multiplication with data at the antenna array.

The problem described here is that beam width is inversely related to spacing between the antenna elements. If we obtain a narrow beam width when the antenna spacing is large, however, it is required that the spacing be less than half the wavelength. Otherwise, spurious beams are obtained apart from the required ones. The number of antenna elements also affects the beam width inversely. That is, the more the elements, the less the beam width. Additionally, we have a reduction in side lobe amplitudes with more antenna elements. Another parameter, as already seen, is the direction in which beam-forming is done. The beam width is much wider in the directions of 0° and 180° when compared with 90°. In order to achieve the above requirements, a set of Yagi-Uda arrays of antenna are put together and they are activated by an adaptive algorithm to shape the necessary beam required for the data. The adaptive algorithm utilizes a method is also known as Minimum Variance Distortionless Response (MVDR) filtering beam-forming. It is a method for computing the direction of arrival using Capon's spatial spectrum formula which gives the output power of the array as a function of the angle of arrival.

The input data is divided into set of blocks and the covariance matrix is estimated over each block consisting of 'K input samples, followed by the spectrum estimation. The same process of estimating spectrum is repeated for many blocks and an average is considered over them to obtain the estimate of Capon's spectrum. The peaks in the spectrum determine the transmitting user location. The method requires estimation of matrix inverse, which could be highly complex in the case of large arrays.

Finally, Fig. 7 illustrates the comparison between the transmission energy per symbol with the technique of the present invention and with the WIMAX used technique. Note that the Riemann surface FFT and IFFT computation reduces the transmission power by a factor of three, on average, for the same MSS bit error rate.

In accordance with the foregoing, it will be apparent that there has been provided a new, useful and non-obvious synchronization method for use with communications systems, and a communications system that uses this multi-user resource allocation and power-minimizing method for synchronization within the communications system, the system comprising at least one transmitter and at least one receiver, the transmitter and the receiver being connected by a channel wherein information transmitted by the transmitter passes through the channel and then reaches the receiver, and the channel comprises a number of sub-channels in frequency domain and a number of slots in time domain and each sub-channel is comprised of a combination of sub-carriers, wherein sub-carrier allocation is obtained.

Claims

I claim:

1. A method for reducing the complexity of a communication system by calculating the Fast Fourier Transform (FFT) and the Inverse Fast Fourier Transform (IFFT) using the Riemann surface technique.

2. The method of claim 1 wherein the transmission power and the computational power in the physical layer are minimized.

3. A communication system that uses a method for reducing the complexity of the communication system by calculating the Fast Fourier Transform (FFT) and the Inverse Fast Fourier Transform (IFFT) using the Riemann surface technique.

4. The system of claim 3 wherein the transmission power and the computational power in the physical layer are minimized.