BR102012009581B1 - Smooth concurrent backpropagation process for temporal equalization in ofdm systems - Google Patents

Abstract

SMOOTH COMPETITIVE BACKPROPAGATION PROCESS FOR TEMPORAL EQUALIZATION IN OFDM SYSTEMS. The present patent application refers to a Smooth Concurrent Backpropagation process, which efficiently propagates the useful information present, in the frequency domain, in order to update the temporal equalizer coefficients. The objective of the present Smooth Concurrent Backpropagation process is to increase the data throughput in the OFDM system more efficiently, as it allows the cyclic prefix of the OFDM symbol to be reduced or even eliminated.

Description

field of invention

The present patent application refers to a Concurrent Backpropagation process, which efficiently propagates the useful information present, in the frequency domain, in order to update the temporal equalizer coefficients. The objective of the present Concurrent Backpropagation process is to increase the data throughput in the OFDM system more efficiently, as it allows the cyclic prefix of the OFDM symbol to be reduced or eliminated.

It has industrial applicability aimed at being used in coherent receivers for very high capacity optical communications, as well as in receivers of communication standards such as IEEE 802.11, IEEE 802.16, digital television standards, including DVB-T, ISDB-T and SBTVD. It can also be used in the newly established standard for cellular mobile telephony, LTE (Long Term Evoluton).

Fundamentals of the invention

From the 2000s onwards, with the acceleration in the process of digitization of cellular mobile telephony and digital television plants, started in the 1990s, combined with new communications standards such as IEEE802.16, IEEE 802.11, LTE (Long Term Evoluton ) and applications in optical fibers to meet the demands of rates in the order of terabits per second, increased the demand for using the frequency spectrum and available bandwidth. This whole scenario was being developed in parallel with the industry of digital signal processing devices, which in the 2010s, allows access to these media in a personal and portable way with reduced cost for the user. An example of this scenario is the use of portable devices, known as tablets and fourth generation cell phones, which may soon become popular in many parts of the world.

However, for this scenario to be fully used, it is necessary to use the available spectrum efficiently. The fact is that the frequency spectrum is a limited resource. Thus, new technologies were proposed to meet the growing demand for information transfer in the scenario that was being established. The OFDM (Orthogonal Frequency Division Multiplexing) system was one of the technologies developed with the purpose of allowing a greater throughput of data. This technology also enables the development of communication systems with greater robustness against imperfections in the communications media, whether in free space or in an optical fiber.

In this digital system it is possible to transmit audio, video, still images and texts. The OFDM system is present as a project platform in European, Japanese and Brazilian digital television standards, in addition to the fourth generation of cell phones and in the IEEE 802.16 and 802.11 standards. Another important application, in evidence, is the use of the OFDM system in optical fibers to transmit information in the terabits per second range. This application allows new services such as cloud computing and ultra-high definition three-dimensional digital television to be transmitted over the media efficiently.

In the state of the art of the present patent application we can cite documents such as US20040076249, WO/2002/071607 and US7050490. However, none of them are intended to be applied to systems with OFDM modulation, which is one of the most advanced techniques for digital communications.

The OFDM system is designed to mitigate the interference imposed by the communication medium, whether free space or an optical fiber, employing a guard time, which is responsible for minimizing these interferences, called cyclic prefix.

However, the cyclic prefix, which is an extension of the transmitted OFDM symbol itself, penalizes the data throughput. This stems from the very nature of the time interval in which the cyclic prefix is transmitted, in order to provide robustness to the system, as it only carries redundant information.

As current communication standards need to provide bandwidth for the user to consume the information that can be processed by electronic and optical devices, it is extremely important to prioritize maximizing data throughput. In this way, it is evident that it is a priority to transmit useful information in all available time slots for transmission.

To increase the transmission rate in the OFDM system, devices known as temporal equalizers or Pre-FFT (Fast Fourier Transformer1) equalizers were proposed. The purpose of these devices is to shorten the duration of the cyclic prefix and, therefore, introduce more useful information into this interval. The main purpose of an equalization system is to minimize the interference between the symbols coming from a communication medium.

However, for OFDM systems, most equalizers need a training sequence together with a channel encoder, to operate efficiently, which also causes redundancy in the transmitted data.

Another class of equalizers known as self-taught or blind does not require a training sequence. However, not all equalizers of this class do without a channel coding process to assist in the correct reception of information transmitted in the OFDM system.

In 2001, a new equalization concept called competitor was presented, whose patent has already been granted. This equalization process operates the well-known CMA (Constant Modulus Algorithm) and DD (Directed Decision) algorithms cooperatively. This cooperation between the algorithms results in a greater speed of convergence of the equalizer coefficients compared to the traditional equalization models proposed so far. In the evolution of this process, a more efficient equalizer was presented in 2004 from the point of view of convergence. This equalizer, called Smooth Competitor, has become the state of the art in equalization without associated channel coding.

However, the concurrent equalizer was developed with two digital filters and for systems with a single transmission carrier. As the OFDM system is a multi-carrier model, significant modifications are required for the system to operate satisfactorily.

The concurrent smooth back propagation process proposes to propagate the information present in the frequency domain to update the equalizer coefficients that can operate in the OFDM system. In principle, the backpropagation proposal can be used in conjunction with any type of algorithm. The present proposal foresees the creation of a back-propagation process applied in OFDM systems to operate the concurrent algorithm.

In this way, it is possible to minimize the cyclic prefix, combat the interference caused by the communication channel and, as a consequence, increase the transmission rate of the OFDM system with a very good performance compared to the OFDM technique with cyclic prefix, or even with the use of conventional temporal equalizers. Furthermore, an equalization system with only one filter is proposed, in order to reduce the computational complexity of the concurrent backpropagation process. The backpropagation process is a little more complex than the conventional OFDM system, but it is justified by the increase in the transmission rate. The effort to develop the back-propagation process is motivated by the increase in demand that the future communications scenario projects.

Therefore, the present invention was developed with the objective of providing the necessary information so that the coefficients of a self-taught equalizer can adapt efficiently and in a short time. In this way, the throughput is increased, as the cyclic prefix is minimized even without the use of training sequences or channel coding.

Brief description of the invention

The present patent application refers to a concurrent smooth back-propagation process for OFDM systems, which has the ability to provide, at the same time, information about the behavior of the receiving signal constellation and the information present at the input. of the OFDM receiver to adapt the temporal equalizer coefficients. This process was proposed for the state of the art in terms of equalization, called concurrent. The main advantages of this process are to provide efficient information for the self-taught temporal equalizer to mitigate interference between symbols, to allow the minimization of the cyclic prefix, to increase the data throughput in wireless and optical receivers that operate on the OFDM platform, to obtain performance superior to the conventional method with the cyclic prefix.

The present patent application therefore deals with a soft concurrent back-propagation process for self-taught temporal equalization in OFDM systems, in which the referred process propagates information present in the frequency domain so that algorithms such as CMA and SDD (Soft DD ), acting in cooperative mode, can efficiently adapt the temporal equalizer coefficients. The objective of this back-propagation process for temporal equalization in OFDM systems is to minimize the interference between the symbols, caused by the dispersive effect of the communication medium.

Once the dispersive effect of the communication channel has been mitigated, by the back-propagation process associated with temporal equalization, it is no longer necessary to use the cyclic prefix, allowing an increase in the throughput of useful data, given that the cyclic prefix transmits only information redundant. The process has the following working principle: Equalization is performed by a single filter, highlighted here as “c”, whose filtering result defines the output signal after the FFT as rn(/c), which will be used in the process of concurrent backpropagation structure. In the process in question, this structure back propagates the stochastic error gradient, measured in the frequency domain, as useful information to adapt the temporal equalizer coefficients. This strategy allows the use of previously known information about the signal constellation in the subcarriers, in order to minimize the cost functions of traditional adaptation algorithms. The filter coefficients are adapted through gradient methods, or equivalent, based on a cost function that, depending on the algorithm used, can measure a statistical dispersion of rn(/c) or be based on a cost function that measures the distance from rn(7c) to the closest symbol of the digital alphabet in order to respect some criterion such as the MAP (Maximum to Posterior), which is a learning process of the Probability from Maximum to Posteriori. The index n represents an instant of time and k the index referring to the k-th sub-carrier involved in the transmission process. In this back-propagation process, the algorithms involved act in a cooperative or concurrent way. The main advantage of this process is the efficient operation of the concurrent equalization structure, which allows the minimization or in some scenarios even the elimination of the cyclic prefix.

The back-propagation process can be implemented in wireless communication systems and in fiber optic receivers that use the OFDM technique as a communication platform.

It is important to emphasize that the object of the patent is the process of back-propagation for temporal equalization systems in OFDM systems and not the process of competition between the algorithms, which is already patented in some parts of the world with the numbers US20040076249 and WIPO Patent Application. WO/2002/071607. Although the process of concurrency between algorithms is already patented for communication systems with a single carrier, there is no patent proposal for concurrent temporal equalization in OFDM systems. Thus, it is intended to conclude that the smooth concurrent backpropagation process is a new method capable of providing a performance and a throughput comparatively superior to the traditional method employing the cyclic prefix as a solution to minimize the interference between the OFDM symbols.

The smooth concurrent backpropagation process has the advantages of sending useful information and efficiently for the rapid convergence of the temporal equalizer coefficients, the minimization of the cyclic prefix, allowing the increase in the transmitted data throughput without allocating more frequency band, good performance against channels with multiple paths and use in high-speed optical communications systems using the OFDM platform.

Brief description of figures

Figure 1 illustrates the representation, through a FIR filter, of the impulse response of the communication channel. Figure 2 illustrates the simplified baseband diagram, representing the process of replacing the cyclic prefix by a temporal equalizer in an OFDM system, where the temporal equalizer aims to mitigate interference caused by dispersion in the impulse response of the communication channel . The communication channel can be considered any medium capable of carrying information belonging to a digital alphabet. Figure 3 illustrates the block diagram of the concurrent baseband backpropagation process for the temporal equalizer. Figure 4 illustrates the OFDM reception system with the inclusion of the EDT and EDF equalizer. Figure 5 illustrates the decision region for the SDD algorithm. Figure 6 illustrates the system performance, given by BER x Eb/NQ, for θ first scenario of Table 2, with PC = 0, insufficient to prevent interference between OFDM symbols. Figure 7 illustrates the system performance, given by BER x Eb/N0, for the second scenario in Table 2, with PC - 0, insufficient to prevent interference between OFDM symbols. Figure 8 illustrates the system performance, given by BER x Eb/N0, for the third scenario in Table 2, with PC = 0, insufficient to prevent interference between OFDM symbols. Figure 9 illustrates the system performance, given by BER x Eb/N0, for the fourth scenario in Table 2, with PC = 0, insufficient to prevent interference between OFDM symbols. Figure 10 illustrates the constellation diagram of the 64 QAM signal, after the convergence of the equalization process, for an Eb/N0 ratio of 60 dB, using the Brazil A channel, with PC = 1/128. Figure 11 illustrates the constellation diagram of the 64 QAM signal, after the convergence of the equalization process, for an Eb/N0 ratio of 60 dB, using the Brazil B channel, with PC = 1/128. Figure 12 illustrates the constellation diagram of the 64 QAM signal, after the convergence of the equalization process, for an Eb/N0 ratio of 60 dB, using the Brazil E channel, with PC = 1/128. Figure 13 illustrates the constellation diagram of the 64 QAM signal, after the convergence of the equalization process, for an Eb/N0 ratio of 60 dB, using the DVB channel, with PC = 1/128.

Detailed description of the invention

The present patent application relates to a smooth concurrent backpropagation process, which efficiently propagates the useful information present, in the frequency domain, for the purpose of updating the temporal equalizer coefficients. Basically, this process starts with the following steps: 1. Initialize the vector “c” of the temporal equalizer coefficients with the unit value. This vector has dimension J. The initialization of the vector with the temporal equalizer coefficients must be performed in such a way that only one of the coefficients has this unit value. 2. Start the indexer of samples received by channel fractional sampling: q = 0. 3. Start the channel regressor indexer: n = 0. 4. Get the nth channel regressor for the temporal equalizer input, hn (q), where this represents the sequence of samples received by fractional sampling Ts/2 of the channel, with q = 0,2,4,6,8, where M is the total number of samples of an OFDM symbol and PC is the length of the cyclic prefix. 5. Obtain the temporal equalizer output for the OFDM symbol at instant n: 6. Update the temporal equalizer coefficients through the smooth concurrent backpropagation process, calculating all parameters, such as error, stochastic gradient, probability function, which allow the updating of the temporal equalizer coefficients. 7. Increment indexes: q = q + 2, n = n + 1. 8. End the process.

The systems designed with the OFDM technique are considered efficient against scenarios that present superposition of propagation rays. This superposition is known in the telecommunications area as multiple path. This type of interference causes overlapping between the transmitted symbols, leading to bit error and consequently to a decrease in the transmission rate.

The origin of the superposition of transmitted rays occurs as a result of the dispersion in the impulsive response of a practical communication channel. Scatter is related to an impulsive channel response that does not assume null values over sample intervals.

Considering the transmitted data sequence as s(n) and the communication channel impulse response profile as h(n), the communication channel dispersion is understood as the result of the sum of the product between the past samples of the data sequence transmitted and the response h(n). The mathematical symbology used for this operation is given by x(n) = h(n) * s(n). Therefore, this expression can be written as x(n) = h(0)s(n) + h(l)s(n - 1) + ••• + h(M - l)s(n - M + 1 ), where M is the index representing the maximum channel dispersion value. This expression can be modeled through a filtering structure known as FIR(F/n/t and Impulse Response) illustrated in Figure 1.

The term T represents the delay of a sample in the FIR structure. In this way, channel dispersion can be attributed to the effect that each received sample s(n) associates as a function of the echoes of samples already existing in the memory of the impulsive response h(n) of the FIR filter illustrated in Figure 1. With the value of this association it is possible to obtain an index of the interference between the symbols caused by the number of symbols superimposed on each other.

The mitigation of this type of interference, in OFDM systems, is solved through the use of the cyclic prefix. This prefix is an extension of the transmitted symbol itself.

When the dispersion of the communication channel is less than the duration of the cyclic prefix interval, it is possible to mitigate the harmful effects on the received data. As the motivating factor in the design of OFDM technology was to increase the data throughput, the insertion of a cyclic prefix is not an ideal solution, because in the time interval destined to the cyclic prefix, no new information is transmitted.

Thus, the temporal equalization process is an interesting alternative to be proposed in systems that employ the OFDM technique. Figure 2 illustrates the simplified diagram of the equalization process responsible for minimizing or even eliminating the cyclic prefix.

Regardless of the communication channel (electromagnetic, optical, acoustic, etc.) used in the transmission of information between two geographically distinct points, the trend of modern digital systems is that they are designed to meet a growing demand in information transfer. This demand is, in part, being driven by personal devices such as Tablets, the fourth generation cellular mobile communication system, and new media that are being designed to support third-dimensional applications, as already mentioned in the Fundamentals of Invention section. .

In this scenario, the communication market demands high information transfer rates. Knowing that the available frequency band resource is limited and is already saturated by several applications, civil and military, it is worth mentioning that any device or artifice that can increase the throughput of the systems without allocating more frequency band is welcome.

Aware of this commercial scenario on demand in the transfer of information, the Self-taught Smooth Concurrent Retropropagation Process for equalization in OFDM systems is proposed as the object of this patent application. The self-taught philosophy refers to the ability of a device to automate a process, without prior knowledge of any information from the source. This class of devices in the study of equalization is called blind equalizers. The Concurrent back propagation process for temporal equalization proposed in this description is designed to be self-taught. Therefore, there is no need for training information issued by the source to operate. In this way, it is possible to collaborate even more with the reduction of the necessary bandwidth in the communication, because in addition to the concurrent back-propagation process allowing a reduction in the cyclic prefix, it is not necessary to send training information to the OFDM system. It is important to emphasize that in this patent application, in particular, the process was tested for concurrent equalization, which is the state of the art in channel equalization.

The Smooth Concurrent Backpropagation process presented in this patent application is a contribution to receiver designs in wireless and optical OFDM systems.

The block diagram of the OFDM receiver resulting from the inclusion of the backpropagation process is illustrated in Figure 3. The invention was conceived in conjunction with a fractional temporal equalizer. The objective is to accomplish this task using an adaptation process for the temporal equalizer coefficients, similar to the LMS algorithm (Leasí Mean Square), but using the backpropagation of the stochastic error gradient, measured in the frequency domain, as useful information. to adapt the temporal equalizer coefficients. This strategy makes it possible to use previously known information about the signal constellation in the subcarriers, in order to minimize cost functions such as those of the CMA and SDD (Soft Decision Direct) algorithms. Furthermore, a scheme is proposed for the CMA and SDD algorithms to act concurrently.

The development of the smooth concurrent backpropagation process was done in two steps. In the first step, a derivation with the CMA algorithm was performed, and the second a derivation with the SDD algorithm. The explanation of the process begins considering the output of the Pre-FFT equalizer given by dnpÍQ) — ■^•np(Q)^np(Q) θ ^ní(Q) where xrípÇ(j') and Xnitq) represent the inputs of the fractional temporal equalizer data, with cnp and cni being the even and odd coefficients of the equalizer, respectively, as shown in Figure 3.

To explain the development of the backpropagation process referring to the CMA algorithm, consider the OFDM reception system, with emphasis on EDT (Time Domain Equalizer) and EDF (Frequency Domain Equalizer), as illustrated in Figure 4.

The principle of the mathematical methodology used to make the backpropagation process possible to present effective results, using the CMA algorithm, was developed by deriving the output rn(k), after the FFT, with respect to the coefficients of the temporal equalizer c7. In this way, the temporal equalizer coefficients c7 are adapted to each OFDM symbol by back propagation of the stochastic gradient cost function of the calculated error in the frequency domain to the time domain. Therefore, this strategy makes it possible to use previously known information about the signal constellation in the sub-carriers, in order to minimize the CMA cost function.

In this text the index k is assumed to be the kth coefficient of the sub-carrier that is received by the EDF and the index n corresponds to the nth OFDM symbol.

. Porém, esta função de customização é útil para minimizar o erro apenas em uma das portadoras do sistema OFDM. Para minimizar o erro em todas as portadoras, é necessária uma alteração na função de custo do algoritmo CMA para contemplar todas as portadoras, levando a equação dada por

. O vetor com os valores do gradiente estocástico é definido por

ondθ j é o índice que representa o número de coeficientes do equalizador temporal em cada braço par e ímpar do equalizador. O sub-índices R e I representam a parte real e imaginária, respectivamente, dos coeficientes complexos em um conjunto . Neste conjunto os coeficientes do equalizador para o termo par

são complexos e dados por

. A mesma representação se aplica para o termo fracionário ímpar. Por motivo de simplicidade, o algoritmo de retro-propagação é derivado neste texto somente para atualizar os coeficientes pares do equalizador. A mesma abordagem e resultados são obtidos para os coeficientes ímpares.The algorithm design considers the cost function of the well-known CMA algorithm given by

. However, this customization function is useful to minimize the error in only one of the carriers of the OFDM system. To minimize the error on all carriers, it is necessary to change the cost function of the CMA algorithm to cover all carriers, leading to the equation given by

. The vector with the stochastic gradient values is defined by

ondθ j is the index that represents the number of temporal equalizer coefficients in each even and odd equalizer arm. The subscripts R and I represent the real and imaginary part, respectively, of the complex coefficients in a set. In this set the equalizer coefficients for the even term

are complex and given by

. The same representation applies for the odd fractional term. For simplicity, the backpropagation algorithm is derived in this text only to update the even coefficients of the equalizer. The same approach and results are obtained for the odd coefficients.

. Para encontrar o gradiente é necessário resolver derivadas de primeira ordem. O desenvolvimento será conduzido para uma única portadora e na análise final será estendida para todas as sub-portadoras.Considering the general term of the even arm, we can write the equations as

. To find the gradient it is necessary to solve for first order derivatives. Development will be conducted for a single carrier and in the final analysis it will be extended to all subcarriers.

caminhamos para as seguintes equações

Solving the real and imaginary term in the gradient equation

we go to the following equations

θ substituindo na equação do gradiente

, resulta na equação

Note que o termo

corresponde ao conjugado da transformada de Fourier. Se T é o operador da transformada de Fourier, esta equação torna- se

. Desde que 0 termo

θ sabendo que

, a equação resulta em

onde

e a matriz com M linhas e uma coluna, representando os coeficientes de Fourier para cada subportadora. Definindo

a equação do gradiente estocástico considerando todos os coeficientes do equalizador para o braço par no gradiente, é dada por

Rewriting the equations for

θ substituting in the gradient equation

, results in the equation

Note that the term

corresponds to the conjugate of the Fourier transform. If T is the Fourier transform operator, this equation becomes

. Since 0 term

θ knowing that

, the equation results in

Where

and the matrix with M rows and one column, representing the Fourier coefficients for each subcarrier. defining

the stochastic gradient equation considering all equalizer coefficients for the even arm in the gradient, is given by

foi obtida para a k-ésima subportadora. Para obter a equalização de atualização final para o l-ésimo coeficiente, é preciso considerar a contribuição de todas as sub- portadoras no sentido de encontrar a equação. Desta forma a equação para atualização dos coeficientes é descrita por

The expression of the stochastic gradient,

was obtained for the kth subcarrier. To obtain the final update equalization for the lth coefficient, it is necessary to consider the contribution of all subcarriers in order to find the equation. In this way, the equation for updating the coefficients is described by

Considering 57-1 as the inverse Fourier transform operator, we have the equation for updating the l-th coefficient of the even arm dad0 P°r

Para ° braço par e

para o braço ímpar.Considering all coefficients, the equation for updating these coefficients can be written as

For ° even arm and

for the odd arm.

O vetor

pode ser definido por

para

pode ser definido por

The IFFT(/nverse Fast Fourier Transformei1) has M terms being used to update the equalizer coefficients. This equalizer has only J coefficients, where J < M. Therefore, it is necessary to truncate the IFFT in J terms. Thus, the inverse Fourier transform matrix in can be written as

the vector

can be defined by

for

can be defined by

representa a saída quantizada do equalizador definida por

The second part of the procedure was developed for the derivation of the concurrent backpropagation process SDD. The treatment in development is the same as in the design of the CMA backpropagation process. The objective is to provide the temporal equalizer with information about the state of the interference intensity between the symbols, before the amplitude and phase, for each sub-carrier, are corrected by the EDF. The fundamental change is in the traditional cost function of the DD algorithm which is given by

represents the quantized equalizer output defined by

onde

sendo L um número inteiro.The term sü represents one of the decision region points, resulting in the division of the complex plane into M/4 regular regions, illustrated in Figure 5. Thus, the term sa is a symbol of the M-QAM constellation, inside a group of points defined by

Where

where L is an integer.

After convergence, the output of the equalizer represents the version of the quantized information added to the Gaussian noise. Thus, if the equalizer coefficients are properly configured, the equalizer output can be modeled by M Gaussian clusters. Each cluster is represented by

onde Pqi são as probabilidades a priori dadas por

According to these considerations, the a posteriori probability density function rn(k) can be approximated by

where Pqi are the a priori probabilities given by

To minimize computational complexity, the algorithm is designed in a local array. The objective is to contemplate only four exponential functions. In this way, the constellation plane is divided into M/4 regions with a regular density function, which is illustrated in figure 5. Each region has four constellation symbols, which is given by

onde cada probabilidade foi igualmente distribuída pelo valor 1/4 . Porém, esta proposta só seria interessante para uma equalização ótima. Para otimizar este resultado é proposta a tradicional solução MAP(Maximum A Posteriori).However, if rn(/c) is within the Sa region, an approximation of the a posteriori density function is obtained, given by

where each probability was evenly distributed by the value 1/4 . However, this proposal would only be interesting for an optimal equalization. To optimize this result, the traditional MAP solution (Maximum A Posteriori) is proposed.

The objective is to design the smooth concurrent backpropagation process with the CMA and SDD algorithms operating cooperatively. The function of the CMA algorithm is to reduce the error to allow the correct performance of the SDD. The SDD algorithm is designed to meet the MAP criterion by maximizing the logarithm of the local probability density function, given by

Os coeficientes pares e ímpares de adaptação são dados por

onde

Adjusting the coefficients of the stochastic gradient algorithm, we obtain

The even and odd coefficients of adaptation are given by

Where

Tabela 1: Sumário geral das operações realizadas pelo processo de Retro- Propagação Concorrente Suave para sistemas OFDM de comunicação. portadoras de dados são moduladas com 64-QAM e os tons pilotos com BPSK. Os parâmetros para o processo de retro-propagação concorrente suave aplicado no equalizador temporal, apresentados na Tabela 3, constam do número de coeficientes representado pelo termo J, a posição do coeficiente 5 unitário usado na inicialização do equalizador dada por P, o passo de adaptação usado para o equalizador concorrente, dados por μCMA μSDD, e o parâmetro de forma do SDD dado por p.Table 1 describes the general procedure for the smooth concurrent backpropagation process applied to one-channel equalization with fractional sampling.

Table 1: General summary of operations performed by the Smooth Concurrent Back Propagation process for communication OFDM systems. data carriers are modulated with 64-QAM and pilot tones with BPSK. The parameters for the smooth concurrent backpropagation process applied to the temporal equalizer, presented in Table 3, are the number of coefficients represented by the term J, the position of the unit coefficient 5 used in the initialization of the equalizer given by P, the adaptation step used for the concurrent equalizer, given by μCMA μSDD, and the SDD shape parameter given by p.

The ITU agency standardizes the channel profile as a function of the delay and gain of the multipath components. The component phase was randomly generated to simulate the positioning of the receiver antenna and was kept constant throughout all simulations. The channel digitization was done by truncating the delay profile upwards. The digitized channel non-zero coefficients are shown in Table 4.

In order to verify the performance of the smooth concurrent back propagation process, PC values equal to 1/128 and zero were tested. The motivation for choosing these values was established by the channel profiles presented in Table 4. The PC duration in μs is given, for the system considered here, by 2048 x PC x Ts. As an example, the value of PC = 1/64 corresponds to a duration of 3.9375 μs. Therefore, considering the maximum delay of the Brazil A channel as 5.93 μs, it is concluded that the PC value less than or equal to 1/64 does not prevent interference between the symbols in the Brazil A channel.

The simulation results were obtained for each point of Eb/N0 by estimating the mean f of the BER(B/t Error Rate) at L = 20 25 experiments performed (simulation), as shown in the equation

In calculating the 95% CI (Confidence Interval), the parameter "c" is given by the inverse t-student cumulative distribution function evaluated in

The BERxEb/N0 performance curves are then presented with a solid line for the average BER estimate and with a dashed line for the upper and lower limits of the confidence interval. It is important to highlight that the channel coding scheme was not used in the simulation, aiming to emphasize only the performance of the smooth concurrent backpropagation process in temporal equalization.

The simulations are guided by the scenarios presented in Table 2. The first column informs the scenario number. The second and third columns show the channel profile and maximum delay in μs, respectively. The fourth column presents the value of the PC ratio in the OFDM symbol, which for all simulated profiles is insufficient to avoid interference between the symbols. The fifth column shows the duration of the cyclic prefix (DPC) in .. The last column-transform JJL1, feri pf.v.ii.-infiil r^|uudi <di u communication channel with backpropagation process.

The purpose of the simulation is to test the smooth concurrent backpropagation process together with temporal equalization, for scenarios with insufficient PC to avoid interference between symbols.

All scenarios, in Table 2, are proposed with null cyclic prefix. Thus, it is important to emphasize that the concurrent smooth backpropagation process in conjunction with the temporal equalizer is responsible for mitigating interference between symbols. The linear interpolation estimator does not employ any time protection. This is proposed to show that when the cyclic prefix is not enough to prevent this interference, the FFT orthogonality is lost and the interference between carriers degrades the BER performance. Thus, the results inform saturation for one-dimensional linear interpolation, showing the need for an adequate PC or a temporal equalizer to avoid interference between OFDM symbols when only EDF is used. The supervised temporal equalizer is presented in the simulation as a benchmark for superior temporal equalization performance. Theoretical and simulated AWGN curves are positioned in the simulations only to act as an upper performance limit.

Figures 6, 7, 8 and 9 illustrate the performance results achieved with the simulation for the scenarios proposed in Table 2. The smooth concurrent backpropagation process, in Figures 6, 7, 8 and 9, is highlighted as Pre- competitor FFT. The designation of Concurrent Pre-FFT is another name given to a concurrent temporal equalization process in OFDM systems, as this equalization operation occurs before the FFT processing in the receiver. The results show that the proposed process for temporal equalization results in a shortened equivalent channel and improves system performance in scenarios with insufficient PC. In practice, this performance gain can make it possible to increase the capacity or improve the coverage of OFDM systems. It is also noteworthy that the performance of the smooth concurrent backpropagation process applied to the temporal equalizer or pre-FFT, follows the curve obtained for the supervised equalizer, in most of the proposed scenarios. In the scenarios for the Brazil B channel, the performance curve saturated close to a BER of 1 x 10~5. This is the biggest difference found in the performance for the simulated scenarios, even so only for Eb/NQ values above 30 dB.

Figures 10, 11, 12 and 13 illustrate constellation diagrams employing 64 QAM modulation. These results were obtained in the simulations after the convergence of the smooth concurrent backpropagation process for the channel profiles presented in Table 4. It is observed that the smooth concurrent backpropagation process manages to compose the constellation in the position of amplitude and phase in that the symbols were transmitted to the situation where the PC is insufficient.

The source used in the simulation emits a sequence of data through the channel with zero mean, unit variance and uniform distribution.

Tabela 2: Cenários para avaliação do desempenho do processo de retro- propagação concorrente suave para sistemas OFDM.

Tabela 3: Parâmetros de Simulação - Processo de retro-propagação Concorrente

Tabela 4: Perfil do Canal.The simulation results show that the OFDM system implemented with the concurrent smooth back propagation process represents a viable alternative to avoid interference between symbols, at the cost of an increase in the computational complexity of the receiver. However, this cost is justified since there is an increase in data throughput without compromising performance.

Table 2: Scenarios for evaluating the performance of the smooth concurrent backpropagation process for OFDM systems.

Table 3: Simulation Parameters - Concurrent Backpropagation Process

Table 4: Channel Profile.

Claims (6)

1. Smooth concurrent backpropagation process for temporal equalization in OFDM systems characterized by the equalization being performed by a single filter, here highlighted as “c”, whose filtering result defines the output signal, after the FFT as rn(k ), which will be used in the process of the concurrent backpropagation structure; in the process in question this back-propagation structure the stochastic error gradient, measured in the frequency domain, as useful information to adapt the temporal equalizer coefficients; this strategy makes it possible to use previously known information about the signal constellation on the subcarriers; the filter coefficients are adapted through gradient methods, or equivalent, based on a cost function that, depending on the algorithm used, can measure a statistical dispersion of rn(k) or be based on a cost function that measures the distance from rn(k) to the symbol closest to the digital alphabet in order to respect some criterion such as the MAP (Maxima a Posteriori), which is a learning process from Maximum Probability to Posteriori; the index n represents an instant of time and k the index referring to the k-th sub-carrier involved in the transmission process. 2. Smooth concurrent backpropagation process for temporal equalization in OFDM systems, according to claim 1, characterized in that the algorithms involved act in a cooperative or concurrent manner. 3. Smooth concurrent back propagation process for temporal equalization in OFDM systems, according to claim 1, characterized in that it can be implemented in wireless communication systems and in optical fiber receivers that use the OFDM technique as a communication platform. 4. Smooth concurrent backpropagation process for temporal equalization in OFDM systems, according to claim 1, characterized by being self-taught. 5. Smooth concurrent backpropagation process for temporal equalization in OFDM systems, according to claim 1, characterized in that the coefficients are performed in such a way that there is always the use of information from the frequency domain that is positioned after the FFT and information that is present at the input of the OFDM receiver, which are also used as part of the back-propagation process (figure 3). 6. Smooth concurrent back propagation process for temporal equalization in OFDM systems, according to claims 1 to 5, characterized in that it can be used in digital telecommunications systems in general (cellular telephony, digital television, digital radio, optical fiber ); wireless communications systems; optical communications systems; navigation aid systems; magnetic storage systems; radar systems; sonar systems, remote sensing systems.

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