ABSTRACT In this letter, we aim to identify the optimal isotropic mother wavelet for a given spat... more ABSTRACT In this letter, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find the unique analytic solutions. In the one- and two-dimensional cases, the derived wavelets are well known.
It is known that the Karhunen-Loève transform (KLT) of Gaussian first-order auto-regressive (AR(1... more It is known that the Karhunen-Loève transform (KLT) of Gaussian first-order auto-regressive (AR(1)) processes results in sinusoidal basis functions. The same sinusoidal bases come out of the independent-component analysis (ICA) and actually correspond to processes with completely independent samples. In this paper, we relax the Gaussian hypothesis and study how orthogonal transforms decouple symmetric-alphastable (SαS) AR(1) processes. The Gaussian case is not sparse and corresponds to α = 2, while 0 < α < 2 yields processes with sparse linear-prediction error. In the presence of sparsity, we show that operator-like wavelet bases do outperform the sinusoidal ones. Also, we observe that, for processes with very sparse increments (0 < α ≤ 1), the operator-like wavelet basis is indistinguishable from the ICA solution obtained through numerical optimization. We consider two criteria for independence. The first is the Kullback-Leibler divergence between the joint probability density function (pdf) of the original signal and the product of the marginals in the transformed domain. The second is a divergence between the joint pdf of the original signal and the product of the marginals in the transformed domain, which is based on Stein's formula for the mean-square estimation error in additive Gaussian noise. Our framework then offers a unified view that encompasses the discrete cosine transform (known to be asymptotically optimal for α = 2) and Haar-like wavelets (for which we achieve optimality for 0 < α ≤ 1).
IEEE 10th INTERNATIONAL CONFERENCE ON SIGNAL PROCESSING PROCEEDINGS, 2010
... 10, pp. 2616-2627, Oct. 1994. [12] Saif al Zahir, Aimen El-Maleh, and Esam Khan, An efficien... more ... 10, pp. 2616-2627, Oct. 1994. [12] Saif al Zahir, Aimen El-Maleh, and Esam Khan, An efficient test vector compression technique based on geometric shapes, Proceedings of the 8th International Conference on Electronics, Circuits and Systems, ICECS 2001, vol. 3, no. 2-5, pp. ...
2011 18th International Conference on Telecommunications, 2011
Recently, a new class of binary codes for overloaded CDMA systems are proposed that not only has ... more Recently, a new class of binary codes for overloaded CDMA systems are proposed that not only has the ability of errorless communication but also suitable for detecting active users. These codes are called COWDA [1]. In [1], a Maximum Likelihood (ML) decoder is proposed for this class of codes. Although the proposed scheme of coding/decoding show impressive performance, the decoder can be improved. In this paper by assuming more practical conditions for the traffic in the system, we suggest an algorithm that increases the performance of the decoder several orders of magnitude (the Bit-Error-Rate (BER) is divided by a factor of about in some ⁄ 's). The algorithm supposes the Poison distribution for the time of activation/deactivation of the users.
2010 IEEE International Conference on Communications, 2010
In this paper we propose a new model for the near-far effect in a CDMA system. We derive upper an... more In this paper we propose a new model for the near-far effect in a CDMA system. We derive upper and lower bounds for the maximum near-far effect for errorless transmission. Using these bounds, we propose some near-far resistant codes. Also a very low complexity ML decoder for a subclass of the proposed codes is suggested.
2012 IEEE International Symposium on Information Theory Proceedings, 2012
In this paper the existence of capacity achieving linear codes with arbitrarily sparse generator ... more In this paper the existence of capacity achieving linear codes with arbitrarily sparse generator matrices is proved. In particular, we show the existence of capacity achieving codes for which the density of ones in the generator matrix is arbitrarily low. The existing results on the existence of capacity achieving linear codes in the literature are limited to the codes whose generator matrix elements are zero or one with necessarily equal probability, yielding a non-sparse generator matrix. This will imply a high encoding complexity. An interesting trade-off between the sparsity of the generator matrix and the value of the error exponent is also demonstrated. Compared to the existing results in the literature, which are limited to codes with nonsparse generator matrices, the proposed approach is novel and more concise. Although the focus in this paper is on the Binary Symmetric and Binary Erasure Channels, the results can be easily extended to other discrete memoryless symmetric channels.
It is known that the Karhunen-Loève transform (KLT) of Gaussian first-order auto-regressive (AR(1... more It is known that the Karhunen-Loève transform (KLT) of Gaussian first-order auto-regressive (AR(1)) processes results in sinusoidal basis functions. The same sinusoidal bases come out of the independent-component analysis (ICA) and actually correspond to processes with completely independent samples. In this paper, we relax the Gaussian hypothesis and study how orthogonal transforms decouple symmetric-alphastable (SαS) AR(1) processes. The Gaussian case is not sparse and corresponds to α = 2, while 0 < α < 2 yields processes with sparse linear-prediction error. In the presence of sparsity, we show that operator-like wavelet bases do outperform the sinusoidal ones. Also, we observe that, for processes with very sparse increments (0 < α ≤ 1), the operator-like wavelet basis is indistinguishable from the ICA solution obtained through numerical optimization. We consider two criteria for independence. The first is the Kullback-Leibler divergence between the joint probability density function (pdf) of the original signal and the product of the marginals in the transformed domain. The second is a divergence between the joint pdf of the original signal and the product of the marginals in the transformed domain, which is based on Stein's formula for the mean-square estimation error in additive Gaussian noise. Our framework then offers a unified view that encompasses the discrete cosine transform (known to be asymptotically optimal for α = 2) and Haar-like wavelets (for which we achieve optimality for 0 < α ≤ 1).
In this paper, we study binary and ternary matrices that are used for CDMA applications that are ... more In this paper, we study binary and ternary matrices that are used for CDMA applications that are injective on binary or ternary user vectors. In other words, in the absence of additive noise, the interference of overloaded CDMA can be removed completely. Some new algorithms are proposed for constructing such matrices. Also, using an information theoretic approach, we conjecture the extent to which such CDMA matrix codes exist. For overloaded case, we also show that some of the codes derived from our algorithms perform better than the binary Welch Bound Equality codes; the decoding is ML but of low complexity.
2009 IEEE International Conference on Communications, 2009
In this paper we introduce a new class of codes for over-loaded synchronous wireless CDMA systems... more In this paper we introduce a new class of codes for over-loaded synchronous wireless CDMA systems which increases the number of users for a fixed number of chips without introducing any errors. In addition these codes support active user detection. We derive an upper bound on the number of users with a fixed spreading factor. Also we propose an ML decoder for a subclass of these codes that is computationally implementable. Although for our simulations we consider a scenario that is worse than what occurs in practice, simulation results indicate that this coding/decoding scheme is robust against additive noise. As an example, for 64 chips and 88 users we propose a coding/decoding scheme that can obtain an arbitrary small probability of error which is computationally feasible and can detect active users. Furthermore, we prove that for this to be possible the number of users cannot be beyond 230.
EURASIP Journal on Wireless Communications and Networking, 2011
This paper is a tutorial review on important issues related to code-division multiple-access (CDM... more This paper is a tutorial review on important issues related to code-division multiple-access (CDMA) systems such as channel capacity, power control, and optimum codes; specifically, we consider optimum overloaded codes that achieve errorless transmission in the absence of noise for the binary and nonbinary cases. A survey of lower and upper bounds for the sum channel capacity of such systems is given in the presence and absence of channel noise. The asymptotic results for the channel capacity are also investigated. The channel capacity, errorless transmission codes, and power estimation for near-far effects are also explored. The emphasis of this tutorial review is on the overloaded CDMA systems.
In CDMA systems, the received user powers vary due to moving distance of users. Thus, the CDMA re... more In CDMA systems, the received user powers vary due to moving distance of users. Thus, the CDMA receivers consist of two stages. The first stage is the power estimator and the second one is a Multi-User Detector (MUD). Conventional methods for estimating the user powers are suitable for underor fully-loaded cases (when the number of users is less than or
In this paper the existence of capacity achieving linear codes with arbitrarily sparse generator ... more In this paper the existence of capacity achieving linear codes with arbitrarily sparse generator matrices is proved. In particular, we show the existence of capacity achieving codes for which the density of ones in the generator matrix is arbitrarily low. The existing results on the existence of capacity achieving linear codes in the literature are limited to the codes whose
In this paper, we explore the mystery of synchronous CDMA as applied to wireless and optical comm... more In this paper, we explore the mystery of synchronous CDMA as applied to wireless and optical communication systems under very general settings for the user symbols and the signature matrix entries. The channel is modeled with real/complex additive noise of arbitrary distribution. Two problems are addressed. The first problem concerns whether overloaded error free codes exist in the absence of additive noise under these general settings, and if so whether there are any practical optimum decoding algorithms. The second one is about the bounds for the sum channel capacity when user data and signature codes employ any real or complex alphabets (finite or infinite). In response to the first problem, we have developed practical Maximum Likelihood (ML) decoding algorithms for overloaded CDMA systems for a large class of alphabets. In response to the second problem, a general theorem has been developed in which the sum capacity lower bounds with respect to the number of users and spreading ...
ABSTRACT We investigate a stochastic signal-processing framework for signals with sparse derivati... more ABSTRACT We investigate a stochastic signal-processing framework for signals with sparse derivatives, where the samples of a Lévy process are corrupted by noise. The proposed signal model covers the well-known Brownian motion and piecewise-constant Poisson process; moreover, the Lévy family also contains other interesting members exhibiting heavy-tail statistics that fulfill the requirements of compressibility. We characterize the maximum-a-posteriori probability (MAP) and minimum mean-square error (MMSE) estimators for such signals. Interestingly, some of the MAP estimators for the Lévy model coincide with popular signal-denoising algorithms (e.g., total-variation (TV) regularization). We propose a novel non-iterative implementation of the MMSE estimator based on the belief-propagation (BP) algorithm performed in the Fourier domain. Our algorithm takes advantage of the fact that the joint statistics of general Lévy processes are much easier to describe by their characteristic function, as the probability densities do not always admit closed-form expressions. We then use our new estimator as a benchmark to compare the performance of existing algorithms for the optimal recovery of gradient-sparse signals.
In this paper we introduce a new class of codes for over-loaded synchronous wireless and optical ... more In this paper we introduce a new class of codes for over-loaded synchronous wireless and optical CDMA systems which increases the number of users for fixed number of chips without introducing any errors. Equivalently, the chip rate can be reduced for a given number of users, which implies bandwidth reduction for downlink wireless systems. An upper bound for the maximum number of users for a given number of chips is derived. Also, lower and upper bounds for the sum channel capacity of a binary over-loaded CDMA are derived that can predict the existence of such over-loaded codes. We also propose a simplified maximum likelihood method for decoding these types of over-loaded codes. Although a high percentage of the over-loading factor 3 degrades the system performance in noisy channels, simulation results show that this degradation is not significant. More importantly, for moderate values of ܧ ܰ Τ (in the range of -ͳͲ dB) or higher, the proposed codes perform much better than the binary Welch bound equality sequences.
In this paper, we obtain a family of lower bounds for the sum capacity of Code Division Multiple ... more In this paper, we obtain a family of lower bounds for the sum capacity of Code Division Multiple Access (CDMA) channels assuming binary inputs and binary signature codes in the presence of additive noise with an arbitrary distribution. The envelope of this family gives a relatively tight lower bound in terms of the number of users, spreading gain and the noise distribution. The derivation methods for the noiseless and the noisy channels are different but when the noise variance goes to zero, the noisy channel bound approaches the noiseless case. The behavior of the lower bound shows that for small noise power, the number of users can be much more than the spreading gain without any significant loss of information (overloaded CDMA). A conjectured upper bound is also derived under the usual assumption that the users send out equally likely binary bits in the presence of additive noise with an arbitrary distribution. As the noise level increases, and/or, the ratio of the number of users and the spreading gain increases, the conjectured upper bound approaches the lower bound. We have also derived asymptotic limits of our bounds that can be compared to a formula that Tanaka obtained using techniques from statistical physics; his bound is close to that of our conjectured upper bound for large scale systems.
In this paper, we explore some of the fundamentals of synchronous Code Division Multiple Access (... more In this paper, we explore some of the fundamentals of synchronous Code Division Multiple Access (CDMA) as applied to wireless and optical communication systems under very general settings (of any size) for the user symbols and the signature matrix entries. The channel is modeled by real/complex additive noise of arbitrary distribution. Two problems are addressed. The first problem concerns whether
... The authors are with the Advanced Communication Research Institute (ACRI), Electrical Enginee... more ... The authors are with the Advanced Communication Research Institute (ACRI), Electrical Engineering Department, Sharif University of Tech-nology, Tehran, Iran (e-mail: {pedram pad, faraji}@ee.sharif.edu, mar-vasti ... [13] P. Pad, F. Marvasti, K. Alishahi, and S. Akbari, A class of ...
ABSTRACT In this letter, we aim to identify the optimal isotropic mother wavelet for a given spat... more ABSTRACT In this letter, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find the unique analytic solutions. In the one- and two-dimensional cases, the derived wavelets are well known.
It is known that the Karhunen-Loève transform (KLT) of Gaussian first-order auto-regressive (AR(1... more It is known that the Karhunen-Loève transform (KLT) of Gaussian first-order auto-regressive (AR(1)) processes results in sinusoidal basis functions. The same sinusoidal bases come out of the independent-component analysis (ICA) and actually correspond to processes with completely independent samples. In this paper, we relax the Gaussian hypothesis and study how orthogonal transforms decouple symmetric-alphastable (SαS) AR(1) processes. The Gaussian case is not sparse and corresponds to α = 2, while 0 < α < 2 yields processes with sparse linear-prediction error. In the presence of sparsity, we show that operator-like wavelet bases do outperform the sinusoidal ones. Also, we observe that, for processes with very sparse increments (0 < α ≤ 1), the operator-like wavelet basis is indistinguishable from the ICA solution obtained through numerical optimization. We consider two criteria for independence. The first is the Kullback-Leibler divergence between the joint probability density function (pdf) of the original signal and the product of the marginals in the transformed domain. The second is a divergence between the joint pdf of the original signal and the product of the marginals in the transformed domain, which is based on Stein's formula for the mean-square estimation error in additive Gaussian noise. Our framework then offers a unified view that encompasses the discrete cosine transform (known to be asymptotically optimal for α = 2) and Haar-like wavelets (for which we achieve optimality for 0 < α ≤ 1).
IEEE 10th INTERNATIONAL CONFERENCE ON SIGNAL PROCESSING PROCEEDINGS, 2010
... 10, pp. 2616-2627, Oct. 1994. [12] Saif al Zahir, Aimen El-Maleh, and Esam Khan, An efficien... more ... 10, pp. 2616-2627, Oct. 1994. [12] Saif al Zahir, Aimen El-Maleh, and Esam Khan, An efficient test vector compression technique based on geometric shapes, Proceedings of the 8th International Conference on Electronics, Circuits and Systems, ICECS 2001, vol. 3, no. 2-5, pp. ...
2011 18th International Conference on Telecommunications, 2011
Recently, a new class of binary codes for overloaded CDMA systems are proposed that not only has ... more Recently, a new class of binary codes for overloaded CDMA systems are proposed that not only has the ability of errorless communication but also suitable for detecting active users. These codes are called COWDA [1]. In [1], a Maximum Likelihood (ML) decoder is proposed for this class of codes. Although the proposed scheme of coding/decoding show impressive performance, the decoder can be improved. In this paper by assuming more practical conditions for the traffic in the system, we suggest an algorithm that increases the performance of the decoder several orders of magnitude (the Bit-Error-Rate (BER) is divided by a factor of about in some ⁄ 's). The algorithm supposes the Poison distribution for the time of activation/deactivation of the users.
2010 IEEE International Conference on Communications, 2010
In this paper we propose a new model for the near-far effect in a CDMA system. We derive upper an... more In this paper we propose a new model for the near-far effect in a CDMA system. We derive upper and lower bounds for the maximum near-far effect for errorless transmission. Using these bounds, we propose some near-far resistant codes. Also a very low complexity ML decoder for a subclass of the proposed codes is suggested.
2012 IEEE International Symposium on Information Theory Proceedings, 2012
In this paper the existence of capacity achieving linear codes with arbitrarily sparse generator ... more In this paper the existence of capacity achieving linear codes with arbitrarily sparse generator matrices is proved. In particular, we show the existence of capacity achieving codes for which the density of ones in the generator matrix is arbitrarily low. The existing results on the existence of capacity achieving linear codes in the literature are limited to the codes whose generator matrix elements are zero or one with necessarily equal probability, yielding a non-sparse generator matrix. This will imply a high encoding complexity. An interesting trade-off between the sparsity of the generator matrix and the value of the error exponent is also demonstrated. Compared to the existing results in the literature, which are limited to codes with nonsparse generator matrices, the proposed approach is novel and more concise. Although the focus in this paper is on the Binary Symmetric and Binary Erasure Channels, the results can be easily extended to other discrete memoryless symmetric channels.
It is known that the Karhunen-Loève transform (KLT) of Gaussian first-order auto-regressive (AR(1... more It is known that the Karhunen-Loève transform (KLT) of Gaussian first-order auto-regressive (AR(1)) processes results in sinusoidal basis functions. The same sinusoidal bases come out of the independent-component analysis (ICA) and actually correspond to processes with completely independent samples. In this paper, we relax the Gaussian hypothesis and study how orthogonal transforms decouple symmetric-alphastable (SαS) AR(1) processes. The Gaussian case is not sparse and corresponds to α = 2, while 0 < α < 2 yields processes with sparse linear-prediction error. In the presence of sparsity, we show that operator-like wavelet bases do outperform the sinusoidal ones. Also, we observe that, for processes with very sparse increments (0 < α ≤ 1), the operator-like wavelet basis is indistinguishable from the ICA solution obtained through numerical optimization. We consider two criteria for independence. The first is the Kullback-Leibler divergence between the joint probability density function (pdf) of the original signal and the product of the marginals in the transformed domain. The second is a divergence between the joint pdf of the original signal and the product of the marginals in the transformed domain, which is based on Stein's formula for the mean-square estimation error in additive Gaussian noise. Our framework then offers a unified view that encompasses the discrete cosine transform (known to be asymptotically optimal for α = 2) and Haar-like wavelets (for which we achieve optimality for 0 < α ≤ 1).
In this paper, we study binary and ternary matrices that are used for CDMA applications that are ... more In this paper, we study binary and ternary matrices that are used for CDMA applications that are injective on binary or ternary user vectors. In other words, in the absence of additive noise, the interference of overloaded CDMA can be removed completely. Some new algorithms are proposed for constructing such matrices. Also, using an information theoretic approach, we conjecture the extent to which such CDMA matrix codes exist. For overloaded case, we also show that some of the codes derived from our algorithms perform better than the binary Welch Bound Equality codes; the decoding is ML but of low complexity.
2009 IEEE International Conference on Communications, 2009
In this paper we introduce a new class of codes for over-loaded synchronous wireless CDMA systems... more In this paper we introduce a new class of codes for over-loaded synchronous wireless CDMA systems which increases the number of users for a fixed number of chips without introducing any errors. In addition these codes support active user detection. We derive an upper bound on the number of users with a fixed spreading factor. Also we propose an ML decoder for a subclass of these codes that is computationally implementable. Although for our simulations we consider a scenario that is worse than what occurs in practice, simulation results indicate that this coding/decoding scheme is robust against additive noise. As an example, for 64 chips and 88 users we propose a coding/decoding scheme that can obtain an arbitrary small probability of error which is computationally feasible and can detect active users. Furthermore, we prove that for this to be possible the number of users cannot be beyond 230.
EURASIP Journal on Wireless Communications and Networking, 2011
This paper is a tutorial review on important issues related to code-division multiple-access (CDM... more This paper is a tutorial review on important issues related to code-division multiple-access (CDMA) systems such as channel capacity, power control, and optimum codes; specifically, we consider optimum overloaded codes that achieve errorless transmission in the absence of noise for the binary and nonbinary cases. A survey of lower and upper bounds for the sum channel capacity of such systems is given in the presence and absence of channel noise. The asymptotic results for the channel capacity are also investigated. The channel capacity, errorless transmission codes, and power estimation for near-far effects are also explored. The emphasis of this tutorial review is on the overloaded CDMA systems.
In CDMA systems, the received user powers vary due to moving distance of users. Thus, the CDMA re... more In CDMA systems, the received user powers vary due to moving distance of users. Thus, the CDMA receivers consist of two stages. The first stage is the power estimator and the second one is a Multi-User Detector (MUD). Conventional methods for estimating the user powers are suitable for underor fully-loaded cases (when the number of users is less than or
In this paper the existence of capacity achieving linear codes with arbitrarily sparse generator ... more In this paper the existence of capacity achieving linear codes with arbitrarily sparse generator matrices is proved. In particular, we show the existence of capacity achieving codes for which the density of ones in the generator matrix is arbitrarily low. The existing results on the existence of capacity achieving linear codes in the literature are limited to the codes whose
In this paper, we explore the mystery of synchronous CDMA as applied to wireless and optical comm... more In this paper, we explore the mystery of synchronous CDMA as applied to wireless and optical communication systems under very general settings for the user symbols and the signature matrix entries. The channel is modeled with real/complex additive noise of arbitrary distribution. Two problems are addressed. The first problem concerns whether overloaded error free codes exist in the absence of additive noise under these general settings, and if so whether there are any practical optimum decoding algorithms. The second one is about the bounds for the sum channel capacity when user data and signature codes employ any real or complex alphabets (finite or infinite). In response to the first problem, we have developed practical Maximum Likelihood (ML) decoding algorithms for overloaded CDMA systems for a large class of alphabets. In response to the second problem, a general theorem has been developed in which the sum capacity lower bounds with respect to the number of users and spreading ...
ABSTRACT We investigate a stochastic signal-processing framework for signals with sparse derivati... more ABSTRACT We investigate a stochastic signal-processing framework for signals with sparse derivatives, where the samples of a Lévy process are corrupted by noise. The proposed signal model covers the well-known Brownian motion and piecewise-constant Poisson process; moreover, the Lévy family also contains other interesting members exhibiting heavy-tail statistics that fulfill the requirements of compressibility. We characterize the maximum-a-posteriori probability (MAP) and minimum mean-square error (MMSE) estimators for such signals. Interestingly, some of the MAP estimators for the Lévy model coincide with popular signal-denoising algorithms (e.g., total-variation (TV) regularization). We propose a novel non-iterative implementation of the MMSE estimator based on the belief-propagation (BP) algorithm performed in the Fourier domain. Our algorithm takes advantage of the fact that the joint statistics of general Lévy processes are much easier to describe by their characteristic function, as the probability densities do not always admit closed-form expressions. We then use our new estimator as a benchmark to compare the performance of existing algorithms for the optimal recovery of gradient-sparse signals.
In this paper we introduce a new class of codes for over-loaded synchronous wireless and optical ... more In this paper we introduce a new class of codes for over-loaded synchronous wireless and optical CDMA systems which increases the number of users for fixed number of chips without introducing any errors. Equivalently, the chip rate can be reduced for a given number of users, which implies bandwidth reduction for downlink wireless systems. An upper bound for the maximum number of users for a given number of chips is derived. Also, lower and upper bounds for the sum channel capacity of a binary over-loaded CDMA are derived that can predict the existence of such over-loaded codes. We also propose a simplified maximum likelihood method for decoding these types of over-loaded codes. Although a high percentage of the over-loading factor 3 degrades the system performance in noisy channels, simulation results show that this degradation is not significant. More importantly, for moderate values of ܧ ܰ Τ (in the range of -ͳͲ dB) or higher, the proposed codes perform much better than the binary Welch bound equality sequences.
In this paper, we obtain a family of lower bounds for the sum capacity of Code Division Multiple ... more In this paper, we obtain a family of lower bounds for the sum capacity of Code Division Multiple Access (CDMA) channels assuming binary inputs and binary signature codes in the presence of additive noise with an arbitrary distribution. The envelope of this family gives a relatively tight lower bound in terms of the number of users, spreading gain and the noise distribution. The derivation methods for the noiseless and the noisy channels are different but when the noise variance goes to zero, the noisy channel bound approaches the noiseless case. The behavior of the lower bound shows that for small noise power, the number of users can be much more than the spreading gain without any significant loss of information (overloaded CDMA). A conjectured upper bound is also derived under the usual assumption that the users send out equally likely binary bits in the presence of additive noise with an arbitrary distribution. As the noise level increases, and/or, the ratio of the number of users and the spreading gain increases, the conjectured upper bound approaches the lower bound. We have also derived asymptotic limits of our bounds that can be compared to a formula that Tanaka obtained using techniques from statistical physics; his bound is close to that of our conjectured upper bound for large scale systems.
In this paper, we explore some of the fundamentals of synchronous Code Division Multiple Access (... more In this paper, we explore some of the fundamentals of synchronous Code Division Multiple Access (CDMA) as applied to wireless and optical communication systems under very general settings (of any size) for the user symbols and the signature matrix entries. The channel is modeled by real/complex additive noise of arbitrary distribution. Two problems are addressed. The first problem concerns whether
... The authors are with the Advanced Communication Research Institute (ACRI), Electrical Enginee... more ... The authors are with the Advanced Communication Research Institute (ACRI), Electrical Engineering Department, Sharif University of Tech-nology, Tehran, Iran (e-mail: {pedram pad, faraji}@ee.sharif.edu, mar-vasti ... [13] P. Pad, F. Marvasti, K. Alishahi, and S. Akbari, A class of ...
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