Description Additional information In recent years, a wealth of research has emerged addressing various aspects of mobile communications signal processing. Rental Time perpetual. Read more. In recent years, a wealth of research has emerged addressing various aspects of mobile communications signal processing.
New applications and services are continually arising, and future mobile communications offer new opportunities and exciting challenges for signal processing. The Signal Processing for Mobile Communications Handbook provides a comprehensive survey of signal processing techniques used in mobile communications that concern the transmitter, the receiver, and the propagation channel. In addition, the effect of spreading noise power while local- tical spectral shape but with different time-frequency signatures . In the area of DOA finding, the izing the user energy in the time-frequency plane amounts to increased robustness of the STFD-bascd estimation of the signal and noise subspaces from the STPDs highly improves the angular resolution approaches with respect to noise.
In other words, the eigenvectors of the signal subspace obtained from an performance. Hence, the performance of the STFD-based approaches can be significantly improved, represents the projection matrix onto the row space of U. Therefore, Equation Moreover, in  it is proved approximation. An alternative solution consists of exploiting the existence of only one source at some that the traditional covariance-based subspace methods Jfe low-dimensional cases of the STFD subspace autoterm points.
For simplicity, the following criterion can be used: A statistical test to decide whether a time-frequency point is dominated by auto- or cross-terms is The above equation shows that the projection of the STFD over the time domain is nothing more than the proposed in [ The latter consider the following test statistic: traditional covariance matrix. This means that the space spanned Therefore, the Rn-based techniques can be seen as a low-dimension special case of the D02 lI, k -based ones. This To discriminate between noise and either auto- or cross-term, the variance of the test statistic is used.
Obviously, the details and signatures of the signal will be described more accurately variance is estimated using a bootstrap resampling technique [88,92].
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Once the noise regions in the time- and finely in higher-dimension space. In fact, this is the reason that the STFD-based methods have better frequency domain are identified, a threshold is set to distinguish the auto terms from the cross-terms. In . This In the case of noisy signals, in the Time-Frequency Domain reference  describes a detection criteria of cross- and auto-terms in the time-frequency plane by STPD-based methods require computation of STFDs at different time-frequency points.
At autoterm introducing two thresholds based on the Bayesian and Neyman-Pearson approaches. And the success into a joint diagonalization OD technique or eigendecomposed after simple averaging over the source of any STFD-based technique depends highly on the performance of the employed autoterm selection signatures of interest to estimate the mixing, or the array manifold matrix. At cross-term points, where procedure. The above intuitive procedure has shown some In order to obtain the mobile users' spatial information and achieve the space-division multiple access limitations in practical situations.
A projection-based selection procedure of cross-terms and autoterms SOMA , the DOA estimation oHar field sources from the mu]tiantenna outputs is one of the important has been proposed in [83J. The latter exploits the off-diagonal structure ofthe cross-source STFDs and issues in next-generation wireless communications. Thanks to their super resolution and robustness, the proceeds on whitened data STFDs. However, all these subspace methods assume the signals impinged Trace!! In addition, several nonspatial features such as time and frequency signatures of the signals are ignored in conventional methods.
In the underdeterminedcase i. One can exploit this information not only matrixU see Section Recently, several traditional DOA estimation techniques have been extended to nonstationary signals thanks to the use ofSTFD instead of the covariance matrix.. Below, we describe only mixture can be either instantaneous or convolutive. The first solution was based on the cancellation of higher-order moments assuming non-Gaussian and independent and identically distributed i.
In the case of non-i. In this context, the underlying problem can be Assuming a noise-free environment, the structure of the STFD associated with the above model is given regarded as signal synthesis from the time-frequency plane with the incorporation of the spatial diversity by provided by the antennae.
Below, we describe applications of the STFDs for the separation of both instantaneous and convolutive mixtures. The problem under consideration consists of identifying the matrix A and recovering the sourcc signals s n up to a fixed permutation and some complex factors. The missing unitary matrix U is retrievcd up to permutation and phase ofthe time-frequency point n,k , Equation The above JD is defined as the maximization of the following criterion: version of Da n, k over the source signatures of interest.
Signal Processing For Mobile Communications Handbook
But indeterminacy arises in the case where P L Dss n,k is singular. The unitary matrix U is found up to permutation and phase shifts Equation Currently, blind source separation is considered one of most promising techniques in wireless commu- Once the unitary matrix U is obtained from cither the TO, JOD, or combined JDIJOD, an estimate nications and more specifically in multiuser detection.
Thc underlying problem consists of recovering of the mixing matrix A can be computed by the product W U, where W is the whitening matrix see the original waveforms of the user-emitted signals without any knowledge on their linear mixture. This Section An estimate of the source signals s n can then be obtained by the product A z n. Note that the block diagonal structure first time in [J while separating discrete sources.
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Since then, several other works based on a priori comes from the fact that the cross-terms between 5, n and si n - d , where d is some delay, are not zero knowledge of the probability density functions of the sources! In [lOS], an and depend on the local correlation structure of the signal. This block diagonal structure is exploited to approach for the resolution of the aforementioned problem exploits the concept of disjoint orthogonality achieve the separation of the convolutive mixture.
The First the data vector z n is whitened. The idea of the algorithm consists of ifW is a whitening matrix, then clustering together the autoterm points associated with the same principal eigenvector of Dzz n, k rep- resenting a particular source signal. An advanced clustering technique of the above diagonal. The whitening matrix W can be determined from the eigendecomposition of the data covariance autoterms based on gap statistics is proposed in .
The sources are assumed to have different time-frequency signatures, and the channel matrix 1, AIL] AKL According to Equations C' is chosen such that respectively. To avoid interblock interference, guard intervals can be used, as in OFDM, for example. This can be done by forcing either the last L rows of the precoding matrix or the first L columns of the decoding matrix to zero . Precoding of lTV channels can be optimized by a priori knowledge of the channel temporal evolution. This knowledge can be provided by a feedback channel such that the receiver estimates periodically the channel parameters, also called channel status information CSI [, and sends them back to the Receiver transmitter.
The latter uses this CSI to predict the channel evolution within a finite time interval and commutes the optimal precodcr.
Under the constraint of a fixed average trammit power, the optimal precoder, i. Doppler shift and multipath fading  in wireless communications. In addition, they are bandwidth In  10], a physical interpretation of the optimal preceding fer time- and frequency-dispersive channels efficient [J.
Under the compared to FSK. In the same reference, it is also shown to send the information" . Chirp modulation was first suggested in  by using a pair of linear under mild conditions often met in practice that the TFDs of the right singular vectors of the LTV channel chirps with opposite chirp rates for binary signaling.
A system for multiple access within a common are mainly concentrated along the curves where the energy in the time-frequency domain of the channel frequency band was proposed in  by assigning pairs of linear chirps with different chirp rates to equals the square of the associated singular value. The TFDs of the left singular vectors are simply time- and several users.
In this system, the number of users simultaneously accessing the shared resources is limited frequency-shift versions of the TFDs of the right singular vectors. This interpretation clearly establishes the by the MAl for a given time-bandwidth product. To reduce this shortcoming, the chirp signals are selected optimal power allocation in the time-frequency domain as a generalization of the well-known water-filling in  such that they all have the same power as well as the same bandwidth, offering inherent protection principle [, ].
The above interpretation also allows an approximate computation of the channel against frequency-selective fading.
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Further, the combination of chirp modulation signaling with frequency- singular vectors and values directly from the time-frequency representation of the LTV channel, without hopping FH multiple access was proposed in . The obtained hybrid system Figure In , the chirp parameters, to be used in chirp modulation signaling, Indeed, chirp signals or, equivalently, linear FM signals have been widely used in sonar applications for It requires a number of signal transmission paths that carry the same information but have uncorrelated multipath fadings.
A circuit to combine the received signals or select one of the paths is necessary. Diversity techniques take advantage of the fact that signals exhibit fades 15The channel matrix is the transfer matrix from the transmitted block vector to the received block vector. Herein, we review a method that can overcome this problem.
When considering narrowband communications erties of TFSP to the problems encountered in wireless communications. Similarly, time-frequency array processing techniques are where w, t represents the baseband signal and to is the carrier frequency. The received signal K t will well suited for source localization and blind source separation. Other application issues in wireless com- munications that we are briefly discussed show that there are great potential benefits in further explor- then be expressed as ing the use of TFSP techniques for current issues in wireless communications and, more generally, in In such systems, the need to combat interuser interference and interchannel interference leads The special structure of the envelope spectrum Equation Conse- quently, the detection of FM signals through the Rayleigh Hat fading environment can be achieved in the above time-frequency plane without the use of the conventional diversity techniques or higher-order Acknowledgments spectra approach .
The first author acknowledges the funding received from the Australian Research Council. The authors also acknowledge the assistance provided by G. Azemi, A. Khalighi, and S. Alvarez in the review of Using Time-Frequency Processing Many wireless communications systems require prior knowledge of the mobile velocity.
This knowledge References allows compensation of distortions introduced by the communications channel. In addition, reliable esti- mates of the mobile velocity are useful for effective dynamic channel assignment and for the optimization  H. Poor and G. Warnell, Eds. In another chapter of , an overview of existing velocity estimators is Englewood Cliffs, NT: Prentice Hall, In contrast to  B. Boashash, Ed.