scholarly journals Time Coding OTDM MIMO System Based on Singular Value Decomposition for 5G Applications

2019 ◽  
Vol 9 (13) ◽  
pp. 2691 ◽  
Author(s):  
Rana M. Aly ◽  
Amira Zaki ◽  
Waleed K. Badawi ◽  
Moustafa H. Aly
Keyword(s):  
Singular Value Decomposition ◽  
Impulse Response ◽  
Space Time ◽  
Data Rate ◽  
Singular Value ◽  
Basis Functions ◽  
Channel Impulse Response ◽  
Modulation Techniques ◽  
Time Coding ◽  
Value Decomposition

For 5G and beyond cellular communication systems, new coding and modulation techniques are suggested to reach the requirements of high data rate and quality of service. In this paper, a new space-time coded orthogonal transform division multiplexing (STC OTDM) technique is proposed for 5G applications. The proposed system is used to enhance the data rate and performance of the orthogonal transform division multiplexing (OTDM) technique. The proposed system is based on using space-time coding (STC) with OTDM to increase the system diversity and consequently the system performance. The OTDM technique is based on transmitting data on orthogonal basis functions obtained from the Singular Value Decomposition (SVD) of the channel impulse response of the desired user. Various modulation techniques like QPSK, 64-QAM, and 256-QAM are investigated using different subcarriers and channel models. The simulation results show that the proposed system achieved a better performance when compared to classical and recent multicarrier techniques. The proposed technique increases the diversity gain resulting in a decrease in the fading effect of the multipath channel and an enhancement in the bit error rate (BER) performance. The proposed technique also provides a secure data transmission to the desired user as his data is sent on the basis functions extracted from his own channel impulse response that cannot be decoded by other users.

scholarly journals On temporal codes and the spatiotemporal response of neurons in the lateral geniculate nucleus

1994 ◽  
Vol 72 (6) ◽  
pp. 2990-3003 ◽  
Author(s):  
D. Golomb ◽  
D. Kleinfeld ◽  
R. C. Reid ◽  
R. M. Shapley ◽  
B. I. Shraiman
Keyword(s):  
Singular Value Decomposition ◽  
Firing Rate ◽  
Impulse Response ◽  
Linear Response ◽  
Impulse Response Function ◽  
Singular Value ◽  
Temporal Coding ◽  
Temporal Mode ◽  
Temporal Modes ◽  
Value Decomposition

1. The present work relates recent experimental studies of the temporal coding of visual stimuli (McClurkin, Optican, Richmond, and Gawne, Science 253: 675, 1991) to the measurements of the spatiotemporal receptive fields of neurons within the lateral geniculate of primate. 2. We analyze both new and previously described magnocellular and parvocellular single units. The spatiotemporal impulse response function of the unit, defined as the time-resolved average firing rate in response to a weak stimulus flashed at a given location and time, is characterized by the singular value decomposition. This analysis allows one to represent the impulse response by a small number, two to three, of spatial and temporal modes. Both magnocellular and parvocellular units are weakly nonseparable, with major and minor modes that account, respectively, for approximately 78 and 22% of the response. The major temporal mode for both types is essentially identical for the first 100 ms. At later times the response of magnocellular units changes sign and decays slowly, whereas the response of parvocellular units decays relatively rapidly. 3. The spatiotemporal impulse response function completely determines the response of a unit to an arbitrary stimulus when linear response theory is valid. Using the measured impulse response, combined with a rectifying neuronal input-output relation, we calculate the responses to a complete set of spatial luminance patterns constructed of "Walsh" functions. Our predicted temporal responses are in qualitative agreement with those reported for parvocellular units (McClurkin, Optican, Richmond, and Gawne, J. Neurophysiol. 66: 794, 1991). Under the additional assumptions of Poisson statistics for the probability of spiking and a plausible background firing rate, we predict the performance of a unit in the Walsh pattern discrimination task as quantified by mutual information. Our prediction is again consistent with the reported results. 4. Last, we consider the issue of temporal coding within linear response. For stimuli presented for fixed time intervals, the singular value decomposition provides a natural relation between the temporal modes of the neuronal response and the spatial pattern of the stimulus. Although it is tempting to interpret each temporal mode as an independent channel that encodes orthogonal features of the stimulus, successively higher order modes are increasingly unreliable and do not significantly increase the discrimination capabilities of the unit.

Evaluating EM waveforms by singular‐value decomposition of exponential basis functions

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 64-74 ◽  
Author(s):  
Edward M. Stolz ◽  
James Macnae
Keyword(s):  
Singular Value Decomposition ◽  
Pulse Length ◽  
Singular Value ◽  
Basis Functions ◽  
Step Response ◽  
Waveform Data ◽  
Time Constants ◽  
Exponential Basis ◽  
Response Systems ◽  
Value Decomposition

Exponential basis functions preconvolved with the system waveform are used to convert measured transient decays to an ideal frequency‐domain response that can be modeled more easily than arbitrary waveform data. Singular‐value decomposition (SVD) of the basis functions are used to assess which specific EM waveform provides superior resolution of a range of exponential time constants that can be related to earth conductivities. The pulse shape, pulse length, transient sampling scheme, noise levels, and primary field removal used in practical EM systems all affect the resolution of time constants. Step response systems are more diagnostic of long time constants, and hence good conductors, than impulse response systems. The limited bandwidth of airborne EM systems compared with ground systems is improved when the response is sampled during the transmitter on time and gives better resolution of short time constants or fast decays.

To: “Evaluating EM waveforms by singular‐value decomposition of exponential basis functions” (E. M. Stolz and J. Macnae, GEOPHYSICS, 63, 64–74)

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 310-310
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Basis Functions ◽  
Exponential Basis ◽  
Value Decomposition ◽  
Wrong Sign

We thank Andy Green for pointing out the following errata to us. Equation (10) has the wrong sign on the RHS and should read [Formula: see text] and equation (11) has the wrong sign as in equation (1) plus the wrong signs on the last two exponents. It should read [Formula: see text].

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