Keywords

Convex optimization, multiuser wireless communication, multipleinput multipleoutput (MIMO), orthogonal frequencydivision multiplexing (OFDM), peaktoaverage (power) ratio (PAR) reduction, pre coding 
INTRODUCTION

Largescale multipleinput multipleoutput (MIMO) wireless communication is a promising means to meet the growing demands for higher throughput and improved qualityofservice of nextgeneration multiuser (MU) wireless communication systems. The vision is that a large number of antennas at the basestation (BS) would serve a large number of users concurrently and in the same frequency band, but with the number of BS antennas being much larger than the number of users, say a hundred antennas serving ten users. Largescale MIMO systems also have the potential to reduce the operational power consumption at the transmitter and enable the use of lowcomplexity schemes for suppressing MU interference (MUI). All these properties render largescale MIMO a promising technology for nextgeneration wireless communication systems. 
While the theoretical aspects of largescale MUMIMO systems have gained significant attention in the research community, much less is known about practical transmission schemes. As pointed out in practical realizations of largescale MIMO systems will require the use of low cost and lowpower radiofrequency (RF) components. To this end, reference proposed a novel MU pre coding scheme for frequencyflat channels, which relies on perantenna constant envelope (CE) transmission to enable efficient implementation using nonlinear RF components. Moreover, the CE pre coder of forces the peaktoaverage (power) ratio (PAR) to unity, which is not necessarily optimal as in practice there is always a tradeoff between PAR, errorrate performance, and power amplifier efficiency. 
Practical wireless channels typically exhibit frequency selective fading and a lowPAR pre coding solution suitable for such channels would be desirable. Preferably, the solution should be such that the complexity required in each (mobile) terminal is small (due to stringent area and power constraints),where as heavier processing could be afforded at the BS. Orthogonal frequencydivision multiplexing (OFDM) is an efficient and wellestablished way of dealing with frequency selective channels. In addition to simplifying the equalization at the receiver, OFDM also facilitates pertone power and bit allocation, scheduling in the frequency domain, and spectrum shaping. However, OFDM is known to suffer from a high PAR, which necessitates the use of linear RF components (e.g., power amplifiers) to avoid outofband radiation and signal distortions. Unfortunately, linear RF components are, in general, more costly and less power efficient than the ironlinear counterparts, which would eventually result in exorbitant costs for largescale BS implementations having hundreds of antennas. Therefore, it is of paramount importance to reduce the PAR of OFDMbased largescale MUMIMO systems to facilitate corresponding lowcost and lowpower BS implementations. 
To combat the challenging linearity requirements of OFDM, a plethora of PARreduction schemes have been proposed for pointtopoint singleantenna and MIMO wireless systems. For MUMIMO systems, however, a straight forward adaptation of these schemes is nontrivial, mainly because MU systems require the removal of MUI using a precoder, PARreduction schemes suitable for the MUMISO and MUMIMO downlink were described and, respectively, and rely on TomlinsonHarashima precoding. Both schemes, however, require specialized signal processing in the (mobile) terminals (e.g., modulo reduction), which prevents their use in conventional MIMOOFDM systems, such as IEEE 802.11n or 3GPP LTE . 
FITRA: The (smallest) Lipschitz constant of the gradient corresponds which can be calculated efficiently using the power method. To compute the proximal map for (PINFL), we define the auxiliary vector 

which enables us to rewrite the proximal map in more compact form as 

Unfortunately, does in contrast to l1norm regularized LS not have a simple closedform solution for (PINFL). Nevertheless, standard algebraic manipulations enable us to evaluate the proximal map efficiently using the following two step approach: First, we compute 

for which generalpurpose scalar optimization algorithms, such as the bisection method , can be used. 
Literature Survey:

we present numerical simulation results to demonstrate the capabilities of the proposed MUMIMOOFDM downlink transmission scheme. Specifically, we analyze the tradeoffs between PAR, errorrate performance, and outofband radiation, and we present a comparison with conventional pre coding schemes. In this implementation we have to compare with the scarcity signal with our PMP pre coding signal .such that we have say that PAR is again decreased by 2db by this l1 minimization of the signal. 
EXISTING METHOD

1)MIMOOFDM:

The growing demand of multimedia services and the growth of Internet related contents lead to increasing interest to high speed communications. The requirement for wide bandwidth and flexibility imposes the use of efficient transmission methods that would fit to the characteristics of wideband channels especially in wireless environment where the channel is very challenging. In wireless environment the signal is propagating from the transmitter to the receiver along number of different paths, collectively referred as multipath. While propagating the signal power drops of due to three effects: path loss, macroscopic fading and microscopic fading. Fading of the signal can be mitigated by different diversity techniques. To obtain diversity, the signal is transmitted through multiple (ideally) independent fading paths e.g. in time, frequency or space and combined constructively at the receiver. Multiple input multipleoutput (MIMO) exploits spatial diversity by having several transmit and receive antennas. However the paper “MIMO principles” assumed frequency flat fading MIMO channels. 
OFDM is modulation method known for its capability to mitigate multipath. In OFDM the high speed data stream is divided into Nc narrowband data streams, Nc corresponding to the subcarriers or sub channels i.e. one OFDM symbol consists of N symbols modulated for example by QAM or PSK. As a result the symbol duration is N times longer than in a single carrier system with the same symbol rate. The symbol duration is made even longer by adding a cyclic prefix to each symbol. Aslong as the cyclic prefix is longer than the channel delay spread OFDM offers intersymbol interference (ISI) free transmission. Another key advantage of OFDM is that it dramatically reduces equalization complexity by enabling equalization in the frequency domain. OFDM, implemented with IFFT at the transmitter and FFT at the receiver, converts the wideband signal, affected by frequency selective fading into N narrowband flat fading signals thus the equalization can be performed in the frequency domain by a scalar division carrierwise with the subcarrier related channel coefficients. The channel should be known or learned at the receiver. The combination MIMOOFDM is very natural and beneficial since OFDM enables support of more antennas and larger bandwidths since it simplifies equalization dramatically in MIMO systems. MIMOOFDM is under intensive investigation by researchers. This paper provides a general overview of this promising transmission technique.The general transceiver structure of MIMOOFDM is presented in Fig.2. The system consists of N transmit antennas and M receive antennas. In this paper the cyclic prefix is assumed to be longer than the channel delay spread. The OFDM signal for each antenna is obtained by using inverse fast Fourier transform (IFFT) and can be detected by fast Fourier transform (FFT). The received MIMOOFDM symbol of the n:th subcarrier and the m:th OFDM symbol of the i:th receive antenna after FFT can be written as where Aj[ n,m] is the transmitted data symbol on n:th carrier and m:th OFDM symbol, Wi[n,m] is the additive noise contribution at i:th receive antenna for the corresponding symbol in frequency domain and Hi,j[n,m] is the channel coefficient in the frequency domain between the j:th transmit antenna and the i:th receive antenna. The channel coefficients in frequency domain are obtained as linear combinations of the dispersive channel taps. 
2).PAPR

A major problem of multicarrier systems is that they show great sensitivity to nonlinear distortions. Inband and outof band interferences caused by nonlinear distortions degrade BER performance of the system and give rise to interference to adjacent frequency bands, respectively. At the transmitter, the high power amplifier (PA) is the main source of nonlinear distortions. Due to the fact that amplifier nonlinearity is amplitude dependent, the amplitude fluctuations of the input signal are of a concern. The peaktoaverage power ratio (PAPR), which is defined as the ratio of the peak power of the signal to its average power, is a measure of the amplitude fluctuations of the signal. Any multicarrier signal with a large number of subcarriers may have a high PAPR due to occasional constructive addition of subcarriers.In OFDM, when the number of carriers is large, the central limit theorem holds and the time domain samples of the OFDM signal, sampled at Nyquist rate, are approximately zeromean complex Gaussian random variables. The problem of this PAPR approximation is that it is derived for the Nyquist rate sampled version of a continuous signal. The continuous signal may have higher amplitude peaks than our maximum sample would imply and this analysis underestimates the distribution of the PAPR. It can also be noted that the Gaussian distribution has infinite values but the largest amplitude value of an OFDM [9]signal is only N times the average amplitude of the carriers thus the approximation does not hold very accurately on large amplitudes i.e. the shape of the PAPR distribution is does not follow Gaussian in the tails of the distribution. The Gaussian approximation is compared to a CCDF of a Nyquist rate sampled signal and to CCDF of an oversampled signal with oversampling factor 16. 
Example of PAPR reduction in MIMOOFDM

A number of techniques have been proposed to reduce PAPR and they can be divided in two kinds of approaches. In the first approach, PAPR reduction can be obtained with help of redundancy and the second one is to apply a correcting function to the signal to eliminate the high amplitude peaks. This is very simple approach but it causes interference. Adding redundancy does not cause any interference but it adds complexity of the transmitter and lowers the net transmission rate. Selective mapping (SLM) belongs to the first approach. In SLM, V statistically independent sequences are generated from the same information by multiplying with a certain vector and that sequence with the lowest PAPR is selected. The information of the vector used to generate the selected sequence has to be sent to the receiver. Detection of the signal depends also on the errors on the side information transmission. 
PROPOSED METHOD

1)Continuation strategies applicable to FITRA ALGORITHM

Compressed Sensing is the name assigned to the idea of encoding a large sparse signal using a relatively small number of linear measurements, and minimizing the `1norm (or its variants)in order to decode the signal. New results reported by Candes et al Donoho et al and others stimulated the current burst of research in this area. Applications of compressed sensing include compressive imaging , medical imaging, multisensory and distributed compressed sensing analogtoinformation conversion , and missing data recovery . Compressed sensing is attractive for these and other potential applications because it reduces the number of measurements required to obtain a given amount of information. The tradeof is the addition of a nontrivial decoding process.CS channel estimation method concerns the sparse reconstruction problem of estimating an unknown sparse channel vector from an observed vector of measurements R∈CM based on the linear model, namely the measurement by omitting the superscript for brevity. R=ψh+Z’ where ψ is a known measurement matrix, Z' is the measurement noise vector, and channel vector h is L sparse,where L is the number of multipath and is much 

Secondly, the measurement matrix ψ should satisfy the RIP, namely, for all Lsparse vector h, we have 

?.? is the l2norm.For the concerned ψ=ø_{m}F in another word, the RIP requires the rows {ø_{m,j}} of m, φ cannot sparsely represent the column {F_{i}} of F and vice versa. Now we prove the RIP of the measurement matrix = m ψ φ F .As we mentioned above, mφ is the mbyN matrix which consists of m unit vectors { } i e , and it is the unit matrix I_{N} when the number of pilot m is N. F is the NbyN DFT matrix, which is also the unitary matrix. Since I=F^{H}F , every row of I, can be expressed as where is the conjugate operation, F is the (j, i) th element of DFT matrix F , and F is the jth column vector of F. Clearly the motivation to use compressive sensing in channel estimation is the observation that some channels are characterized by sparse multipath by that we mean that there are much fewer distinct arrivals as there are baseband channel taps. With this in mind compressive sensing promises to estimate the channel with much less pilot over head or at higher accuracy with a constant number of pilots. The common assumption is that a sparse multipath channel leads to a baseband channel model where most taps are negligible .We take a closer look at this and find that in a channel modeled by seculars (point) scatterers the number of nonzero baseband taps depends very much on what one defines as negligible .Using instead an oversampled baseband model ,the representation of the channel becomes ambiguous, but also more sparse. 
SIMULATION RESULTS FOR FITRA

Description: The figure 49 shows that comparison of PAR for scarcity, LS,PMP Signals .From these we have observed that scarcity achieves the LOW PAR Compared to all other .From this l1 minimization we have to get this sparse signal with low par. 
CONCLUSION AND FUTURE SCOPE

The proposed joint pre coding, modulation, and PAR reduction framework, referred to as PMP, facilitates an explicit tradeoff between PAR, SNR performance, and outofband interference for the largescale MUMIMOOFDM downlink. As for the constantenvelope pre coder, the fundamental motivation of PMP is the large number of DoF offered by systems where the number of BS antennas is much larger than thenumber of terminals (users). Essentially, the downlink channel matrix has a highdimensional nullspace, which enables usto design transmit signals with “hardwarefriendly” properties, such as low PAR. In particular, PMP yields perantenna constantenvelope OFDM signals in the largeantenna limit,i.e., for N ! 1. PMP is formulated as a convex optimization problem for which a novel efficient numerical technique, called the fast iterative truncation algorithm (FITRA), was devised. Finally, further reducing the computational complexity of FITRA, e.g using continuation strategies like L1 minimization is vital for a practical realization of PMP in hardware.This is substantial benefits of compressive sensing for underwater acoustic Communications over long dispersive channels with large Doppler spread. 

Figures at a glance






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