Time-Domain Dual Component Computation Diversity Based on Generalized Hybrid Carrier

Yuqing Feng,Xuejun Sha,Yong Li,2,3,*,Xiaojie Fang,Yusi Zhang

1 School of Electronics and Information Engineering,Harbin Institute of Technology,Harbin 150001,China

2 Science and Technology on Communication Networks Laboratory,Shijiazhuang 050080,China

3 The 54th Research Institute of China Electronics Technology Group Corporation,Shijiazhuang 050081,China

4 Engineering Research Center for Dedicated Communication System,Ministry of Education,Harbin 150080,China

Abstract:In this paper,the concept of computation diversity is proposed by employing generalized hybrid carrier(GHC)system.The signal is backed up by transform-domain computation to enhance the anti-fading capability.Theoretical analysis is presented to demonstrate the superiority of the proposed method.Numerical simulations in doubly-selective fading channels are provided to verify the results.The bit error rate(BER)performance is guaranteed with a small computational complexity increment.The proposed method not only extends the new diversity dimension,but also improves the diversity gain of the system without occupying additional wireless resources.Moreover,the proposed method shows good adaptability with single carrier modulation and improves diversity performance.As the simulation results shown,time-domain dual component computation diversity(TDC-CD)has 1dB BER gain and 0.1 diversity gain at high signal-to-noise ratio,and single carrier system with TDC-CD achieves 2dB BER gain at 10－4.

Keywords:TDC-CD;transform domain;GHC system;diversity order

I.INTRODUCTION

Diversity schemes provide attractive alternations for current wireless communication systems due to high diversity gain or considerable spectral efficiency,making huge effect on the development of communication technology.Different methods applied to various scenes in terms of the comprehensive utilization of time,frequency and space resources in multi-antenna scenarios have been widely studied[1].The diversity schemes are generally divided into receive diversity and transmit diversity.Performance analysis of typical diversity combining techniques,such as maximal ratio combining and selection combining,are provided in[2,3].High energy consumption of receiver antenna has also been partially solved by sensor network and other related researches[4—6].

The transmit diversity schemes often bring more performance improvement for more available resources in transmitter,where the degree of freedom provided by the antenna plays an important role.By constructing cooperative communication schemes based on rateless network coding,the coding capacity performance is guaranteed in distributed MIMO systems without perfect synchronization[7].The diversity gain and multiplexing gain are obtained by using the multi-antenna diversity technology[8,9].Accordingly,the Space-time Block Code(STBC)is proposed by combining the spatial diversity with the time diversity(TD)achieving full diversity order.On that basis,a variety of more general STBCs,such as orthogonal space-time block codes,have been proposed with limited the coding gain.In that case,Space Time Trellis Code(STTC)is obtained by using the grid structure and Viterbi decoding,reaching full diversity gain and high coding gain at the same time with limited bandwidth[10,11].Diversity gain and multiplexing gain in communication systems are contradictory goals.Though tradeoffs exist as discussed by Bell Labs Layered Space-Time[12],it is still difficult to meet two requirements in a real-world system.To solve the above problems,[13]provides a scheme that is selected according to the actual channel situation;[14]maximizes diversity gain of optical wireless MIMO system utilizing spatial repetition coding,and is also analyzes the outage probability;[15]presents the tradeoff scheme and specific curve of MIMO system.Diversity methods for high frequency communication systems are also investigated to improve the link quality,link success rate and the channel diversity[16,17].Space-frequency block coding achieves reducing PAPR without the side information through structural advantages,thus keeping a low bit error rate and low computational complexity[18].Space-time codes are an important method to obtain diversity gain of multi-antenna systems.However,it takes up more space resources than traditional diversity strategies.Obviously,space-time codes cannot achieve diversity gain without increasing the number of antennas,which is exactly the key point.

Considering the requirement of less resource utilization,extra physical layer resources such as time,frequency,and space are utilized in above diversity techniques,which is in contradiction with the further diversity technology.Extending the new diversity dimension of statistical independence to increase the degree of freedom in signal design enables to obtain additional diversity gain.On the basis of Weightedtype Fractional Fourier Transform(WFRFT)[19],by selecting the extension form with two components,a new statistically independent diversity dimension without spreading resource block is studied to expand the statistical dimension of channel resources.The energy of a bit is arranged in two different locations in a block,so that the energy loss from channel fading of that bit can be reduced.Thus,WFRFT is widely used to counteract the channel fading[20]and enhance the communication security[21].However,frequency components suffer seriously in Single Carrier(SC)system.Dual time-domain components can be obtained in Generalized Hybrid Carrier(GHC)system transmitting signal with more uniform power distribution[22].Such fact makes GWFRFT more compatible with the SC system and more suitable for doubly selective channels.By selecting more suitable parameters,the signal energy distribution will be optimized more reasonably,thus improving the system performance[23].

To further improve the diversity gain of traditional communication system,the Computation Diversity(CD)extending new independent dimension employing GHC are proposed in this paper.This approach increases the freedom of signal design and improves the diversity gain without requiring extra physical layer resources.In this paper,Time-domain Dual Component Computation Diversity(TDC-CD)is designed for single-carrier systems,the theoretical mechanism of CD is elaborated,and the specific design of joint application with single carrier system is proposed and simulated.The proposed diversity method brings higher diversity gain.

The remaining of this paper is organized as the following:in Section II,the basic theory and GHC are addressed.While in Section III,we describe the computation diversity method in details.Meanwhile,the simulation results are presented in Section IV to explain the superiority of the proposed scheme.Section V conclude important notes.

II.BASIC THEORY AND GENERALIZED HYBRID CARRIER SYSTEM

In this section,we characterize the theoretical basis of TDC-CD based on GHC.TDC-CD obtains the transmitted signal through the transformation domain calculation,which acquires different signal components by calculation,and achieves the combined signal after the statistical independent channel.In that case,two signals can transmit independently without interference no matter which encoding method or energy distribution is adopted.Besides,the spectrum efficiency can be improved while maintaining diversity gain.Assume a typical SISO wireless communication model subject to the total power budget and timefrequency resource constraints.The generalized hybrid carrier system can be expressed as a weighted sum of four state functions[24].

where,

G(x)is the frequency-domain signal corresponding to the time-domain signalg(x);g(-x)andG(-x)are the corresponding inversion signals;θlis a transformation whose value is specified in[22];andwl(l=0,1,2,3)is the weighted coefficient of the basis function.The operation satisfies the reversibility and does not reduce signal-to-noise ratio in the receiver.Compared with the traditional 4-WFRFT,the GHC involves classical(WFRFT)transform zone and could be reduced to the 4-WFRFT whenθl=πlα/2.Considering that the current carrier system and the time-frequency properties of the signal cannot be modified,the GHC transformation can obtain the performance gain of the single dispersive channel without changing the carrier system.

The transmitted signal of GHC system only retains the advantage brought by the backup signal and thus it avoids the problem brought by the frequency domain component.This method does not change the physical layer resources occupied by the signal.Fully utilizing the structural characteristics of signal replication and energy characteristics of even distribution,the computation diversity expands the statistical independent dimension of the signal by introducing the GHC system into CD.In addition,it also improves the error ratio performance of the receiver and realizes the extended diversity receiving method under the constraint of physical layer resources.This method extends the available dimension of the diversity and increases the diversity efficiency.This is where we come up with computational dimensions other than the time domain,the frequency domain,or the spatial domain.

III.TIME DOMAIN COMPUTATION DIVERSITY

3.1 Time Domain Dual Component Computation Diversity Theory

Computation Diversity could be described as a process of obtaining signal components and merging them by computation.Different signal components are firstly obtained by computing the transformation,and then each signal component goes through the statistical independent channel.Finally,the merged signal is obtained by transform-domain calculating.

By passing the above sequence through the reverse transformation system of GHC,the estimated signal can be obtained as

The core idea of TDC-CD is to add independent fading signal backup since copies of each other on multiple independent fading channels are the less likely to experience deep fading at the same time.The receiver can filter the backup signal with low fading and high reliability for processing,which reduces the error probability of transmission.TDC-CD contains only two time-domain components.The information bits of the original signal are dispersed into a data block twice as long by means of double-slot expansion.It reduces the probability of common fading and improves the system error performance.Figure 2 is a schematic diagram of anti-fading principle of TDC-CD.Suppose a deep fading in the orange region,thei-th bit of s1and the(N+i-1)-th bit of s2both lose half energy other than an overall fading in thei-th bit of s1.Under the condition of equal power distribution,if a bit suffers from deep fading and the backup is not affected,the signal-to-noise ratio(SNR)only decreases by 3dB,which guarantees the bit error rate performance.

Figure 1.Block diagram of TDC-CD and SC:(a)transmitter of TDC-CD;(b)receiver of TDC-CD;(c)SC system adopting TD.

Figure 2.Anti-fading principle of TDC-CD.

Figure 3.The theoretical curves of original signal and TDC-CD with BPSK modulation under typical Rayleigh fading channel.

Figure 4.Frame structures of TD,CD and TDM.

Consider BPSK modulation withx1=±aand mutually independent Rayleigh Fading Channel.Conditioned on a given channel vector h,the average error probability can be derived exactly as in[25]

where,SNR is the average received signal-to-noise ratio per symbol time,andf(x)is the density distribution of channel.Under Rayleigh fading with each gain i.i.d.,the densityf(x)of the Chi-square distributed is given by

where,Lis the number of dimensions of the channel vector.The average error probability of original signal without diversity,time diversity withL= 2,and TDC-CD can be explicitly computed to be

The calculation results are shown in Figure 3.The theoretical and practical curves of non-diversity,2-order time diversity and TDC-CD are simulated respectively,where the transmitted power of all compared data streams are the same.The results show that all theoretical curves consist with the actual ones.As the SNR increases,the performance advantage of TDC-CD algorithm increases,and the TDC-CD curve lies between non-diversity and time diversity.For i.i.d channel model,characteristic curves of TDC-CD with one/two data streams are nearly identical,and perform slightly better than time diversity with power control.

The double-selective channels are closed to the real channels.But the complex channel model brings more complex calculator to the study of analytical solutions.Therefore,the performance under doubleselective channel will be illustrated by simulation in the Section IV.

3.2 Improved TD and TDM with TDC-CD

In order to explore the difference between TDC-CD and traditional TD and its joint application with the existing carrier system,the joint application of computation diversity method is studied.

The advantage of TDC-CD is the adjustability of the data form to meet communication requirements.Compared with traditional TD,TDC-CD can transmit only one data stream and provide diversity gain like TD;moreover,the second data stream can be inserted at any time without affecting the transmission of the first data stream.Figure 4 shows the frame structure comparison among TD,TDM and the proposed TDCCD.The height of the block represents the energy,and the pink box represents the position of the same bit in the frame.For the scenario that maximize diversity gain with a single data stream,the traditional approach is repetition coding,as shown in Figure 4(a).While TDC-CD transmits data 1 through zero padding and GHC transform to distribute all the energy evenly in two time slots,as shown in Figure 4(b).After the above transformation,TDC-CD achieves the same diversity gain as TD with only half of the time resource.Its most prominent advantage is that it does not occupy the physical layer resources of the second slot.If there is a need to transmit other signals,it can be directly loaded for transmission.For the independent channels,the correlation of the signals at two consecutive slots does not influence the BER performance.However,for dependent channels,the forward sequence has positive correlation with the reversed sequence on the center of the whole data block,which increase the probability of identical bits fading together.In that case,a flip for the second time slot is conducted to avoid the deterioration caused by signal correlation.

In terms of TDC-CD with two streams shown in Figure 4(c),the diversity gain can make a limited reduction to improve the Spectrum Efficiency(SE).When two time slots are loaded with different signals,the bit error rate(BER)performance is reduced but the SE is doubled.The two data blocks are respectively zero padded in the front and end,and the signal to be transmitted is accumulated after GHC transformation.The purpose is to divide each bit signal into two parts,transmit at different locations,backup each other,and improve BER performance under the same SE.Traditional TDM is shown in Figure 4(d).

3.3 Improved SC System with TDC-CD

TDC-CD can not only be used as an independent diversity method,but also can improve the existing SC systems according to the actual communication needs.Both SC system and TDC-CD bring more obvious performance advantage under the time-dispersion channel.Figure 5 depicts the frame structure of the improved SC system.Each data block is divided into two parts.GHC transformation is carried out after zero padding,and the signal to be transmitted is obtained after accumulation.After such processing,the complexity of transmitter increases,but the time-frequency property of the improved single carrier system remains unchanged.

Figure 5.Frame structures of improved SC system and classical SC system.

As for the distribution of bit energy,it is reasonable to make the signal energy evenly distributed for achieving better performance with unknown CSI and random channel fading[22].If deep fading occurs determined location in the channel,it is obvious that better reliability can be obtained by allocating less energy to that location.Thus,in the case of known CSI,TDCCD adjusts the signal energy distribution by changing the GHC parameters to reduce the energy loss of effective information.However,the traditional repetition coding and interleaving cannot change the energy distribution of the signal,which is a fundamental difference.The performance of the improved algorithm will be verified in Section IV.

IV.SIMULATION AND DISCUSSION

In this section,the performance of the proposed method is verified by simulation and compared with the traditional method.The transmitted signal has a center frequency of 3.5GHz and a bandwidth of 500MHz,and QPSK modulation is employed.Suppose the CSI is unknown with random decay.In order to achieve the best equal power distribution,select the appropriate weight coefficient that meets the conditionsθ0=θ2,θ1=θ3andθ0-θ1=±π/2.In particular casesθ0=0,weight coefficients are expressed as

The phases that satisfy the conditions are equivalent to the phase rotation of one set of parameters,which will not affect the anti-fading characteristics of the signal.To avoid the influence of symbol rate,the normalized doppler shift(FDT)is used to describe the channel.

Figure 6 and Figure 7 illustrate BER and SE of different diversity and multiplexing systems under the channel FDT = 0.002,τ=[0,1,2]·Ts,respectively.The diversity gain is defined asd=-logPe/logSNR,and the spectral efficiency is defined byη=(1-Pe)×LB/[(LCP+LB)×Ts×B][26].Simulation results show that the TDC-CD with single data stream has the same BER,diversity gain and SE as the traditional TD method at low SNR regime while the BER reveals a slim improvement over TD at high SNR regime.Besides,TDC-CD also performs slightly better in terms of spectral efficiency from enlarged image.On this occasion,TDC-CD still enables to transfer another data stream,which TD cannot.It can be concluded that TDC-CD is a better replacement of TD.

Figure 6.BER comparison of different diversity and multiplexing schemes under double-selective channel.

Figure 7.Spectral efficiency comparison of different diversity and multiplexing schemes under double-selective channel.

When two data streams are transferred,the BER over independent channels essentially coincides with that of one data stream as discussed in 3.1.It is obvious that the performance of TDC-CD is still better than TDM.For the green curve under the dependent channels in Figure 6 and Figure 7,the TDC-CD algorithm has a lower BER and higher SE than TDM though both transfer twice information.TDC-CD with two data streams has 1dB gain at a BER of 10－3and 0.1 diversity gain at 22dB,and TDC-CD with one data stream has 0.3dB gain at a BER of 5×10－5.While compared with traditional TD under the same conditions,TDCCD achieves twice SE by sacrificing a small amount of BER performance.

Figure 8.BER comparison among legacy SC system,improved SC system and OFDM system under doubleselective channel 1.

Figure 9.BER comparison among legacy SC system,improved SC system and OFDM system under doubleselective channel 2.

Figure 10.Spectral efficiency comparison between legacy SC system and improved SC system under double-selective channel 1.

Another performance superiority is that the TDCCD algorithm can further improve the performance of current SC systems.As shown in Figure 8 and Figure 9,compared with the traditional SC system,the improved SC system with TDC-CD obtain obvious performance advantages in terms of bit error rate under different dual-dispersion channels.When the FDT is 0.05 and multipath delay spread isτ=[0,1]·Ts(Channel 1),SC with TDC-CD achieves about 7dB BER gain atEb/N0=4×10－3.When the FDT is 0.01 and multipath delay spread isτ=[0,1,2,3,4,5]·Ts(Channel 2),SC with TDC-CD achieves 2dB BER gain at 10－4.All performance gain of TDC-CD is obtained by computation dimension extension without extra physical layer resources.TDC-CD can improve the BER performance of SC system under any doubleselective channel.

On the other hand,the BER performance of OFDM in different channels are also simulated in Figure 8 and Figure 9 respectively.Channel 1 dominated by timeselective fading is the dominant channel of OFDM,at which OFDM has the lowest bit error rate as red curve shown in Figure 8.At this time,TDC-CD still provides some gain for SC and narrow the gap between SC and OFDM.In the case of channel 2 dominated by frequency selective fading,the performance of SC system is better than OFDM,and the appearance of TDC-CD further enhances the advantage of SC.

It should be noted that the carrier system adopted is generally determined by the corresponding communication standards,and the TDC-CD method proposed in this paper is applicable to all systems using SC.

Spectral efficiency comparison between legacy SC system and improved SC system under doubleselective channel is simulated in Figure 10.The simulation results indicate that the SE is also improved correspondingly.TDC-CD achieves 0.01 bps/Hz SE gain atEb/N0=15dB under Channel 1.

V.CONCLUSION

In this paper,the concept of computational domain is proposed and applied to the field of diversity technology.It increases the freedom of signal design and is a new extended domain independent of time,frequency and space.On the premise of occupying the same time-frequency resources,the TDC-CD uses the transform-domain calculation to merge signals,and obtains additional diversity gain at the cost of computational complexity.Both theoretical deduction and simulation analysis are given to show the superiority of the proposed scheme.The TDC-CD with one or two data streams can be used as a substitution for TD and TDM respectively.The TDC-CD is also used to improve substitution SC system.It provides better BER,SE and diversity gain.In the long term,the TDC-CD algorithm obtains the diversity gain from the internal construction of the code block,which is a good combination with the existing space time code and other diversity technologies.

ACKNOWLEDGEMENT

This work was supported in part by Natural Science Foundation of Heilongjiang Province of China under Grant YQ2021F003,in part by the National Natural Science Foundation of China under Grant 61901140,in part by China Postdoctoral Science Foundation Funded Project under Grant 2019M650067 and in part by Science and Technology on Communication Networks Laboratory under Grant SCX21641X003.