Signal Processing Techniques for 5G:An Overview

Fa-Long Luo

（Element CXI，San Jose，California 95131，USA）

Signal Processing Techniques for 5G:An Overview

Fa-Long Luo

（Element CXI，San Jose，California 95131，USA）

This paper gives an outline of the algorithms and implementation of the main signal processing techniques being developed for 5G wireless communication.The first part contains a review and comparison of six orthogonal and non-orthogonal waveform-generation and modulation schemes:generalized frequency-division multiplexing（GFDM），filter-bank multicarrier（FBMC），universal filtered multicarrier（UFMC），bi-orthogonal frequency-division multiplexing（BFDM），sparse-code multiple-access（SCMA），and non-orthogonal multiple access（NOMA）.The second part discusses spatial signal processing algorithms and implementations for massive multiple-input multiple-output（massive-MIMO），3D beamforming and diversity，and orbital angular momentum（OAM）based multiplexing.The last part gives an overview of signal processing aspects of other emerging techniques in 5G，such as millimeter-wave，cloud radio access networks，full duplex mode，and digital radio-frequency processing.

3D beamforming 5G；massive MIMO；GFDM and spatial multiplexing

1 Introduction

S ignal processing techniques have had the most important role in wireless communications since the second generation of cellular systems.In 2G，3G and 4G，the peak service rate has been the dominant metric for performance.Each generation has a development cycle of about ten years and is defined by a standout signal processing technology that represents the most important advancement in that generation.In 2G，this technology was time-division multiple access（TDMA）；in 3G，it was，code-division multiple access（CDMA）；and in 4G，it is orthogonal frequency-division multiple access（OFDMA）.However，this will not be the case for 5G systems—there will be no dominant performance metric that defines requirements for 5G technologies.Instead，a number of new signal processing techniques will be used to continuously increase peak service rates，and there will be new emphasis on greatly increasing capacity，coverage，efficiency（power，spectrum，and other resources），flexibility，compatibility，and convergence.In this way，5G systems will be able to handle the explosion in demands arising from emerging applications such as big data，cloud services，and machine-to-machine（M2M）communication.

A number of new signal processing techniques for 5G systems have been proposed and are being considered for international standardization and deployment.This article gives an overview of promising signal processing techniques，both from a practical and standardization point of view.In particular，it emphasizes orthogonal and non-orthogonal modulation techniques as well as spatial processing techniques such as massive multiple-input multiple-output（massive-MIMO），three-dimensional beamforming and diversity，and multiplexing based on orbital angular momentum（OAM）.

The rest of this paper is organized as follows.In section 2，we present six modulation schemes that offer better data transmission and higher peak rates than existing modulation schemes.The six modulation schemes we present are:generalized frequency-division multiplexing（GFDM）［1］，filter bank multi-carrier（FBMC）［2］，universal filtered multi-carrier（UFMC）［3］，bi-orthogonal frequency division multiplexing（BFDM）［4］，sparse-code multiple access（SCMA）［5］，and nonorthogonal multiple access（NOMA）［6］.In section 3，we discuss spatial signal processing for 5G，focusing on massive-MIMO，adaptive 3D beamforming，and OAM-based multiplexing. In section 4，we give an overview of signal processing-aspects of emerging 5G techniques，such as millimeter wave，cloud radio access，full duplex access，and digital radio-frequency processing.In section 5，we offer some conclusions.

2 Signal Processing Algorithms for Modulation and Waveform Generation

Modulation processing involves using data and information to be transmitted to change the signal waveforms in specific al-gorithms.Such processing determines many factors in a wireless system，including transmission speed，spectral efficiency，power consumption，signal-to-noise ratio，and implementation complexity.OFDM and OFDMA are used in 4G systems and have the following advantages:

·They eliminate inter-cell interference by ensuring orthogonality between each subcarrier.

·They use fast Fourier transform（FFT），which means they can be easily implemented and integrated with MIMO and multiple antennas.

·They can average the interferences within a cell by using allocation with cyclic permutation.

·They adapt transmission power according to the bit rate of the user.

·They ensure frequency diversity by spreading the carriers across the used spectrum.

·They are robust to inter-symbol interference（ISI）and multipath distortion. OFDM and OFDMA have the following main disadvantages:

·a relatively high peak-to-average power ratio（PAPR）due to the fact that modulated symbols are transmitted in parallel and each contains part of the transmission，

·limited spectral efficiency due to the need for a cyclic prefix（CP）and null guard tones at the spectral edges，

·high sensitivity to frequency offsets and phase noise and the need for strict synchronization.

These disadvantages prevent OFDMA schemes from being immediately used in 5G systems，and more advanced modulation schemes，such as GFDM，F(xiàn)BMC，UFMC，BFDM，SCMA and NOMA，have been investigated.

2.1 GFDM

Equations（1）and（2）are the simplified equations for modulating a time-domain symbol in the OFDM scheme and GFDM scheme，respectively.Modulation of the time-domain signal occurs before CP processing.

where n is the time index，k is the sub-carrier index，m is the time-symbol index，M is the number of symbols per sub-carrier，K is the number of active sub-carriers，N is the total number of sub-carriers（the length of Discrete Fourier Transform），x（n）is the transmitted samples，g［n］is the coefficients of the shaping filter，and d（k，m）is the coded data related to mth symbol.With OFDM，only one symbol can be modulated over active subcarriers（frequency bins）；however，with GFDM，multiple symbols can be modulated over active subcarriers.This means that GFDM allocates the data in a two-dimensional time-frequency block structure by introducing flexible pulse shaping for the individual subcarriers.Because GFDM modulates multiple symbols per subcarrier through a two-dimensional time-frequency structure，it has a number of benefits in terms of efficiency，performance，and complexity:

·GFDM can control out-of-band（OOB）emission and reduce PAPR much more than OFDM by adjusting the shaping filters.OOB emission and PAPR are two of the major drawbacks of OFDM for advanced wireless systems.In addition，GFDM allows fragmented spectrum and dynamic spectrum allocation without these severely interfering with existing services or other users.

· Orthogonality between the subcarriers is dismissed in GFDM，and variable pulse-shaping filters reduce the effect of frequency offset and phase noise without the need for strict synchronization processing of symbols.

·A short CP is a simple way of reducing the multipath distortion.A matched filter receiver with iterative interference cancellation can also reduce ISI and intercarrier interference（ICI）caused by subcarrier filtering.More importantly，by adding a single CP for an entire block that contains multiple symbols，GFDM can be used to improve the spectral efficiency of the system.

From（2），the filter processing，i.e.，the circular convolution in the time domain or multiplication in the frequency domain，significantly increases computational complexity in a GFDM system.On the other hand，GFDM has advantages，such as reduced PAPR，that result in the reduction or even elimination of other processing units，such as digital pre-distortion（DPD）or crest-factor reduction（CFR），both of which are essential in current wireless and broadcasting systems［7］.

Equation（1）is a special case of（2）.In（1），M and coefficients are all unity，i.e.，only one symbol and rectangular-form filtering shape.In other words，a GFDM system can made compliant and easily integrates with existing OFDM systems.

2.2 FBMC

Equation（1）can be generalized to the following，which is used in FBMC:

wheregk（n）is the impulse response of the kth filter.The relationship between the indexes m and n is not shown in（3）. FBMC can be described as a synthesis-analysis filter-bank-based modulation scheme，where synthesis filtering is introduced using FFT/IFFT and a poly-phase filter structure.

In FBMC，the modulated data at each subcarrier is shaped by a well-designed prototype filter that is different from the rectangular pulse filter in OFDM.This prototype filter has many degrees of freedom to use different waveform shapes and can greatly suppress a signal's side-lobes，making them strictly band-limited.By filtering on a per-subcarrier basis，intercarrier interference can be greatly reduced when there is fre-quency jitter and offset due to the Doppler Effect or misaligned oscillators.This strict band-limiting requirement makes the transmit filter impulse response long.Typically，the filter has three or four times the length of the symbols.As a result，F(xiàn)BMC can only provide good spectral efficiency if the number of transmit symbols is large.Unlike GFDM，F(xiàn)BMC is not suitable in low-latency scenarios，where efficiency must be high for bursty transmission.

Because there is no CP in an FBMC system，a more complex equalization system is required at the receiver side of the system to resolve multipath issues and further reduce ISI.Meanwhile，F(xiàn)BMC requires much more additional processing than OFDM to insert the CP in the transmitter and remove the CP at the receiver side.

Equation（3）shows that the OFDM scheme is a special case of FBMC，where a prototype filter with a rectangular impulse response is applied，and the overlap factor is the unity.This suggests that FBMC is compatible with OFDM-based systems and also has a large PAPR，which is similar to OFDM.This makes FBMC systems especially vulnerable to nonlinearity in the transceiver chain，which includes power amplifier，digitalto-analog converter，and analog-to-digital converter.More importantly，existing techniques for reducing PAPR in OFDM cannot be immediately used in an FBMC system［8］.These techniques include amplitude clipping，coding，interleaving，partial transmit sequence，selected mapping，tone reservation，tone injection，and active constellation extension.It is highly desirable to develop more efficient algorithms to reduce PAPR in an FBMC system.

2.3 UFMC

FBMC introduces filtering on a per-subcarrier basis；therefore，the lengths of the filter are comparatively long.To overcome this problem，filtered OFDM can be used.With filtered OFDM，filtering is introduced over the whole band.As a result，the filter bandwidth is much higher，and the filter length is much shorter than that in FBMC.For more flexibility and greater generalization，UFMC introduces filtering to subsets of the whole band instead of to a single subcarrier or the whole band. Modulation processing in UFMC can be simplified as

where B is the number of sub-bands，Kbis the number of subcarriers in the bth sub-band，andgk（b，n）is the impulse response of the corresponding kth filter in bth sub-band.

UFMC becomes filtered OFDM if filtering is introduced across the whole band（Kbis the unity）and becomes FBMC if filtering is introduced for a single subcarrier（B is the unity）. As a result，UFMC has the advantages of both FBMC and filtered OFDM but does not have any new drawbacks.On the other hand，extensive design trade-offs in terms of performance，complexity，latency and spectrum are needed in UFMC to determine the number of sub-bands and subcarriers in each subband.For example，if UFMC is applied when there is fragmented spectrum，B should be selected according to the number of available spectral sub-bands.Furthermore，B may even vary with time if some of the spectral sub-bands are only occasionally populated by other wireless services.There is an optimal combination of B andKbfor a given performance index，such as bit error rate（BER），packet error rate（PER），signal-to-interference noise ratio（SINR），or PAPR.Moreover，the number of subcarriers in one sub-band used in UFMC may be different from that in another sub-band.In other words，Kbin（4）could be a variable，which allows greater flexibility in designing a UFMC system.In addition，the single sub-band may be subdivided into smaller chunks of different sizes in every sub-band. This streamlines the overall system and enables more finegrain control of spectral characteristics at the cost of increased implementation complexity.

The design of the filter responsegk（b，n）is another important aspect of a UFMC system because side-lobe attenuation determines the reduction of OOB and filter length，both of which greatly contribute to implementation complexity.On the other hand，many well-designed filters，such as finite impulse response（FIR）filters（defined by Dolph-Chebyshev windows），could be used in UFMC to reach a good compromise between complexity and performance.

2.4 BFDM

BFDM changes the set of signals at the transmitter and receiver sides so that they are bi-orthogonal instead of orthogonal.This gives the time-frequency representations of these signals pairwise（not individual）orthogonality and enables greater flexibility in terms of side-lobe attenuation，filter response，and implementation complexity when designing a transmission prototype［9］.

An important reason for introducing BFDM in a 5G network is efficiently support machine-type-communication（MTC），characterized by a dramatic increase in sporadic traffic.Bulky 4G random-access procedures cannot handle such traffic［4］. Unlike LTE，where data is only carried using the physical uplink shared channel（PUSCH），BFDM-based schemes enable small user data packets to be transmitted through the available physical layer random-access channel（PRACH）.A new data section，called Data-PRACH，is introduced between synchronous PUSCH and PRACH to support efficient asynchronous data transmission and to significantly reduce signaling overhead.In the proposed Data-PRACH processing，a pulse sequence shapes the spectrum of the preamble signal by using of PRACH guard bands under acceptable interference.

Bi-orthogonality and relatively long PRACH symbols ensure the BFDM scheme is more robust than conventional OFDM to frequency offset and phase noises during transmission.In other words，the main advantage of BFDM over conventional OFDM is a better compromise on performance degradation caused bytime and frequency offset.However，the effect of frequency offset and phase noise on BFDM is still much higher than that on GFDM，F(xiàn)BMC，and UFMC.

All the other advantages of OFDM still remain in BFDM—ISI and multipath distortion are easily reduced by CP，BFDM is easy to implement because of FFT and IFFT processing. However，BFDM needs to handle long pulse tails，which reduces efficiency of bursty transmission.This efficiency is critical for low-latency and M2M applications.More importantly，the BFDM scheme discussed here cannot be easily integrated with massive MIMO unless modifications，such as generalization of the above concepts to UFMC or GFDM，are made［10］，［11］.

2.5 SCMA

Modulation processing involves changing the source binary sequences to a new binary sequence before being sent to the transmitter front-end.There are many ways to do the desired modulation processing.SCMA is，in effect，a modified version of multicarrier CDMA based on low-density signature（LDS），where mapped symbols，following forward error correction（FEC），are allocated according to a pre-designed low density spreading sequence.In this way，near maximum likelihood（ML）performance is achieved at the receiver side［5］，［12］.

Unlike the above two-step processing，SCMA merges the mapping of the bits that are coded by FEC into complex symbols with the spread of these mapped symbols.This results in one-step processing.In other words，SCMA directly maps the binary outputs of FEC to a complex code word that is in a multidimensional domain and should be selected from a predefined codebook called SCMA codebook.By generating multiple different codebooks that are predefined for different users or layers，SCMA supports multiple access.In fact，each user has a unique codebook in SCMA.Code words in the SCMA code books are sparse，so the iterative message-passing algorithm can still be used for near-optimal detection without significantly increasing the processing complexity.Any increase in such complexity can be compensated to some extent by the advantages（in terms of hardware implementation）resulting from one-step processing.

SCMA codebook based on multidimensional lattice constellation exploits shaping and coding gain，which helps SCMA increase spectral efficiency and makes link adaptation more reliable because of related interference averaging and management.Moreover，SCMA enables massive connectivity while having good features，such as overloaded signal superposition，low signaling overhead，low latency，and high flexibility in the link-adaptation mechanism［13］.

Designing SCMA codebooks for multiple users or layers is very complicated in terms of optimization and programming. Practical solutions are highly desirable and still being developed.One-step processing to map the binary sequences that are output from the FEC to code word could be considered as complex nonlinear mapping.This mapping could be performed by universal mapping neural networks，such as multilayer-perceptron（MLP）neural networks and radial-basis-function（RBF）neural networks［14］.Furthermore，the related global optimized learning rules in these mapping neural networks could be applied to the design of an SCMA codebook.

2.6 NOMA

In addition to the time and frequency domains（used in the modulation schemes previously mentioned）and the spatial domain（used in MIMO，beamforming，and OAM multiplexing），NOMA makes use of the power domain for modulation processing and multiplexing according to the power difference and loss between users.Specifically，NOMA superposes multiple users in the power domain and forms superposition coding，where users are separated by successive-interference cancellation（SIC）and available capacity-achieving channel codes，such as Turbo code and low-density parity check（LDPC）.A user with high channel gain is allocated less power，and a user with low channel gain is allocated more power［6］.In this way，all users with different channel gains have similarly high decoding probability and similarly large interference cancellation.This increases system capacity and coverage and supports mass connectivity.Moreover，NOMA promises robust performance in practical wide-area deployments despite mobility or channel-state information（CSI）feedback latency because user multiplexing in NOMA does not require fine feedback signaling from the user side，frequency selective channel quality indicator（CQI），or CSI.

The authors of［6］and other related publications have studied NOMA in terms of multiuser power allocation，signaling overhead，SIC error propagation，performance enhancement in high-mobility scenarios，and integration with MIMO and have shown that NOMA increases capacity and cell-edge throughput.The basis carrier waveforms in NOMA can still be generalized from OFDMA or FBMC，which means that NOMA retains the advantages of OFDMA and FBMC.

Table 1 shows a side-by-side comparison of the six algorithms discussed so far.From a standardization point of view，in -depth investigation and testing are required before any individual algorithm can be included in 5G specifications.It is perhaps more practical to develop one new algorithm that combines all the advantages of the six algorithms and minimizes the disadvantages.Moreover，crossover between and combination of FEC，modulation processing，and even source coding could be another direction towards achieving a better system.

Previous wireless standardization has occurred without enough consideration of hardware chips and real silicon（computing platforms and digital signal processors）.Thanks to great advancements in computing and processing technology，in particular system-on-chip（SoC）and reconfigurable processing technology，a fully software-defined modulator and waveform generator is even possible in 5G standards.A system with these technologies could support multiple algorithms or evenany algorithm，without any performance cost，by simply changing related software.In other words，the 5G standard only needs to define the related interfaces and control information and allow all other processing units，from FEC through modulation，to be open and software-programmable［15］，［16］.

▼Table 1.Six modulation algorithms

3 Spatial Signal Processing for 5G

Spatial-domain signal processing techniques such as MIMO，beamforming and antenna diversity have primarily been used in 4G and digital broadcasting systems.In 5G，these spatial signal processing techniques will be further improved，and related new algorithms，such as massive MIMO［17］-［19］and three-dimensional beamforming［20］-［22］，are being developed with an emphasis reaching a good compromise between processing complexity and performance.OAM-based spatial-processing techniques could be used improve a number of factors in 5G，such as capacity，efficiency and coverage［23］-［26］. Here，we discuss important practical aspects of these spatial signal processing techniques.

3.1 Massive MIMO

Strictly speaking，original MIMO is actually a kind of multichannel time-domain processing，where processing is mainly done in the baseband alone and not much in the spatial domain.However，in 4G，MIMO uses multiple antennas at both the transmitter side and receiver side in order to multiply the capacity of a radio link by exploiting multipath propagation. That is，4G MIMO exploits spatial-domain properties or，for example，spatial multiplexing，by allowing a base station to simultaneously serve multiple users who are using the same time-frequency resource.

Although the number of antennas is not strictly specified in current standards，four or eight antennas are most common. Massive MIMO expands on MIMO by dramatically increasing the number of antennas used at the base station（on the order of hundreds）.This suggests that the number of antennas is significantly higher than the number of users being simultaneously served in the same time-frequency block.Hundreds of antennas serving dozens of users simultaneously increase spectral efficiency five-to ten-fold，and many degrees of freedom become available to increase SINR through transmission signal shaping，interference nullification，and formation of desired directional patterns.

Channel estimation，signal detection，pre-coding，and pilot contamination reduction are the main aspects of signal processing in massive MIMO.Channel estimation involves estimating the coefficients（parameter matrix）of channels according to the available samples and optimization criterion，such as minimum mean-square error（MMSE）or least square（LS）.Signal detection in massive MIMO involves detecting the desired data streams from the samples，which are affected by interference and noise in the either passive or active form.Pre-coding could be considered for multiplying the original signal vector from all channels（antennas）at the transmitter side.In massive MIMO based on time-division duplexing（TDD），pilot sequences transmitted from users in the uplink become active interference sources and affect channel estimation processing.Eigenvalue-based filtering can be introduced to reduce the effect of pilot contamination.

Computation in massive MIMO mainly involves matrix multiplication，matrix inverse，eigenvalue decomposition（ED），or singular-value decomposition（SVD）.The key to implementing massive MIMO in 5G is ensuring that the implementation of these very large dimensional matrix computations in real silicon is effective in terms of power，price and performance.One promising architecture being developed is reconfigurable computing array.With this architecture，the matrix computations required in massive MIMO can be performed in a manner as good as that of ASIC，as flexible as FPGA/DSP，and as easy as C language because the architecture has homogeneous interfaces and heterogeneous processing units［15］，［16］.

3.2 3D Beamforming and Diversity

Beamforming is a major spatial signal processing technique where using multiple antennas are used to change the beam pattern and steer the beam in a specific direction so that SINR is increased.With diversity technology，multiple antennas are used at the receiver side，and spatial filtering is introduced to optimize reception in noisy and mobile environments.

Traditionally，beamforming is only designed for the horizontal plane and is thus called two-dimensional beamforming.The spatial-domain information and properties in the vertical plane are unused.3D beamforming，which encompasses both the elevation and azimuth planes，could open up more space to improve performance at the cost of increased processing complexity.In a 5G system，3D beamforming can increase user capaci-ty，coverage，and spectral and energy efficiency，and it can reduce inter-cell and inter-sector interference［20］-［23］.For example，different power levels can be allocated to the 3D beam patterns that serve the cell edge and cell center separately so that inter-cell interference is more effectively reduced.Both the vertical and horizontal beam patterns can be shaped and steered by adjusting the antenna tilt，the angle between the horizontal plane and boresight direction of the antenna.

At the receiver side，both the azimuth and elevation of arrivals can also be used，and additional degrees of freedom are available to improve the performance of antenna diversity.3D techniques can also provide more flexibility in the design and configuration of an antenna array.Planar，circular，spherical，cylindrical，uniform，non-uniform，and end-fire topologies can be used.Also，both the co-polarized and cross-polarized antenna elements can be included in the antenna array.

Beamforming and diversity processing mainly involves matrix（vector）multiplication units，filtering units，and IFFT/FFT units.These main processing units have linear properties；thus，changing the order of these processing units does not affect system performance but greatly reduces processing complexity.Fig.1 shows a post-FFT diversity scheme where M FFT operations need to be performed and N×M unknown coefficients need to be estimated.The number of antennas is given by M，and the length of the FFT is given by N.As in Fig.2，when the order changes，the number of unknown variables is given by N+M，which is a large reduction the N×M unknown variables in the original post-FFT scheme.Furthermore，only one FFT operation is needed when the order is changed instead of M FFT operations for the post-FFT scheme（Fig.1）. Using the cumulative and distributive properties of linear processing，the output is the same for these two schemes.

3.3 OAM

OAM-based spatial processing is a new tool for increasing capacity，spectral efficiency and scalability and decreasing channel interference in a 5G system.

The angular momentum carried in electromagnetic（EM）fields comprises spin angular momentum（SAM）and orbital angular momentum（OAM）.These describe the polarization state and phase structure distribution，respectively.An EM wave carrying OAM has a helical transverse phase structure exp（j?φ），where φ is the transverse azimuthal angle，and ? is an unbounded integer（the state number of OAM）.Each OAM beam at the same carrier frequency can carry an independent data stream；therefore，an OAM system can increase capacity and spectral efficiency by a factor equal to the values of state number ?.In addition，OAM beams with different ? values are mutually orthogonal，which implies low channel interference and crosstalk in transmitted and received data.Communicating over sub-channels given by OAM states is a subset of MIMO solutions；therefore，it does not provide any additional increase in system capacity if spatial multiplexing uses multiple spatially separated transmitter and receiver aperture pairs to transmit multiple data streams.In other words，multiplexed beams based on OAM should be completely coaxial throughout the transmission medium and use only one transmitter and receiver aperture（with certain minimum aperture sizes）to achieve OAM beam orthogonality and efficient de-multiplexing.

The benefits of OAM-based spatial multiplexing for wireless communication have been shown in millimeter-wave band，which 5G will encompass.However，there needs to be extensive R&D on OAM before OAM-based processing is included in 5G standards.A possible major use of OAM-based systems is to serve the link between wireless and optical channels.

4 Signal processing for Other Emerging 5G Techniques

▲Figure 1.A post-FFT diversity scheme.

▲Figure 2.Version of the post-FFT scheme with order changed.

In addition to advanced modulation algorithms and spatialprocessing，a number of other new techniques will be used in 5G.These techniques relate to system architecture，protocols，physical-layer（downlink and uplink），air-interface，cell acquisition，scheduling and rate adaption，access procedures，relaying，and spectrum allocation.The techniques include centimeter-and millimeter-wave，smart spectrum sharing and access，simultaneous transmission and reception（full-duplex），deviceto-device communication，advanced inter-node ordination，cloud radio access networking（C-RAN），software-defined networking，and digital radio frequency（RF）processing.Signal processing algorithms and implementations will be central to these emerging technologies，enabling them to make 5G a marketable reality.

Because of the much higher frequencies and wider bandwidths in millimeter-wave transmission，the physical propagation channels are more complicated，and advanced algorithms for channel modelling and estimation，signal detection，equalization，and error-correction coding are necessary.The main drawback of millimeter-wave is the high path loss，so new time-varying signal processing techniques，such as rapid beam adaptation，are necessary.In addition，millimeter-wave transmission only complements lower frequencies by providing high capacity and high data rates in dense urban areas instead of replacing lower frequencies，which should remain in the backbone to provide full wide-area coverage［27］.This implies a need for algorithms and implementations that support multiband and wideband.

Full-duplex mode enables simultaneous transmission and reception by sharing available resources between both directions of communication.In theory，this can double the link capacity.More importantly，full-duplex mode benefits the signaling and control layers because the uplink and downlink no longer need to be separated.Cancellation of the self-transmitted signal is the most important issue in full-duplex mode and needs to be done at all stages—from antenna，RF filtering，and digital front-end to baseband processing.The gain of the PA in full-duplex mode might be limited by the level of cancellation of the self-transmitted signal.In other words，a transceiver with a large PA gain becomes unstable in full-duplex mode if the self-transmitted signals are not sufficiently cancelled［28］.

5G systems not only need new and higher frequency bands；they also aim to use the available spectrum as efficiently as possible through spectrum sharing，which can be implemented by authorized shared access（ASA）and co-primary shared access.Signal processing algorithms for spectrum sensing are central to smart spectrum sharing and co-existence.Spectrum sensing involves monitoring other frequency channels that can be used by the primary channel and deciding whether users served in one channel can be switched to the other without interrupting the link.Signal processing related to spectrum sharing include weak-signal detection，signal classification，estimation of location and direction，channel aggregation，and interference cancelation［29］.

C-RAN is a promising architecture for expanding a wireless network.In C-RAN，the baseband processing unit（BBU）is moved from the base station（BS）to the control unit（CU），and the BS operates as the radio unit（RU）.Baseband signals are transferred between the CU and RU through front haul links in complex in-phase and quadrature（IQ）samples.Because of the high bit rate and large bandwidth of the transferred data，effective signal compression prior to transmission on the front haul link is desirable.The signal sampling can be reduced，but this can result in significant performance loss.Nonlinear quantization is the second-simplest solution，but it negatively affects related interfaces.IQ-data-based compression algorithms are being closely investigated and are categorized as point-to-point，multi-terminal，multivariate，and structured coding.These algorithms reach the best compromise between compression rate（efficiency），system complexity，interface compatibility，and implementation cost［30］.

Flexibility is one of the most important features of a 5G systems.Achieving the desired flexibility in a 5G system depends not only on advanced signal processing algorithms but also powerful hardware for processing.As mentioned in section 3，conventional processors，such as ASIC，F(xiàn)PGA and DSP，are not the best practical solution for 5G，and new kinds of processors that take into account the properties of new 5G signal processing algorithms are desirable.Also，new signal processing algorithms need to be designed with hardware architecture and programming model in mind—algorithm development should not be disconnected from hardware implementation.In addition，digital signal processing technologies for RF and frontend have advantages in terms of power efficiency，cost，time-tomarket，and SDR networking.These technologies support multiple bands，multiple standards，and multimode applications in 5G.RF signal processing techniques encompass digital predistortion；digital up-conversion；digital down-conversion；DC-offset calibration；PAPR，CFR；pulse-shaping；delay，gain，and imbalance compensation；noise shaping；numerical controlled oscillator（NCO）；full-duplex decoupling；and MIMO channel calibration［7］.

For more detailed algorithms and implementations of emerging 5G techniques，refer to the publications in the reference list.Excellent representatives include［31］and［32］，which describe full-dimensional MIMO；［33］，which describes 3D channel modeling；and［34］，［35］，which describe millimeter-wave systems.

5 Conclusion

This paper outlines and compares six promising modulation algorithms for 5G in terms of PAPR，OOB，processing and implementation complexity，spectral efficiency，CP requirement and related ISI/multipath distortion，orthogonality and related frequency offset and phase noise，synchronization in the time and frequency domains，latency，compatibility，and integrationwith other processing units.These six algorithms are GFDM，F(xiàn)BMC，UFMC，BFDM，SCMA and NOMA.Spatial signal processing techniques—i.e.，3D beamforming，massive MIMO，and OAM-based multiplexing—have been discussed from both an algorithm and hardware implementation point of view.This paper also briefly discussed signal processing for other emerging technologies in 5G，such as millimeter-wave，C-RAN，fullduplex access，smart spectrum sharing，and digital RF processing.To bring the desired 5G to market，huge effort needs to be put into R&D on algorithms and silicon implementation.

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［7］F.-L.Luo，Digital Front-End in Wireless Communications and Broadcasting:Circuits and Signal Processing，Cambridge，England:Cambridge University Press，Nov.2011.

［8］Z.Kollár and P.Horváth，“PAPR reduction of FBMC by clipping and its iterative compensation，”Journal of Computer Networks and Communications，vol. 2012，article ID 382736.

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［13］M.Taherzadeh，H.Nikopour，A.Bayesteh，and H.Baligh，“SCMA codebook design，”in Proc.IEEE 80th Vehicular Technology Conference，Vancouver，Canada，Sept.2014.

［14］F.-L.Luo and R.Unbehauen，Applied Neural Networks for Signal Processing，Cambridge，England:Cambridge University Press，1997.

［15］F.-L.Luo，Mobile Multimedia Broadcasting Standards:Technology and Practice，Berlin，Germany:Spring Verlag，2008.

［16］F.-L.Luo，W.Williams，M.R.Rao，et al.，“Trends in signal processing applications and industry technology，”IEEE Signal Processing Magazine，vol.29，no.1，pp.174-184，Jan.2012.doi:10.1109/MSP.2011.943129.

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［30］S.-H.Park，O.Simeone，O.Sahin，and S.Shamai，“Fronthaul compression for cloud radio access networks:signal processing advances inspired by network information theory，”IEEE Signal Processing Magazine，vol.31，no.1，pp.69-79，Nov.2014.doi:10.1109/MSP.2014.2330031.

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［33］B.Monday，T.Thomas，E.Visotsky，et al.，“3D Channel Model in 3GPP”，IEEE Communications Magazine，2015（to appear）.

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Manuscript received:2014-08-08

Biographyraphy

Fa-Long Luo（f.luo@ieee.org）is chief scientist at Element CXI，California.He was the founding editor-in-chief of International Journal of Digital Multimedia Broadcasting.He was also the chairman of the IEEE Industry DSP Standing Committee and technical board member of IEEE SPS from 2011 to 2012.He is an elected fellow of the IET.He has been an associate editor of a number of IEEE periodicals，including IEEE SP Magazine and IEEE IoT Journal.He has received many international recognitions in related fields and has published four books，more than 100 technical papers，and 18 patents.