WO2018196996A1

WO2018196996A1 - Single carrier like transceiver which mainatins null subcarriers

Info

Publication number: WO2018196996A1
Application number: PCT/EP2017/060191
Authority: WO
Inventors: Traian ABRUDAN; Stepan Kucera; Holger Claussen
Original assignee: Nokia Technologies Oy
Current assignee: Nokia Technologies Oy
Priority date: 2017-04-28
Filing date: 2017-04-28
Publication date: 2018-11-01
Anticipated expiration: 2019-10-28

Abstract

Processing circuitry, methods and computer program products are disclosed. Processing circuitry for processing a multicarrier data signal prior to transmitting the signal as a communication signal, comprises: an input for receiving the multicarrier data signal; mapping circuitry operable to map the multicarrier data signal to a set of active subcarriers and to add nulls corresponding to a set of inactive subcarriers to generate a mapped multicarrier data signal; and transforming circuitry operable to generate a transformed mapped multicarrier data signal by applying a linear precoder matrix to maintain the nulls corresponding to the inactive subcarriers and encode the active subcarriers as orthogonal frequency-division multiplexed subcarriers. In this way, both a precoded or mapped and orthogonally-modulated signal is provided using a linear operation, which significantly reduces the processing required to produce the transformed mapped multicarrier data signal for subsequent use as a communication signal.

Description

SINGLE CARRIER LIKE TRANSCEIVER WHICH MAINATINS NULL SUBCARRIERS

FIELD OF THE INVENTION

The invention relates to processing of multiple carrier communication signals for wired or wireless transmission.

BACKGROUND

Wired and wireless communication is known. Emerging wireless systems suggest employing visible-light communications (VLC) for transmitting data signals. In such systems the intensity of light sources, such as building lighting, is modulated to transmit the signals and this can currently achieve data rates of the order of Gigabits per second. In particular, VLC enables ubiquitous Gigabit per second per square meter wireless data transmission by modulating the intensity of a light source. Like in most existing and future wireless communication standards (e.g. 4G, 5G), Orthogonal

Frequency Division Multiplexing (OFDM) has been the most promising modulation for VLC as well, due to its high spectral efficiency and unbeatable multipath resilience. However, the high Peak-to-Average Power Ratio (PAPR) of the OFDM signal poses serious constraints on the VLC optical front-end design, and these are even stricter than in radio frequency (RF) communications. Similar problems exist in wired communication systems, such as copper access schemes.

Light sources, typically light emission diodes (LEDs) or laser diodes, exhibit very high nonlinearities which limit the signal dynamic range to a small quasi-linear region. The dynamic range is further reduced if ambient light dimming is required. In addition, VLC poses some specific constraints on the modulated signal, which are not characteristic to RF-based communications. Since light intensity carries no phase information, the modulated signal is constrained to be real-valued and positive.

Moreover, due to the time-varying ambient light conditions, or imperfect electronics, the VLC signal is subject to slow baseline fluctuations, known as DC-wander effects.

Hence, the OFDM subcarrier(s) in the middle of the spectrum cannot carry information (i.e., they are null subcarriers). Also, in order to be able to deliver high data rates the computational complexity of the modulation/demodulation must be low. It would be desirable to provide a practical implementation which provides for one or more of a low- PAPR precoded OFDM transmission which enables on-demand subcarrier nulling for resilience against DC-wander effects; multi-user access; and low computational complexity to make it particularly suitable for very high throughput systems.

SUMMARY

According to a first aspect, there is provided processing circuitry for processing a multicarrier data signal prior to transmitting the signal , the processing circuitry comprising: an input for receiving the multicarrier data signal; mapping circuitry operable to map the multicarrier data signal to a set of active subcarriers and to add nulls corresponding to a set of inactive subcarriers to generate a mapped multicarrier data signal; and transforming circuitry operable to generate a transformed mapped multicarrier data signal by applying a linear precoder matrix to maintain the nulls corresponding to the inactive subcarriers and encode the active subcarriers as orthogonal frequency-division multiplexed subcarriers. The first aspect recognises that existing wired and wireless modulation schemes either exhibit relatively high PAPR, and/or require computationally expensive

modulation/demodulation. A basic DC-biased Offset OFDM (DCO-OFDM) scheme [1] requires a bias voltage value optimization in order to ensure sufficient signal dynamic range and minimize signal clipping, but suffers from high PAPR. Other modulations such as Asymmetrically Clipped Optical OFDM (ACO-OFDM) [2] and Unipolar-OFDM (U-OFDM) [5] have been proposed to overcome the high PAPR. However, the throughput is decreased by half compared to DCO-OFDM. This is because ACO-OFDM only modulates half of the subcarriers, whereas U-OFDM doubles the symbol time duration while maintaining the same amount of data. Carrier-less Amplitude

Modulation method (CAP) [3] achieves lower PAPR than multicarrier modulation. However, CAP does not benefit from the great advantage of OFDM in dealing with multipath (single-tap equalization), and require a very complex equalizer. Single carrier (SC) modulation has also been proposed in order to achieve low PAPR.

However, SC is subject to severe DC-wander effects, which makes it unusable with amplitude modulation, unless up/down-conversion is employed [3], which further increases the transceiver complexity. Enhanced Unipolar OFDM (eU-OFDM) [6] and Enhanced Asymmetrically Clipped Optical OFDM (eACO-OFDM) [7] have been recently introduced to compensate for the spectral efficiency loss of ACO-OFDM and U- OFDM by superimposing multiple data streams. However, full rate is only

asymptotically achieved, for an infinite number of superimposed streams. In addition, a successive interference cancellation is used to recover the original streams. Decoding is very complex since it requires re-encoding and subtraction of the decoded streams. No improvement in terms of PAPR over ACO-OFDM and U-OFDM is achieved, only a partial compensation of the 50% throughput loss.

Accordingly processing circuitry or logic is provided. The processing circuitry may be operable to process or operate on a multicarrier data signal. Such processing may occur prior to or before transmitting the signal as a wired or wireless communication signal. In other words, the processing may prepare the signal for subsequent transmission as a wired or wireless signal. It will be appreciated that further processing may be required to produce a transmittable communication signal. The processing circuitry may comprise an input which may receive the multicarrier data signal. The processing circuitry may comprise mapping circuitry or logic. The mapping circuitry may be operable to generate a mapped multicarrier data signal by mapping or allocating the multicarrier data signal to a set or group of active subcarriers from a total group of available subcarriers and by adding nulls to a set or group of inactive subcarriers from the total group of available subcarriers. The processing circuitry may comprise transforming circuitry or logic. The transforming circuitry may generate a transformed mapped multicarrier data signal by applying a linear precoder matrix to the mapped multicarrier data signal. The linear precoder matrix may maintain or preserve the nulls corresponding to the inactive subcarriers in the transformed mapped multicarrier data signal. The linear precoder matrix may encode the active subcarriers as orthogonal frequency-division multiplexed subcarriers in the transformed mapped multicarrier data signal. In this way, both a precoded or mapped and orthogonally- modulated signal is provided using a linear operation, which significantly reduces the processing required to produce the transformed mapped multicarrier data signal for subsequent use as a communication signal.

In one embodiment, the multicarrier data signal comprises an N subcarrier data signal, the set of active subcarriers comprises M active subcarriers and the set of inactive subcarriers comprise Z inactive subcarriers. In other words, a total set of N subcarriers are available, M of which are set to be used as active or operational subcarriers and Z of which are null or inactive subcarriers (N = M + Z). Typically, Z << M.

In one embodiment, the mapping circuitry is operable to map real-valued data of the multicarrier data signal to M active subcarriers. Typically, such mapping maps the real-valued data to vectors for subsequent processing. In one embodiment, the linear precoder matrix comprises a composite precoding- modulation matrix having an identity matrix summed with a subcarrier nulling matrix. It is recognised that a direct-implementation precoder matrix is close (in Frobenius norm) to an IFFT (modulation) matrix. Therefore, a composite precoding-modulation matrix, which comprises the multiplication of an IFFT with the direct-implementation precoder matrix approximates an identity matrix.

In one embodiment, the composite precoding-modulation matrix is unitary. In one embodiment, the composite precoding-modulation matrix has most eigenvalues equal to one.

In one embodiment, the composite precoding-modulation matrix is real-valued. In one embodiment, the subcarrier nulling matrix is lower-ranked than the composite precoding-modulation matrix.

In one embodiment, the subcarrier nulling matrix has a rank of 2Z. In one embodiment, the identity matrix is an N x N identity matrix.

In one embodiment, the subcarrier nulling matrix comprises a matrix singular value decomposition. In one embodiment, the transforming circuitry is operable to generate the transformed mapped data signal using 2NZ scalar operations. Hence, it can be seen that the transforming circuitry performs a linear operation to obtain the transformed mapped multicarrier data signal, which is computationally-simpler than the direct

implementation scheme.

In one embodiment, the mapping circuitry is operable to map the multicarrier data signal to one of a plurality of sets of active subcarriers and to add nulls corresponding to an associated set of inactive subcarriers to generate the mapped multicarrier data signal and the transforming circuitry is operable to generate the transformed mapped multicarrier data signal by applying one of a corresponding plurality of linear precoder matrices to maintain the nulls corresponding to the inactive subcarriers and encode the active subcarriers as orthogonal frequency-division multiplexed subcarriers. Hence, different linear precoding matrices may be provided, each linear precoding matrix being configured to map different sets of active/inactive subcarriers. This enables dynamic mapping of active/inactive subcarriers to be performed based on user demand.

According to a second aspect, there is provided a method of processing a multicarrier data signal prior to transmitting the signal, the method comprising: receiving the multicarrier data signal; mapping the multicarrier data signal to a set of active subcarriers and adding nulls corresponding to a set of inactive subcarriers to generate a mapped multicarrier data signal; and generating a transformed mapped multicarrier data signal by applying a linear precoder matrix to maintain the nulls corresponding to the inactive subcarriers and encode the active subcarriers as orthogonal frequency- division multiplexed subcarriers.

In one embodiment, the multicarrier data signal comprises an N subcarrier data signal, the set of active subcarriers comprises M active subcarriers and the set of inactive subcarriers comprise Z inactive subcarriers.

In one embodiment, the mapping comprises mapping real-valued data of the multicarrier data signal to M active subcarriers.

In one embodiment, the linear precoder matrix comprises a composite precoding- modulation matrix having an identity matrix summed with a subcarrier nulling matrix.

In one embodiment, the composite precoding-modulation matrix is unitary.

In one embodiment, the composite precoding-modulation matrix has most eigenvalues equal to one.

In one embodiment, the composite precoding-modulation matrix is real-valued.

In one embodiment, the subcarrier nulling matrix is lower-ranked than the composite precoding-modulation matrix.

In one embodiment, the subcarrier nulling matrix has a rank of 2Z. In one embodiment, the identity matrix is an N x N identity matrix. In one embodiment, the subcarrier nulling matrix comprises a matrix singular value decomposition.

In one embodiment, the generating comprises generating the transformed mapped data signal using 2NZ scalar operations.

In one embodiment, the mapping comprises mapping the multicarrier data signal to one of a plurality of sets of active subcarriers and adding nulls corresponding to an associated set of inactive subcarriers to generate the mapped multicarrier data signal and the generating comprises generating the transformed mapped multicarrier data signal by applying one of a corresponding plurality of linear precoder matrices to maintain the nulls corresponding to the inactive subcarriers and encode the active subcarriers as orthogonal frequency-division multiplexed subcarriers. According to a third aspect, there is provided processing circuitry for processing a multi-carrier orthogonal frequency-division multiplexed communication signal to generate a multicarrier data signal, the multi-carrier orthogonal frequency-division multiplexed communication having low amplitude portions corresponding to inactive subcarriers, the processing circuitry comprising: an input for receiving the multi- carrier orthogonal frequency-division multiplexed communication signal; equalisation circuitry operable to perform frequency-domain equalisation on the multi-carrier orthogonal frequency-division multiplexed communication signal; and transforming circuitry operable to generate the multicarrier data signal by applying a linear decoder matrix to maintain the nulls corresponding to the inactive subcarriers and decode the active subcarriers.

In one embodiment, the linear decoder matrix comprises a composite demodulation- decoding matrix having an identity matrix summed with a subcarrier nulling matrix.

In one embodiment, the composite demodulation-decoding matrix is unitary.

In one embodiment, the composite demodulation-decoding matrix has most eigenvalues equal to one. In one embodiment, the composite demodulation-decoding matrix is real-valued.

In one embodiment, the subcarrier nulling matrix is lower-ranked than the composite demodulation-decoding matrix.

In one embodiment, the subcarrier nulling matrix has a rank of 2Z.

In one embodiment, the identity matrix is an N x N identity matrix. In one embodiment, the subcarrier nulling matrix comprises a matrix singular value decomposition.

In one embodiment, the transforming circuitry is operable to generate the multicarrier data signal using 2NZ scalar operations.

In one embodiment, the composite demodulation-decoding matrix is a transpose of the composite precoding-modulation matrix of the first aspect and embodiments.

In one embodiment, the equalisation circuitry is operable to perform single-tap frequency-domain equalisation.

In one embodiment, the equalisation circuitry comprises an FFT matrix, a diagonal matrix and an IFFT matrix. In one embodiment, the diagonal matrix comprises an inverse of an estimated flat- channel frequency response of each active subcarrier along its diagonal, with zeros elsewhere.

In one embodiment, the transforming circuitry is operable to generate the multicarrier data signal by applying one of a corresponding plurality of linear decoder matrices to maintain the nulls corresponding to the inactive subcarriers and decode the active subcarriers.

According to a fourth aspect, there is provided a method of processing a multi-carrier orthogonal frequency-division multiplexed communication signal to generate a multicarrier data signal, the method comprising: receiving the multi-carrier orthogonal frequency-division multiplexed communication signal; performing frequency-domain equalisation on the multi-carrier orthogonal frequency-division multiplexed communication signal; and generating the multicarrier data signal by applying a linear decoder matrix to maintain the nulls corresponding to the inactive subcarriers and decode the active subcarriers.

In one embodiment, the multicarrier data signal comprises an N subcarrier data signal, the set of active subcarriers comprises M active subcarriers and the set of inactive subcarriers comprise Z inactive subcarriers. In one embodiment, the linear decoder matrix comprises a composite demodulation- decoding matrix having an identity matrix summed with a subcarrier nulling matrix.

In one embodiment, the composite demodulation-decoding matrix is unitary. In one embodiment, the composite demodulation-decoding matrix has most eigenvalues equal to one.

In one embodiment, the composite demodulation-decoding matrix is real-valued. In one embodiment, the subcarrier nulling matrix is lower-ranked than the composite demodulation-decoding matrix.

In one embodiment, the subcarrier nulling matrix comprises a matrix singular value decomposition. In one embodiment, the generating comprises generating the multicarrier data signal using 2NZ scalar operations.

In one embodiment, the frequency-domain equalisation comprises single-tap frequency-domain equalisation. In one embodiment, the frequency-domain equalisation is performed by equalisation circuitry comprises an FFT matrix, a diagonal matrix and an IFFT matrix.

In one embodiment, the diagonal matrix comprises an inverse of an estimated flat- channel frequency response of each active subcarrier along its diagonal, with zeros elsewhere.

In one embodiment, the generating comprises generating the multicarrier data signal by applying one of a corresponding plurality of linear decoder matrices to maintain the nulls corresponding to the inactive subcarriers and decode the active subcarriers.

According to a fifth aspect, there is provided a computer program product operable, when executed on a computer, to perform the method of the second or fourth aspects. Further particular and preferred aspects are set out in the accompanying independent and dependent claims. Features of the dependent claims may be combined with features of the independent claims as appropriate, and in combinations other than those explicitly set out in the claims. Where an apparatus feature is described as being operable to provide a function, it will be appreciated that this includes an apparatus feature which provides that function or which is adapted or configured to provide that function.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will now be described further, with reference to the accompanying drawings, in which:

Figure 1 illustrates a transmitter according to one embodiment;

Figure 2 illustrates a receiver according to one embodiment;

Figure 3 illustrates offline and online processing for generating sets of

encoding/ decoding matrices;

Figure 4 illustrates the transmitter of Figure 1 in more detail;

Figure 5 illustrates the receiver of Figure 2 in more detail;

Figure 6 compares the Complementary Cumulative Distribution Function (CCDF) of the PAPR of embodiments with respect to two other relevant schemes;

Figure 7 is a histogram of the oversampled time-domain waveform corresponding to the precoded OFDM signal of embodiments for a 16-QAM input constellation; Figure 8 illustrates an amplitude spectrum of the precoded OFDM signal of

embodiments;

Figure 9 is a flow chart illustrating the main steps performed by the transmitter of Figure 1; and

Figure 10 is a flow chart illustrating the main steps performed by the receiver of Figure 2.

DESCRIPTION OF THE EMBODIMENTS

Before discussing the embodiments in any more detail, first an overview will be provided. Embodiments provide a computationally-simplified encoder and decoder arrangement for use in wired and wireless communications. The encoder of embodiments recognises that the properties of matrices that would be required for a direct implementation of a precoding a subcarrier nulling operation followed by an orthogonal modulation operation are such that these two operations can be combined into a computationally-simplified single operation by applying a nulling matrix, which can be represented by a singular value decomposition. Likewise, the decoder of embodiments recognises that the properties of matrices that would be required for a direct implementation of demodulation and decoding are such that these two operations can be combined into a computationally-simplified single operation by applying a nulling matrix, which can be represented by a singular value decomposition. That nulling matrix may be the transpose of the nulling matrix of the encoder. This provides for significantly fewer computation operations in encoding and decoding compared to a direct implementation approach. Embodiments seek to achieve simultaneously the following four goals in the transceiver design:

• Very low computational complexity (better or similar to the standard OFDM transceivers)

• Ultra-low PAPR level (comparable to the level of single-carrier modulation) · Full throughput (source payload data delivery across the entire frequency band)

• Total control over null subcarrier locations (for DC subcarrier nulling as well as multi-user frequency domain multiplexing). Although the embodiments described below relate to visible light communications, it will be appreciated that with appropriate adaptation of the front-end, this approach may also be used for other types of optical communication (e.g. infrared links and optical fibre), as well as for other types of communication over the air (using radio frequency), or through wires, such as copper access schemes.

Transmitter - General Design

As shown in Figure l, in embodiments, the OFDM transmitter chain 5 uses a precoding module 10 that replaces an Inverse Fourier Transform (IFFT) operation that would normally be provided in a conventional transmitter chain with a specially designed linear precoder. As a result, the corresponding precoding matrix within the OFDM precoder is close to an identity matrix, and therefore, the PAPR level of the pulse- shaped output signal approaches the PAPR level of a SC signal. However, unlike SC modulation, which suffers from severe DC-wander effects, embodiments allow for deep nulling of arbitrary subcarriers, including the middle subcarrier corresponding to the DC component. Nulling is ensured by the subcarrier nulling shown in Figure 1. Since the precoding matrix is very close to an identity matrix, it may be implemented in a computationally-efficient manner by using low-rank matrix decompositions.

Receiver - General Design

As shown in Figure 2, in embodiments, the OFDM receiver chain 15 uses a decoding module 20 preceded by both FFT (Fast Fourier Transform) and IFFT that are necessary to perform low-complexity single-tap frequency-domain equalization. In particular, an IFFT operation that would normally be performed by a conventional OFDM transceiver is moved from the transmitter to the receiver and, therefore, the overall transceiver complexity is similar to the classical OFDM transceiver. Consequently, the complexity is not proportional to the squared number of subcarriers, as is typically the case of full- rank precoding matrices, but it is actually comparable to the FFT and IFFT operations which are present in standard multi-carrier transceivers.

Embodiments perform transmitter precoding and modulation jointly and based on a specially designed precoding and modulation matrix. The precoding and modulation matrix stems from the FFT matrix, which is modified by nulling out some contiguous regions, while still retaining its unitary property. The purpose of this modification is to obtain a quasi-single carrier modulation whose PAPR is comparable to single carrier modulation. However, unlike single carrier modulation, embodiments possess the capability to null out any parts of the signal spectrum in order to avoid the severe DC- wander effects that VLC is subject to, and/or to enable orthogonal frequency division multiplexing access. Precoding takes place before the IFFT operation at transmission, hence, the resulting precoding-modulation matrix is the product between IFFT matrix and the modified FFT matrix. The result is nearly an identity matrix, which may be implemented in a computationally very efficient manner. The receiver is then designed to inverse this process.

More specifically, the precoding-modulation matrix exhibits the following key properties:

1) It is a real orthogonal matrix to ensure that

a) a real -valued input produces a real-valued output (as required in VLC), hence processing requires real-valued operations only instead of complex valued operations, b) the noise covariance is preserved, i.e., no noise colouring takes place at the receiver,

c) the demodulation-decoding matrix is simply the transpose of the precoding- modulation matrix.

2) It is nearly an identity matrix to ensure that

a) the PAPR level of the output signal is almost equal to the PAPR of the input signal (it is a quasi-single-carrier modulation) while permitting on-demand spectral blanking (unlike SC).

3) Most of its eigenvalues are equal to one to ensure that

a) subtracting the identity matrix from it produces a low-rank matrix which can be very efficiently and stably implemented by using low-rank singular value

decomposition (SVD).

4) The multiple SVD matrices may be precomputed offline and proactively stored to ensure that

a) different spectral mask requirements, such as DC subcarrier nulling, and multiuser frequency domain multiplexing can be easily implemented.

Figure 3 illustrates in more detail both phases of offline and online processing that take place in the VLC transceiver of embodiments. Embodiments can operate with various subcarrier nulling profiles, as required by the application. DC (and possibly its neighbouring subcarriers) is always nulled out in order to avoid DC- wander effects. In addition, multi-user access may be ensured by using predefined subcarrier nulling profiles for each user. The precoding-modulation matrices are precomputed offline. Their singular value decompositions (SVDs) are stored in order to enable computationally-simple implementation. In the online phase, precoding matrices can be dynamically selected according to the multi-user requirements, in order to assign the subcarrier domain resources. A control channel may be used to assign the subcarriers to different users. No re-computations of the precoding-modulation and demodulation-decoding matrices are required in the online operation phase, as matrices are precomputed and stored.

Transmitter Architecture

Figure 4 illustrates a more detailed block diagram of the transmission chain 5 containing the OFDM precoder according to one embodiment. We assume a multicarrier transmission with N subcarriers of which M subcarriers are active. Hence, there are Z = N - M null subcarriers. The input serial bit stream is received at an input 40 and is mapped to a vector x containing M/2 parallel, complex-valued constellation symbols whose real and imaginary parts undergo precoding. The matrix B in a mapping unit 30 maps the M real-valued data to the M active subcarriers. The module 10 performs the precoding and OFDM modulation. Its internal structure is described in more detail below. After the cyclic prefix (CP) addition, the precoded OFDM symbols are converted to a serial data stream, which is then up-sampled, pulse-shaped, and converted to an analogue waveform for the optical front-end. Then, DC biasing, pre-equalization and amplification are performed before the signal is converted to visible light.

The idea of this invention is that the IFFT operation in the traditional OFDM

transmitter chain is combined together with the proposed precoder in order to obtain a nearly identity precoding matrix, thus reducing the PAPR and, at the same time, achieving very efficient implementation complexity. On the transmitter side, no FFT/IFFT operations are required (IFFT operation is moved on the RX side). In brief, the proposed precoded transmission is a modified SC transmission that allows subcarrier nulling.

Precoding matrix

The matrix stems from the FFT matrix, which is modified in order to preserve the locations of the null subcarriers. Let m be an JV x 1 binary vector whose entries define the active/null subcarrier pattern as follows: m₌ f 1, if fc e A

m^fe 0, otherwise where A denotes the indices of the active subcarriers.

Let us further define the N x N power-normalized IFFT matrix whose ⁿ) entries are given by:

„ 1 2wk \

{Fk„ = -_7-= exp ( _{+ J}— )

where 3 = v - « is the imaginary unit, *— ^"i> · -^■ > ^{~~ 1} is the frequency-domain index, and n = 0, . . . , N - 1 is the time-domain index.

The precoding matrix is given by:

W = UV^H where U and V are the left and right singular vectors of the matrix:

F^H © [mm^T + (1_N - m)(ljv - m)^T] where I is an JV x l vector of ones, (")^T denotes the matrix transpose, (")^H denotes the Hermitian matrix transpose, and Θ denotes the Hadamard (elementwise) matrix product. The matrix above is essentially a modified IFFT matrix F^H such that the locations of the null subcarriers defined by the vector m are preserved. In addition, since singular vectors are unitary matrices, the resulting precoding matrix W is also unitary. The direct implementation of the precoder would exhibit a complexity of order N², i.e. squared in the number of subcarriers, which for large N, is higher compared to the complexity N ^IOS2 ^N of the radix-2 FFT/IFFT operations in the conventional OFDM transceiver. Apart from that, an additional IFFT operation would still be required. For this reason, the precoding matrix W should not be used separately. In order to circumvent this complexity issue, we exploit the fact that W is close (in

Frobenius norm) to the IFFT matrix. Therefore, the composite precoding-modulation matrix P which consists of the multiplication of IFFT F and the precoding matrix W, defined as:

P = FW is close to the N x N identity matrix IJV. The composite precoding-modulation matrix P has the following three key properties:

1. It is unitary, i.e., P^HP = IJV, being a product of two unitary matrices;

2. Most of its eigenvalues are equal to one, due to its nearness to identity matrix IJV; and

3. It is real-valued, since IFFT is applied to W, whose columns exhibit Hermitian symmetry.

These three properties are exploited in order to achieve a computationally- efficient implementation solution based on Singular Value Decomposition (SVD). We define the matrix:

E = P - l_N

Due to property 3 above, E exhibits a low-rank r = 2Z. Its compact (rank-r) SVD is given by:

E = U_rS_rVi¹

Therefore, the efficient implementation of the composite precoding-modulation matrix P is as follows:

P = I* + U_r∑_rVj^]

Numerical implementation issues - Transmission

In limited precision environments, the columns of the precoding matrix W may not exhibit exact Hermitian symmetry. Therefore, the pre-multiplication by IFFT matrix F^H does not produce an exactly real-valued composite precoding-modulation matrix P. This would ultimately produce a tiny imaginary component in the output signal. In order to ensure that P is purely real-valued, let

be the SVD of the real part of the full-rank matrix FW. In this way, all operations are carried out in the real Euclidean space. The composite precoding-modulation matrix P is then obtained as: Then, the SVD E— U_{r r}V ₀f the new low-rank matrix E = P— I_N is used to implement the precoder as:

P - I* + u_r∑.v:^1-

It can be seen that the composite precoding-modulation matrix P is expressed as the N x N identity matrix IJV plus the SVD of low-rank matrix E. In other words, the output signal consists of the original single-carrier signal plus a subcarrier-nulling signal that ensures the desired null subcarrier pattern defined by vector m. The subcarrier nulling signal is obtained by multiplying the original single carrier signal by matrix E (written in SVD form), which is the subcarrier nulling matrix. It is important to mention that P is a real-valued orthogonal matrix, i.e., P ' P = IJV, and therefore, decoding is trivial, the symbol recovery is achieved via multiplication by its transpose P^T.

The subcarrier nulling matrix E exhibits low rank r = 2Z. Thus, precoding only requires 2NZ scalar real-valued multiplications/ additions. In general, ^2Z < ^lo82 ^N, thus the precoding-modulation operation of embodiments is computationally-simpler than radix-2 FFT/IFFT operations used in conventional OFDM transceivers, which amount for Nlog₂ N In most practical OFDM-based VLC transceivers, the middle subcarrier, as well as the subcarrier at the lower edge of the band are unmodulated (null). The middle subcarrier is null to ensure a stable DC bias for the VLC transmission (i.e. avoid DC-wander effects), whereas the first subcarrier must be null to ensure even FFT size (usually a power of 2). Hence, Z = 2 and the number of operations required by the precoding- modulation would only be AN, i.e., linear complexity in number of subcarriers. In terms of required memory, the N x 2Z real-valued matrix multiplication result U_r∑_r and the N x 2Z real-valued matrix V_R need to be stored. If Z = 2, this only amounts to SN real- valued numbers. The overall signal-processing along the horizontal part of the transmission chain in Figure 4 may be described by the following simple matrix equation which expresses the time-domain precoded OFDM samples as follows:

Re{x}

s = T [½ + (u_r∑_r)v;F] B

v > Im{x}

P where B is an N x M matrix that maps the real and imaginary parts of the complex- valued vector x to the active subcarriers before precoding. The subcarrier mapping matrix B consists of M columns of ΙΛΓ whose indices belong to the set of active subcarriers indices A. Matrix T is the (N +^■£>) x N CP addition matrix which is formed by last L rows of IJV followed by all the rows of IJV itself.

Receiver Architecture

Figure 5 illustrates the receiver block scheme according to one embodiment. The analogue waveform received at an input 50 and from the VLC channel via the optical front-end is digitized and pulse-shaped. Then, after OFDM symbol timing recovery, the serial sequence is down-sampled and converted to vectors y of length N + L. CP is discarded by multiplying the signal vector y by an N x (N + L) matrix R which comprises the last N rows of the {N + L) x (N + L) identity matrix ~*N+L. Then the FFT operation is required in order to perform the single-tap frequency-domain equalization. An equalizer 60 implements the single-tap equalizer which is represented by an N x N diagonal matrix D which contains the inverse of the estimated flat-channel frequency response of each active subcarrier along its diagonal, and zeros in rest. The real-valued orthogonal decoder (which jointly performs the OFDM demodulation and undoes the precoding operation) is represented by the N x N matrix P^T. Again, in order to achieve ultra-low implementation complexity, the demodulation and decoding is achieved by using its SVD representation:

P = IJV + V_r∑_ru^p

> v '

Then, the estimated real and imaginary parts x of the constellation symbols

corresponding to the active subcarriers are obtained, followed by serialization, symbol decision and extraction of data bits.

Numerical implementation issues - Reception On the receiver side, both FFT and IFFT are required in order to perform the trivial single-tap frequency-domain equalization. This is a way to avoid the multiplication by the decoding matrix W^H alone, whose complexity would be of order N². Instead of multiplying by W^H, the equivalent multiplication by P^TP is used, whose complexity is much lower, i.e., N ^loS2 N + 2NZ (demodulation-decoding exhibits lower complexity than FFT, i.e., 2NZ). Single-tap channel estimation and equalization require M operations each, because they are only applied to active subcarriers. Thus, the benefits of trivial channel estimation and equalization fully justify the use of one extra-FFT on the receiver side. This difference becomes less significant if radix-4 FFT is used. In conclusion, the overall computational complexity of the proposed receiver that includes single-tap channel estimation, frequency-domain channel equalization, OFDM demodulation and symbol decoding is of order of ²N ^Io¾ ^N + 2NZ + 2M scalar operations (assuming radix-2 FFT), very similar to the conventional OFDM. The amount of memory required at the receiver is the same as for the transmitter.

The overall signal processing on the horizontal part of the RX chain is described by the following simple matrix equation: FDF^HRy

Figure 9 is a flow chart illustrating the main steps performed by the transmitter. At step Si, the multicarrier data signal is received. As step S2, the transmitter performs mapping of the multicarrier data signal to a set of active subcarriers and adds nulls corresponding to a set of inactive subcarriers to generate a mapped multicarrier data signal. At step S3, the transmitter generates a transformed mapped multicarrier data signal by applying a linear precoder matrix to maintain the nulls corresponding to the inactive subcarriers and encode the active subcarriers as orthogonal frequency-division multiplexed subcarriers. Figure 10 is a flow chart illustrating the main steps performed by the receiver. At step S4, the receiver receives the multi-carrier orthogonal frequency-division multiplexed communication signal. At step S5, the receiver performs frequency-domain

equalisation on the multi-carrier orthogonal frequency-division multiplexed communication signal. At step S6, the receiver generates the multicarrier data signal by applying a linear decoder matrix to maintain the nulls corresponding to the inactive subcarriers and decode the active subcarriers. Table l illustrates a computational complexity comparison between the precoded OFDM transceiver of embodiments and a conventional OFDM transceiver.

Table 1

Table 2 provides a qualitative comparison of the existing modulation schemes with respect to embodiments in terms of PAPR level, achieved throughput, spectrum blanking capabilities and computational complexity.

Transmission PAPR level Throughput Spectrum Implementation Scheme justification justification blanking complexity

capability justification

DCO-OFDM HIGHEST 100% YES LOWEST

[1] bipolar No redundancy (FFT/IFFT and

OFDM single-tap

equalization)

ACO-OFDM MEDIUM 50% YES LOW

[2] unipolar only modulates (FFT/IFFT and

OFDM odd subcarriers single-tap

equalization)

CAP [3] LOW 100% NO HIGH

not No redundancy (complex time- multicarrier domain

equalization)

SC [3] LOWEST 100% NO HIGH

single-carrier No redundancy (up-conversion & down- conversion, filtering at higher sampling rate)

U-OFDM [5] MEDIUM 50% YES LOW

(unipolar double OFDM (FFT/IFFT and OFDM) symbol length single-tap

equalization) eU-OFDM [6] MEDIUM <95% YES HIGH

(unipolar fall rate only (successive OFDM) asymptotically, interference at high SNR cancellation, processing longer data blocks) eACO-OFDM MEDIUM <95% YES HIGH

[7] (unipolar fall rate only (successive

OFDM) asymptotically, interference at high SNR cancellation)

Embodiments LOW 100% YES LOW

(single- No redundancy (FFT/IFFT & carrier like) single-tap

equalization, no up/ down- conversion)

Table 2

The precoded OFDM scheme of embodiments possesses the following advantages:

1. Its PAPR level is very low, just 1-3 dB above the single-carrier modulation, which may be considered the PAPR lower bound;

2. Unlike single carrier modulation it provides full control over the locations of spectral nulls, such as DC component suppression in order to avoid DC-wander effects, and multi-user access across different subcarriers;

3. It is non-redundant, hence it achieves full throughput, not just asymptotically and not just at high SNR, unlike eU-OFDM and eACO-OFDM;

4. Its implementation complexity is comparable to the conventional OFDM, which may be considered the simplest multipath-resilient modulation known to date, that benefits from trivial single-tap channel estimation and equalization; and

5. The precoding-modulation matrix is a real-valued orthogonal transform.

Therefore, the output signal is always real-valued, provided that the input is real-valued as well. In addition, orthogonality preserves the noise covariance, i.e., no noise colouring takes place.

Embodiments provide a superior modulation scheme that outperforms existing schemes in terms of the following four criteria:

PAPR level;

Throughput;

• Ability to control the null subcarriers; and

• Transceiver implementation complexity.

The desirable features of the transceiver of embodiments are presented in more detail below, and compared to the state-of-the-art.

PAPR Reduction:

Figure 6 compares the Complementary Cumulative Distribution Function (CCDF) of the PAPR of embodiments with respect to two other relevant schemes: SC modulation, which can be considered a lower bound in terms of PAPR, but is unusable in VLC systems unless up/down-conversion are employed, and (e)U-OFDM, which is the state- of-the-art in terms of PAPR for VLC. PAPR corresponds to the pulse-shaped signal of a multicarrier transmission with 256 subcarriers, of which 2 (lowest and middle) subcarriers are null, and 16-QAM input constellation. The pulse-shaping filter has a roll-off factor of 0.25, oversampling ratio of 8 and the group delay corresponds to 6 samples at the lower rate. Embodiments achieve ultra-low PAPR, 3-5 dB lower than the state-of-the-art (e)U-OFDM and (e)ACO-OFDM modulations, and is just 1-3 dB above the PAPR level of SC modulation. However, unlike SC, it offers flexible subcarrier nulling to completely mitigate the DC-wander effects, and allows multi-user access across subcarriers. Hence, it can be seen that Figure 6 illustrates that OFDM precoding scheme of embodiments outperforms the existing U-OFDM by 3-5 dB, and is just 1-3 dB above the level of single carrier modulation for 90% of time.

Figure 7 is a histogram of the oversampled time-domain waveform corresponding to the precoded OFDM signal of embodiments for a 16-QAM input constellation. The histogram of the oversampled time-domain waveform also looks like one of a SC waveform, for the same constellation type. This is illustrated in Figure 7, for a 16-QAM input constellation. The 4 prominent peaks corresponding to the 4-PAM real and imaginary parts of the 16-QAM symbols are clearly visible, the same way as in a SC signal. However, unlike existing SC modulation schemes for VLC, it requires no up/down-conversion, hence requires a much simpler transceiver.

Achieved Throughput:

The modulation scheme of embodiments is non-redundant, and therefore, the full data rate of conventional OFDM is achieved (assuming appropriate cyclic prefix length, and the inherent constraint on the real-valued nature of the VLC signal). The scheme of embodiments achieves 50% higher throughput than ACO-OFDM and U-OFDM. It also outperforms the state-of-the-art eU-OFDM and eACO-OFDM by 3-5 dB in terms of PAPR reduction, as shown in Figure 6. In addition, it exhibits much lower decoding complexity compared to eU-OFDM and eACO-OFDM, since no successive interference cancellation is needed. State-of-the-art (e)U-OFDM and (e)ACO-OFDM modulations achieve about 90% throughput, and only at high SNR (more than 20 dB). Spectrum blanking:

Figure 8 illustrates an amplitude spectrum of the precoded OFDM signal of

embodiments. There are five null subcarriers in the middle of the spectrum and one near the edge of the spectrum. The scheme of embodiments allows for on-demand subcarrier nulling, unlike SC modulation, thus avoiding the DC-wander effects the VLC signal is subject to. Deep nulling (40 to 50 dB) is achieved, as shown in Figure 8, where 5 subcarriers in the middle, and one at the edge are nulled out (the total number of subcarriers is 256). Different spectral masks can be used for each user, in order to allow for multi-user frequency domain multiplexing. Computational complexity:

The computational complexity of the scheme of embodiments is comparable to the conventional OFDM transceiver (which enables trivial single-tap channel estimation and equalization). In Table 1, we compare the computational complexity of the precoded OFDM of embodiments vs. conventional OFDM, for both transmission and reception.

We assume N subcarriers, of which Z = N - M are null subcarriers, and radix-2 FFT/IFFT operations. We may notice that the scheme of embodiments exhibits half of the complexity of conventional OFDM at transmission, and slightly more than double complexity at reception. The overall complexity of the proposed precoded OFDM does not exceed 50% of the complexity of conventional OFDM. This is well-justified, considering the substantial reduction in PAPR, flexibility in subcarrier nulling, and full throughput, unlike other existing schemes. This complexity overhead (vs. OFDM) is negligible compared to other computationally-intensive transceiver operations used in the current and future high data rate wireless standards, such as Low Density Parity Check (LDPC) / turbo decoding.

In conclusion, the superior properties of the schemes of embodiments are manifold: ultra-low PAPR;

• full throughput;

• total control over the null subcarriers; and

• low computational complexity.

To date, no other method is known to perform well with respect to all the above criteria.

The modulation scheme of embodiments achieves the lowest PAPR to date, comparable to single carrier modulation, subject to full control over the null subcarriers, which enables multi-user access across subcarriers. Its computational complexity is comparable to the conventional OFDM transceiver, and therefore, it may become part of the ongoing IEEE 802.15.7 Visible Light Communication physical and medium access control standardization efforts.

References:

[1] J. B. Carruthers and J. M. Kahn, "Multiple-subcarrier modulation for nondirected wireless infrared communication," IEEE J. Select. Areas Commun., vol. SAC-14, pp. 538-546, Apr. 1996.

[2] J. Armstrong and A. Lowery, "Power efficient optical OFDM," Electron. Lett., vol. 42, no. 6, pp. 370-372, 2006. [3] Fang-Ming Wu, Chun-Ting Lin, Chia-Chien Wei, Cheng-Wei Chen, Hou-Tzu

Huang, and Chun-Hung Ho, "1.1-Gb/s White-LED-Based Visible Light Communication Employing Carrier-Less Amplitude and Phase Modulation", IEEE Photon. Tech. Lett., vol. 24, no. 19, Oct., 2012 [4] Y- Wang, R. Li, Y. Wang and Z. Zhang, "3.25-Gbps visible light communication system based on single carrier frequency domain equalization utilizing an RGB LED," OFC 2014, San Francisco, CA, 2014, pp. 1-3. [5] D. Tsonev, S. Sinanovic, and H. Haas, "Novel unipolar orthogonal frequency division multiplexing (U-OFDM) for optical wireless," in IEEE 75th Veh. Tech. Conf. (VTC Spring), 2012, 2012, pp. 1-5.

[6] D. Tsonev and H. Haas, "Avoiding spectral efficiency loss in unipolar OFDM for optical wireless communication," in 2014 IEEE Int. Conf. Commun. (ICC), 2014, pp. 3336-3341·

[7] M. Islim, D. Tsonev and H. Haas, "On the superposition modulation for OFDM- based optical communication," in GlobalSip 2015 - Symp. Sig. Proc. Opt. Commun., 2015, pp. 1022-1026.

A person of skill in the art would readily recognize that steps of various above- described methods can be performed by programmed computers. Herein, some embodiments are also intended to cover program storage devices, e.g., digital data storage media, which are machine or computer readable and encode machine- executable or computer-executable programs of instructions, wherein said instructions perform some or all of the steps of said above-described methods. The program storage devices may be, e.g., digital memories, magnetic storage media such as a magnetic disks and magnetic tapes, hard drives, or optically readable digital data storage media. The embodiments are also intended to cover computers programmed to perform said steps of the above-described methods.

The functions of the various elements shown in the Figures, including any functional blocks labelled as "processors" or "logic", may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software. When provided by a processor, the functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared. Moreover, explicit use of the term

"processor" or "controller" or "logic" should not be construed to refer exclusively to hardware capable of executing software, and may implicitly include, without limitation, digital signal processor (DSP) hardware, network processor, application specific integrated circuit (ASIC), field programmable gate array (FPGA), read only memory (ROM) for storing software, random access memory (RAM), and non-volatile storage. Other hardware, conventional and/or custom, may also be included. Similarly, any switches shown in the Figures are conceptual only. Their function may be carried out through the operation of program logic, through dedicated logic, through the interaction of program control and dedicated logic, or even manually, the particular technique being selectable by the implementer as more specifically understood from the context.

It should be appreciated by those skilled in the art that any block diagrams herein represent conceptual views of illustrative circuitry embodying the principles of the invention. Similarly, it will be appreciated that any flow charts, flow diagrams, state transition diagrams, pseudo code, and the like represent various processes which may be substantially represented in computer readable medium and so executed by a computer or processor, whether or not such computer or processor is explicitly shown.

The description and drawings merely illustrate the principles of the invention. It will thus be appreciated that those skilled in the art will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the invention and are included within its spirit and scope. Furthermore, all examples recited herein are principally intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the invention and the concepts contributed by the inventor(s) to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions.

Moreover, all statements herein reciting principles, aspects, and embodiments of the invention, as well as specific examples thereof, are intended to encompass equivalents thereof.

Claims

1. Processing circuitry (5) for processing a multicarrier data signal prior to transmitting said signal as a communication signal, said processing circuitry comprising:

an input (40) for receiving said multicarrier data signal;

mapping circuitry (30) operable to map said multicarrier data signal to a set of active subcarriers and to add nulls corresponding to a set of inactive subcarriers to generate a mapped multicarrier data signal; and

transforming circuitry (10) operable to generate a transformed mapped multicarrier data signal by applying a linear precoder matrix to maintain said nulls corresponding to said inactive subcarriers and encode said active subcarriers as orthogonal frequency-division multiplexed subcarriers.

2. The processing circuitry of claim 1, wherein said multicarrier data signal comprises an N subcarrier data signal, said set of active subcarriers comprises M active subcarriers and said set of inactive subcarriers comprise Z inactive subcarriers.

3. The processing circuitry of claim 1 or 2, wherein said mapping circuitry is operable to map real-valued data of said multicarrier data signal to M active subcarriers.

4. The processing circuitry of any preceding claim, wherein said linear precoder matrix comprises a composite precoding-modulation matrix having an identity matrix summed with a subcarrier nulling matrix.

5. The processing circuitry of claim 4, wherein said composite precoding- modulation matrix is unitary.

6. The processing circuitry of claim 4 or 5, wherein said composite precoding- modulation matrix has most eigenvalues equal to one.

7. The processing circuitry of any one of claims 4 to 6, wherein said composite precoding-modulation matrix is real-valued.

8. The processing circuitry of any one of claims 4 to 7, wherein said subcarrier nulling matrix is lower-ranked than said composite precoding-modulation matrix.

9. The processing circuitry of any one of claims 4 to 8, wherein said subcarrier nulling matrix has a rank of 2Z.

10. The processing circuitry of any one of claims 4 to 9, wherein said identity matrix is an N x N identity matrix.

11. The processing circuitry of any one of claims 4 to 10, wherein said subcarrier nulling matrix comprises a matrix singular value decomposition.

12. The processing circuitry of any preceding claim, wherein said transforming circuitry is operable to generate said transformed mapped data signal using 2NZ scalar operations.

13. The processing circuitry of any preceding claim, wherein said mapping circuitry is operable to map said multicarrier data signal to one of a plurality of sets of active subcarriers and to add nulls corresponding to an associated set of inactive subcarriers to generate said mapped multicarrier data signal and said transforming circuitry is operable to generate said transformed mapped multicarrier data signal by applying one of a corresponding plurality of linear precoder matrices to maintain said nulls corresponding to said inactive subcarriers and encode said active subcarriers as orthogonal frequency-division multiplexed subcarriers.

14. A method of processing a multicarrier data signal prior to transmitting said signal as a communication signal, said method comprising:

receiving (Si) said multicarrier data signal;

mapping (S2) said multicarrier data signal to a set of active subcarriers and adding nulls corresponding to a set of inactive subcarriers to generate a mapped multicarrier data signal; and

generating (S3) a transformed mapped multicarrier data signal by applying a linear precoder matrix to maintain said nulls corresponding to said inactive subcarriers and encode said active subcarriers as orthogonal frequency-division multiplexed subcarriers.

15. Processing circuitry (15) for processing a multi-carrier orthogonal frequency- division multiplexed communication signal to generate a multicarrier data signal, said multi-carrier orthogonal frequency-division multiplexed communication having low amplitude portions corresponding to inactive subcarriers, said processing circuitry comprising:

an input (50) for receiving said multi-carrier orthogonal frequency-division multiplexed communication signal;

equalisation circuitry (60) operable to perform frequency-domain equalisation on said multi-carrier orthogonal frequency-division multiplexed communication signal; and

transforming circuitry (20) operable to generate said multicarrier data signal by applying a linear decoder matrix to maintain said nulls corresponding to said inactive subcarriers and decode said active subcarriers.

16. A method of processing a multi-carrier orthogonal frequency-division multiplexed communication signal to generate a multicarrier data signal, said method comprising:

receiving (S4) said multi-carrier orthogonal frequency-division multiplexed communication signal;

performing (S5) frequency-domain equalisation on said multi-carrier orthogonal frequency-division multiplexed communication signal;

generating (S6) said multicarrier data signal by applying a linear decoder matrix to maintain said nulls corresponding to said inactive subcarriers and decode said active subcarriers.

17. A computer program product operable, when executed on a computer, to perform the method of claims 14 or 16.