WO2017013467A1

WO2017013467A1 - Ofdm transmission systems with reduced peak-to-average power ratio

Info

Publication number: WO2017013467A1
Application number: PCT/IB2015/055494
Authority: WO
Inventors: Denis Mestdagh; Joel Cambonie; Loïc LIETAR; Jorge GULFO-MONSALVE
Original assignee: Greenwaves Technologies
Current assignee: Greenwaves Technologies
Priority date: 2015-07-20
Filing date: 2015-07-20
Publication date: 2017-01-26
Anticipated expiration: 2018-01-20

Abstract

A data transmission method is provided, comprising the steps of providing N values (X) to transmit, where N is a power of 2; dividing the values in M vectors (X_k) of N/M values, where M is a power of 2; applying each vector in parallel to two groups (80a, 80b) of M N/M-point inverse Fourier transforms, producing a first and a second group of M sub-symbols (a_k, b_k); modifying the input of each inverse Fourier transform by a different pseudo-random number sequence (PRNA, PRNB); producing (84) combinations of sums in pairs (σ_u,v) of sub-symbols from the first group with sub-symbols from the second group; and selecting (72) for transmission the sum (σ_p,q) having the lowest peak-to-average power ratio (PAPR).

Description

OFDM TRANSMISSION SYSTEMS WITH REDUCED PEAK-TO-AVERAGE POWER RATIO

Field

The present invention relates to transmission systems, and more particularly to the reduction of the peak-to-average power ratio (PAPR) of the transmitted signal in an orthogonal frequency-division multiplexing (OFDM) system.

Background

In an OFDM system, the transmitted signal is formed of a series of symbols, wherein each symbol is the sum of N subcarriers having different amplitude and phase values. N is usually a power of 2, ranging from several tens to several thousands. The amplitude and phase values depend on the conveyed data and may be considered as random.

In many circumstances, several subcarriers having a relatively high amplitude may happen to be in phase, causing a large peak in the transmitted symbol. The transmitter is usually designed to handle the average level of the transmission signal and peaks that fall below an accepted threshold. Peaks above the threshold are clipped by the digital- to-analog converter or the linear power amplifier of the transmitter, causing distortion and a temporary increase of the bit error rate.

Increasing the accepted threshold may reduce the bit error rate, but increases the power consumption, since the power amplifier of the transmitter is then designed to handle higher amplitudes. As an alternative, the transmission signal may be attenuated, but this reduces the signal-to-noise ratio (SNR) and the communication distance.

PCT patent application WO 2015/028684 discloses a technique for reducing the PAPR statistically, leading to a lower power consumption while maintaining the communication distance, or leading to a higher communication distance with a same power consumption. In summary, instead of transmitting a symbol that conveys N subcarriers, the symbol is split, using temporal diversity properties of Fourier transforms, into M consecutive sub-symbols that each conveys only N/M subcarriers. N and M are each a power of two. As a result, the PAPR is statistically divided by M.

Figure 1 is a block depicting generation of such sub-symbols with M=2 in a transmitter such as disclosed in the above PCT patent application. The data to be transmitted is first mapped to N quadrature amplitude modulation (QAM) constellations. Several QAM types may be used, such as 2-QAM (BPSK), 4-QAM, 8-QAM, 16-QAM, etc. Each constellation is represented by a complex number X(i), where i (varying from 0 to N-l) is the input or frequency index of an N-point Inverse Fast Fourier Transform (N-IFFT). The N-point IFFT produces N time-domain samples x(0) to x(N-l), each also being a complex number. In a conventional OFDM system, the N samples x form a symbol that is transmitted over a symbol period Ts. To guarantee orthogonality between the subcarriers, the subcarriers are equally spaced in frequency and the frequency pitch is equal to the inverse of the symbol period. The real and imaginary parts of the symbol are converted into two separate analog signals that are quadrature modulated on a radiofrequency carrier.

In figure 1, the samples x of the symbol produced by the IFFT are processed, such as by a digital signal processor DSP, to form M sub-symbols including each N/M samples. Each sub-symbol is built such that it conveys a different set of N/M equally spaced subcarriers. In figure 1, with M=2, two sub-symbols go and gi are built, corresponding respectively to the even-ranked subcarriers and the odd-ranked subcarriers. With an arbitrary value for M, a sub-symbol g_k conveys the subcarriers of ranks k+Mi, where i varies between 0 and—— 1.

M

With respect to a conventional N-subcarrier OFDM system, a system such a disclosed in the above PCT application requires additional signal processing resources after the IFFT on the transmitter side and reciprocal processing resources before an FFT on the receiver side.

Summary

The present disclosure generally relates to a data transmission method, comprising the steps of providing N values to transmit, where N is a power of 2; dividing the values in M vectors of N/M values, where M is a power of 2; applying each vector in parallel to two groups of M N/M-point inverse Fourier transforms, producing a first and a second group of M sub-symbols; modifying the input of each inverse Fourier transform by a different pseudo-random number sequence; producing combinations of sums in pairs of sub-symbols from the first group with sub-symbols from the second group; and selecting for transmission the sum having the lowest peak-to-average power ratio (PAPR).

The method may comprise the further steps of frequency-shifting each z^'-th sub-symbol of each group by a step -i/N, where i varies between 0 and M-l, producing in each group M sub-symbols conveying a different set of subcarriers; frequency-shifting all sub-symbols to a common set of subcarriers; and producing the combinations of sums from the frequency-shifted sub-symbols.

The method may comprise the further steps of transmitting the selected sum as a sub- symbol; receiving the transmitted sub-symbol; demodulating the received sub-symbol; and dividing the demodulated sub-symbol by the sum of the pseudo-random sequences used in forming the transmitted sum.

The method may alternatively comprise the further steps of transmitting the selected sum as a sub-symbol with zero-padded intervals; receiving the transmitted sub-symbol; inserting a cyclic prefix at the beginning of the received sub-symbol; applying to the cyclic prefix a multiplication factor based on the common subcarrier set; demodulating the received sub-symbol; and dividing the demodulated sub-symbol by the sum of the pseudo-random sequences used in forming the transmitted sum.

The method may comprise the further steps of changing the common subcarrier set after each transmitted sum according to a pattern; and sharing the pattern with the receiver.

The method may comprise the further steps of changing the pseudo-random sequences after each transmitted sum according to a pattern; and sharing the pattern with the receiver.

The pseudo-random sequences applied in the first group of sub-symbols may be real numbers, and the pseudo-random sequences applied in the second group of sub-symbols may be imaginary numbers.

Brief Description of Drawings

Other potential advantages and features will become more clearly apparent from the following description of particular embodiments of the invention provided for exemplary purposes only and represented in the appended drawings, in which:

^■ Figure 1, previously described, is a block diagram illustrating the generation of a sub-symbol pair in a reduced peak-to-average power ratio OFDM transmitter;

^■ Figure 2 is a block diagram illustrating an exemplary generation of a sub-symbol pair with an embodiment of a low-complexity 8-point IFFT; ^■ Figure 3 is a block diagram illustrating an exemplary generation of a sub-symbol quadruplet with an embodiment of a low-complexity 8-point IFFT;

^■ Figure 4 is a block diagram of a generic embodiment of a low-complexity N- point IFFT used for generating and transmitting a sub-symbol M-uplet; ■ Figure 5A is a block diagram of a first embodiment of receiver circuitry for processing sub-symbol M-uplets;

^■ Figure 5B illustrates generation of a cyclic prefix on the receiver side in the context of a zero-padding transmission;

^■ Figure 6 is a block diagram of another embodiment of receiver circuitry for processing sub-symbol M-uplets;

^■ Figure 7 is a block diagram of an embodiment of transmission circuitry using selective mapping;

^■ Figure 8 is a block diagram of an embodiment of transmission circuitry using high-efficiency selective mapping; and ■ Figure 9 is a block diagram of another embodiment of transmission circuitry using high-efficiency selective mapping.

Description of Embodiments

A reduced PAPR OFDM system as disclosed in PCT patent application WO 2015/028684 adds complexity to a conventional OFDM system due to constraints such as the reusability of existing FFT and IFFT circuitry. In the present disclosure, it is sought to reduce the complexity of the system while maintaining or improving its performance.

The inventors have observed that the sub-symbols built from the output of the inverse FFT in the above PCT application are derivable from intermediate radix stages of the inverse FFT.

Figure 2 illustrates an 8-point inverse FFT circuit in more detail, according to a decimation-in-time (DIT) representation. An inverse FFT circuit, or IFFT may be represented as a succession of radix stages. The simplest radix stage is a second order radix stage, denoted radix-2. A radix-2 stage combines the outputs of two half-size IFFTs into one full-size output. A radix-2 stage in a DIT representation may be illustrated as a butterfly diagram, such that: x(0 = s₀(0 + V · ¾(0

N\

Where x is the N-sample time-domain output, so and si are the sub-symbols respectively output by the two half-size IFFTs, i is the sub-symbol sample index (varying between 0 and j— 1), and W¾ is a so-called twiddle factor. The twiddle factors are N-th roots of unity, where W^¹ = e~^{i2 n}N .

The last radix-2 stage, as shown in figure 2, combines the outputs of two 4-point IFFTs into the 8-sample output symbol x(0), x(l) ... x(7). The first 4-point IFFT operates on the even-ranked sub-carriers, whereas the second 4-point IFFT operates on the odd-ranked sub-carriers (the sub-carrier ranks are defined here as the indexes of the input values X).

In turn, each of the 4-point IFFTs may be represented as a radix-2 stage combining the outputs of two 2-point IFFTs, as shown.

Generally speaking, within an N-point IFFT according to a decimation-in-time representation, a set of M sub-symbols sM₀, sMi... sM_M-i may be produced by M intermediate N/M-point IFFTs, where M and N are powers of 2. Each sub-symbol sM_k is defined such that it conveys the subcarriers of ranks k+Mi, where & is a constant between 0 and M-l, and i varies from 0 to—— 1. The subcarriers of ranks k+Mi will be denoted hereinafter as the subcarrier set k.

It appears that these sub-symbols can be transmitted individually without modification over sub-symbol periods Ts/M to convey the same information as a full symbol over the symbol period Ts. Such an approach is equivalent to using in parallel M conventional N/M- sub carrier OFDM transmitters, with no apparent added value.

Instead of transmitting the sub-symbols sM, it is proposed herein to transmit the sub- symbols as modified by the twiddle factors at the input of the last radix-M stage of a DIT representation of an N-point IFFT. It appears that such sub-symbols, denoted gM, have the temporal diversity properties identified by the above PCT application. Moreover, they have the feature of being devoid of DC components even if the first input of each N/M-point IFFT is used for conveying data. Indeed, the first input of an IFFT produces a DC component in the time domain, whereby the first input of the IFFT in a conventional OFDM system is often set to 0 to avoid transmission of DC components.

As shown in figure 2, for a last radix-2 stage, a sub-symbol g2₀ = s2₀ is extracted directly from the output of the first 4-point IFFT, and a sub-symbol g2i is extracted after application of the twiddle factors 1 ¾ (/^' = 0, -1, -2, -3) to the output s2i of the second 4-point IFFT.

Therefore, the remaining circuitry of the radix-2 stage may be skipped, as shown in gray. In other words, only a partial N-point IFFT is achieved up to the last radix stage.

As shown, the sub-symbols g2₀ and g2i are tapped from the last radix stage, and a cyclic-prefix CP is pre-pended at 20 to each sub-symbol. The cyclic prefix is not formed as in a conventional OFDM system due to the temporal diversity properties of the sub-symbols, here sub-symbol g2i only. The cyclic prefixes for the sub-symbols g2₀ and g2i are the tail ends of the sub-symbols multiplied respectively by 1 and -1.

Each sub-symbol with its cyclic prefix is converted to an analog signal at 22, in fact two signals I and Q corresponding to the real and imaginary parts of the sub-symbol, which are then quadrature modulated and transmitted at 24. Each sub-symbol is thus transmitted over a time Ts/M, where Ts is the full symbol period, equal to the inverse of the frequency pitch of the N sub carriers.

Instead of inserting a cyclic prefix at 20 before each sub-symbol, the sub-symbols may be zero-padded up to the same length as the cyclic prefix, as conventionally done in a so called ZP-OFDM system. Then, on the receiver side, after finding the sub-symbol boundaries, the zero-padded intervals are filled with the corresponding cyclic prefixes before FFT processing. This technique has the feature of cancelling the transmission power in the zero padded intervals. Here too, the cyclic prefixes are subject to the multiplication factors that would have been applied on the transmitter side.

Figure 3 illustrates an 8-point IFFT circuit with a last radix-4 stage, according to a DIT representation. A radix-4 stage combines groups of four inputs to produce respective groups of four outputs, according to the matrix equation:

N

Where i is the sub-symbol sample index varying between 0 and 1, and s4₀ to s4₃ are

N

the four sub-symbols produced respectively by the four—point IFFTs (here 2-point IFFTs with N=8).

For sake of clarity, the radix-4 stage has not been fully shown in figure 3. Only the links for producing the time-domain samples x(2) and x(5) have been shown. The sub- symbols extracted for transmission g4₀ to g4₃ are the outputs of the four N/4-point IFFTs after application of the twiddle factors W^^kl in the radix-4 stage.

Therefore, the remaining circuitry of the radix-4 stage may be skipped, as shown in gray. In other words, only a partial N-point IFFT is achieved up to the last radix-4 stage. The cyclic prefixes for the sub-symbols g4₀ to g4₃ are the tail ends of the sub-symbols multiplied respectively by 1, -j, -1, and j, as illustrated.

More generally, if a radix-M stage is used as the last stage in an N-point IFFT according to a DIT representation, M sub-symbols gM₀ to gM_M-i may be extracted for transmission from the input of the radix-M stage, after application of the twiddle factors in the radix stage. For a sub-symbol gM_k having N/M values, the applicable twiddle where & is a constant between 0 and M-l and i varies between 0 and

In fact, for each sub-symbol sM_k output by the corresponding N/M-point IFFT, the

i

twiddle factors apply to the sub-symbol a frequency shift of step -— to produce the sought sub-symbol gM_k.

The multiplication factors applied in the cyclic prefixes are M-th roots of unity taken in the clockwise direction.

Figure 4 is a block diagram of a generic embodiment of transmitter circuitry applying the above teachings. An N/M-value vector X_k is applied to an N/M-point IFFT circuit 40 that produces a corresponding symbol sM_k. The vector X_k may be formed of the series of frequency-domain values X(k+Mi) input to the N-point IFFT, where k is the rank of the vector in a group of M vectors to transmit, and i varies from 0 to—— 1. The structure of figure 4 however does not require that the values of X_k be mapped to inputs of an N-point IFFT. The symbol sM_k is applied to a programmable frequency-shifter 42, taking the rank k of

i

the vector X_k as a parameter. The value of the frequency shift is -— , which produces a sub-symbol gM_k that conforms to the sub-symbols sought for transmission in figures 2 and 3. The sub-symbol gM_k may then follow the same transmission path as depicted in figure 2. Figure 5 A is a block diagram of a first embodiment of receiver circuitry for processing the sub-symbols transmitted according to figure 4, in an example where M=4 and zero- padding is used between the transmitted sub-symbols g4₀ to g4₃.

The incoming signal is quadrature demodulated at 50, and the resulting in-phase and quadrature signals (I, Q) are separately converted to digital at 52. The resulting digital complex samples form the current sub-symbol, with zero-padded intervals preceding and following the sub-symbol. The start-of-symbol is located at 54. A cyclic prefix is inserted at 56, applying the corresponding fourth root of unity, as explained previously.

An FFT window is applied at 58 to N/4 samples, usually starting at the start-of-symbol detected in 54. The window thus isolates the current sub-symbol g4_k. The sub-symbol

i

g4_k is frequency-shifted by a step— at 60, producing a conventional time-domain sub- symbol s4_k. The sub-symbol s4_k is processed by an N/4-point forward FFT 62 producing frequency-domain values X.

In a conventional N-subcarrier OFDM receiver, the FFT output is usually processed by an N-frequency equalizer 64. However, the FFT 62 outputs only N/4 values that are mapped to suitable frequency inputs of the equalizer. The mapping may be performed by a demultiplexer 66 that receives the output of the FFT and is controlled by value k. Value k causes the demultiplexer to send the N/4 values to the group of frequencies used by the transmitted sub-symbol g4_k, i.e. the frequencies k+4i. As shown for k=l, the consecutive values of the FFT output are mapped to inputs 1, 5... l+4i... N-3. Figure 5B illustrates a process of generating the cyclic prefix on the receiver side with a zero-padding transmission, such as performed in boxes 54, 56 and 58 of figure 5A. An OFDM system is usually designed to account for multi-path signal transmissions. As an example, an OFDM receiver will receive a main, "Line-Of- Sight" (LOS) symbol, and multiple reflections with various delays and attenuations with respect to the LOS symbol, called "Non-Line-Of- Sight" (NLOS) symbols. Figure 5B depicts the LOS symbol and the NLOS symbol having the largest allowed delay, i.e. the duration of a zero-padded interval. Circuit 54 is designed to find the starting point of the LOS symbol, which also defines the starting point of the FFT window in 58. The FFT window will usually correspond to the length of the LOS symbol, as shown. The shown NLOS symbol is such that it starts in the FFT window after its preceding zero-padded interval ZP - its end portion thus exceeds the end of the FFT window by the duration of the zero-padded interval. The symbols LOS and NLOS, and any other symbols with different delays are received added together to form the signal seen in the FFT window. The cyclic prefix is designed to restore the periodic nature of the signal seen in the FFT window.

Conventionally, the cyclic prefix is generated in 56 by adding to the signal at the beginning of the FFT window, the portion of the signal that exceeds the FFT window by the duration of the zero-padded interval. In other words, the tail ends of the NLOS symbols are added in the zero-padded interval that precedes the NLOS symbols.

With the frequency shifted sub-symbols gM_k, the cyclic prefix is obtained differently, as already mentioned. For instance, for a sub-symbol g4i, as shown, the conventional cyclic prefix is multiplied by -j . The applicable factor is 1, -j, -1 and j respectively for the sub-symbols g4₀ to g4₃. For an arbitrary value of M, the factor applicable for a sub- symbol gM_k is the k-th M-th root of unity in the clockwise direction.

Figure 6 is a partial block diagram of another embodiment of receiver circuitry for processing the sub-symbols transmitted according to figure 4, in an example where M=4. Each sub-symbol g4_k from the FFT window 58 is fed individually into a full N-point FFT 68. The sub-symbols having only M=4 samples, each is right-padded with zeros to form a full N-sample symbol.

Each of the sub-symbols g4_k conveys a different set of subcarriers, i.e. subcarrier set k. The FFT circuit may reflect this by producing significant values only on the N/M outputs corresponding to subcarrier set k. For instance, as shown, feeding sub-symbol g4i to the FFT circuit produces N/4 significant values on outputs 1, 5... l+4i... N-3, the remaining outputs being non-significant in theory, as illustrated by zeros in the figure. In practice, each sub-symbol g4_k does not include an integer number of cycles of its subcarriers, because it was frequency-shifted by a step smaller than the pitch of these subcarriers. As a consequence, lobes will appear on several outputs of the FFT. It appears however that such lobes do not affect the sought significant values. The zero- padded N-point FFT can thus produce the sought values without applying the frequency-shift corrections (60 in figure 5A) to the sub-symbols g4_k.

Each of the M zero-padded sub-symbols thus produces significant values on a different set of outputs of the FFT. Once the last sub-symbol has been provided, the FFT will have produced the sought significant values X(0) to X(N-l) over all N outputs. The significant values may be extracted individually from the corresponding outputs of the FFT as they are produced, and reordered in a memory, if required, for further processing. The extraction is preferably carried out after frequency equalization 64.

The resulting values may then be processed further like in a conventional OFDM receiver system. Since the N-point FFT circuitry is designed to always process zero-padded sub- symbols, its structure may be significantly simplified with respect to a full N-point FFT. In particular all the calculation nodes that perform combinations of zero values can be omitted.

Each sub-symbol that is thus individually processed by the FFT conveys data on subcarriers that have a frequency pitch M times larger than the pitch between the N original subcarriers. This decreases the sensitivity to Doppler effect by a factor M with respect to a conventional N-subcarrier OFDM system.

Although each sub-symbol conveys only N/M subcarriers, the system still uses all N subcarriers and offers the robustness of an N-subcarrier OFDM system. For instance, the larger number of subcarriers offers better redundancy, i.e. the possibility to move data between subcarriers when the transmission channel is degraded for specific subcarriers.

Figure 7 is a block diagram of an embodiment of transmission circuitry that may further reduce the peak-to-average power ratio PAPR. The system uses a partial N-IFFT like the one of figure 3 for carrying out a PAPR reduction technique called "selective mapping" or SLM in a cost effective way. Selective mapping was first disclosed in ["A Method to Reduce the Probability of Clipping in DMT -Based Transceivers", Denis J. G. Mestdagh and Paul M. P. Spruyt, IEEE Transactions On Communications, Vol. 44. No 10, October 1996].

Selective mapping as disclosed in the above article consists in multiplying a same set of N IFFT input values with successive different pseudo-random sequences, performing the IFFT for each pseudo-random sequence, thus producing a different randomized symbol corresponding to the same initial values, and transmitting the randomized symbol that exhibits the lowest PAPR. On the receiver side, an inverse pseudo-random sequence is multiplied with the FFT output values to reestablish the original values. This involves knowledge at the receiver side of the pseudo-random sequence used on the transmitter side. Such identification may be transmitted by modulating an OFDM pilot tone that usually does not carry information.

Conventional selective mapping thus involves using the full N-point IFFT in multiple passes during a symbol period for a same set of input values. This limits the number of pseudo-random sequences that can be used and the resulting efficiency of the PAPR reduction. If more pseudo-random sequences are used than the number of passes the IFFT is capable of achieving in one symbol period, several IFFT circuits may be connected for operation in parallel, which increases the hardware cost.

In figure 7, the input frequency-domain vector X_k, such as defined in relation to figure 4, is applied in parallel to M N/M-point IFFTs 40. Each IFFT is followed by a static frequency shifter 70 that applies a different frequency shift among the ones applied by the programmable shifter 42 of figure 4, i.e. the frequency shifters 70 respectively apply shifts by steps 0, -1/N, -2/N... -(M-l)/N. The first frequency shift by 0 is simply a direct connection. In other words, this structure is a "partial N-point IFFT" using a last radix- M stage, as defined in relation to figures 2 and 3. The sub-symbols provided by the frequency-shifters 70 for a same input vector X_k are denoted g_k,o to gk,M-i -

A first approach for reducing the PAPR could be to select and transmit the sub-symbol g_k,q that has the lowest PAPR among the M sub-symbols provided by the frequency shifters, as indicated in 72. This approach is however insufficient, because simulations show that the differences in PAPR between such sub-symbols are insignificant.

A preferred approach is to multiply the input vector X_k by a different pseudo-random number sequence PRNo to PRNM-I before each IFFT 40. The pseudo-random numbers may be complex and have and absolute value of 1 to preserve the amplitude of the values of vector X_k. The first sequence PRNo may be unity, i.e. leave the values unmodified. The differences in PAPR between the thus randomized sub-symbols may be significant, and selecting the randomized sub-symbol g_k,q having the lowest PAPR for transmission will yield a significant global PAPR reduction. The selected randomized sub-symbol g_k,q follows the same transmission path as in the system of figure 4. The multiplication factor for producing the cyclic prefix CP for this sub-symbol, as previously mentioned, depends on the position q that conditions the subcarrier set used in the transmission.

To simplify the hardware, each pseudo-random number may be a random choice between 1 and -1, whereby the multiplication with a complex value of vector X_k simply involves changing or not the signs of the real and imaginary parts. Then, the inverse pseudo-random sequence to apply at the receiver side is the same pseudo-random sequence, i.e. PRNq ¹ = PRNq.

The sub-symbol g_k,q selected for transmission does not use the subcarrier set k corresponding to its order of transmission - it uses the subcarrier set q, where q is arbitrary between 0 and M-l . Processing such sub-symbols on the receiver side generally implies knowledge of q, so that the sub-symbol can be correctly demodulated and the correct inverse pseudo-random sequence PRN_q ^_1 be applied after demodulation.

The value q may be transmitted, for instance, by modulating an OFDM pilot tone, i.e. a subcarrier that conveys no data and that is used for synchronization purposes and estimating the transmission channel characteristics.

Using an N-point FFT with zero padding as depicted in figure 6 for processing randomized sub-symbols on the receiver side may not require knowledge of q, provided the cyclic prefixes are added on the transmitter side. A received sub-symbol g_k,q is then zero-padded to the right and fed to the full N-point FFT 68. The FFT will produce significant values at the output positions that correspond to the actual subcarriers contained in the sub-symbol, i.e. subcarrier set q and positions q+Mi, for i varying between 0 and—— 1.

M

In other words, if the inverse pseudo-random sequences are placed in correspondence with the same time-domain positions as the original pseudo-random sequences in the transmitter, no specific means are necessary to select and apply the correct pseudorandom sequence and frequency equalization channels to the current sub-symbol, since the zero-padded FFT does that naturally. As indicated above, by choosing an original pseudo-random sequence of values 1 or -1, the pseudo-random sequence and its inverse are equal.

The value q being unknown, there is an uncertainty as to which set of outputs of the FFT produces the sought values. The value q may however be evaluated by analyzing the power spectrum of the FFT result and locating the outputs providing peak values, normally the outputs corresponding to the subcarriers used in the current sub-symbol. Such analysis may provide better results when performed after the frequency equalization.

Using a zero-padding transmission implies that the cyclic prefixes are added on the receiver side before demodulation, which implies the knowledge of q for applying the correct multiplication factor in the cyclic prefix (according to figure 5B). Value q being arbitrary and not known in advance by the receiver, the transmitter may be designed to systematically frequency-shift the selected sub-symbol g_k,q to a fixed subcarrier set r, known to both the transmitter and the receiver, as shown by a frequency shifter 74 applying a frequency-shift step of (r-q)/M. With such a choice, the receiver will systematically insert the cyclic prefixes applying the multiplication factor corresponding to subcarrier set r. The knowledge of q is still required to select the pseudo-random sequence and equalization channels to apply to the demodulated sub- symbol. The value r used in frequency shifter 74 may be modified according to a pattern known to both the transmitter and the receiver, for instance according to a shared secret key, to provide a level of encryption. A receiver that has no knowledge of the pattern will be unable to apply the correct multiplication factors for inserting the cyclic prefixes, and will fail to demodulate the sub-symbols. The pseudo-random sequences PRN may similarly be changed according to a pattern known to both the transmitter and the receiver, thus producing a second level of encryption.

Figure 8 is a block diagram of an embodiment of transmission circuitry that may even further reduce the peak-to-average power ratio PAPR. It is based on two partial N-point IFFT circuits 80a and 80b as depicted in figure 7, both receiving the current N/M-value frequency-domain vector X_k. The M inputs to the first partial IFFT circuit 80a are modified by pseudo-random sequences PRNA₀ to PRNA_M-i, whereas the M inputs to the second partial IFFT circuit 80b are modified by pseudo-random sequences PRNB₀ to PR B_M-1- The numbers in the sequences PRNA may be real, for example randomly selected among 1 and -1, whereas the numbers in the sequences PRNB may be imaginary, for example randomly selected among j and -j .

The partial IFFTs 80a and 80b thus produce M randomized sub-symbols ak_,o to ak,M-i and M randomized sub-symbols bk_,o to bk,M-i - All randomized sub-symbols are frequency-shifted at 82 to a same subcarrier set r, i.e. a sub-symbol a_k,i or b_k,i is frequency-shifted by a step (r-i)/M.

Value r is arbitrary between 0 and M-l and may be a fixed value or changed according to a pattern known to both the transmitter and the receiver to provide a level of encryption when zero-padding transmission is used, as explained previously in relation to figure 7.

An addition matrix 84 is configured to produce all the combinations of sums in pairs of the frequency-shifted sub-symbols a with the frequency-shifted sub-symbols b, i.e. produce M² sums of the form o_U;V = a_k,u + b_k,v, where u and v each vary between 0 and M-l . The sums may be divided by a normalization factor Λ/2 to preserve the average amplitude. A purpose of frequency-shifting all sub-symbols to the same subcarrier set is to ensure that each pair of sub-symbols to add conveys the same subcarriers.

Choosing real numbers for the sequences PRNA and imaginary numbers for the sequences PRNB (or the other way round) ensures in a relatively simple way that all sums are different and non-zero (provided the sequences PRNA are different, and the sequences PRNB are different). Any other choice for the pseudo-random numbers may be used to satisfy this property.

Like in figure 7, the PAPR of each of the M² sums o_U;V is evaluated in 72 and the sum σ_Μ having the lowest PAPR is selected for transmission. Such a sum thus uses the subcarrier set r, and has been randomized with sequences PRNA_P and PRNB_q.

On the receiver side, value r is known and defines the multiplication factor of the cyclic prefix (when zero-padding transmission is used) and the FFT positions conveying the sought data (when a zero-padded N-point FFT is used, as in figure 6). Values p and q are arbitrary and may be transmitted to the receiver in various know manners, such as by modulating one or several pilot tones. Values p and q may then be used in the receiver to identify the two pseudo-random sequences to use for recovering the original vector X_k from the FFT output. The original values of the vector X_k may be obtained by the following equation: X r + Μι) ·

f^{c W ~} PRNA_p(i) + PRNB_q (i)

Where X designates the N-value output vector of the N-point FFT, the indexes in parenthesis identify the values of the vectors, for i varying between 0 and N/M-1, and a is the inverse of the normalization factor used in the transmitter for producing the sums, here equal to 2. The receiver may also be configured as in figure 5A, using an N/M-point FFT producing an N/M-value vector X. Then the term X(r+Mi) in the above equation is replaced by X(i).

Since the above equation in fact involves vectors of same size, it may be said that the original vector X_k is recovered by dividing the demodulated sub-symbol by the sum of the pseudo-random sequences used in randomizing the transmitted sub-symbol, considering the division as a term-by-term division between vectors.

Figure 9 is a block diagram of a simplified version of the transmitter of figure 8 that may be used in certain applications. Instead of using two partial N-point IFFTs, the structure uses two groups of M N/M-point IFFTs 40. With this configuration, the sub-symbols a_k and b_k produced by the IFFTs all use the same N/M subcarriers, whereby no frequency-shifting is required before producing the sums in 84. The sum selected for transmission σ_Μ conveys the same N/M subcarriers.

The receiver side uses an N/M-point FFT and an N/M-frequency equalizer, requiring no frequency shifting and output remapping. The cyclic prefix uses no variable multiplication factor.

The transmission system is thus simpler than that of figure 8, but the system doesn't offer the encryption mechanism provided by the variable multiplication factor applied in the cyclic prefixes. Moreover, to avoid transmitting DC levels, data may be omitted on the first input of each IFFT circuit, i.e. Xk(0) = 0, which reduces the bit rate. The system is less robust to transmission channel deterioration, since fewer subcarriers are available for redistributing data transmitted on heavily attenuated subcarriers.

Claims

A data transmission method, comprising the following steps:

• providing N values (X) to transmit, where N is a power of 2;

• dividing the values in M vectors (X_k) of N/M values, where M is a power of 2;

• applying each vector in parallel to two groups (80a, 80b) of M N/M-point inverse Fourier transforms, producing a first and a second group of M sub- symbols (a_k, b_k);

• modifying the input of each inverse Fourier transform by a different pseudorandom number sequence (PRNA, PRNB);

• producing (84) combinations of sums in pairs (o_U;V) of sub-symbols from the first group with sub-symbols from the second group; and

• selecting (72) for transmission the sum (o_P;q) having the lowest peak-to- average power ratio (PAPR).

The method of claim 1, comprising the steps of:

• frequency-shifting (70) each z^'-th sub-symbol of each group by a step -i/N, where i varies between 0 and M-l, producing in each group M sub-symbols (g_k) conveying a different set of subcarriers;

• frequency-shifting (82) all sub-symbols to a common set of subcarriers (r); and

• producing the combinations of sums from the frequency-shifted sub-symbols. The method of claim 1, comprising the steps of:

• transmitting the selected sum as a sub-symbol;

• receiving the transmitted sub-symbol;

• demodulating the received sub-symbol; and

• dividing the demodulated sub-symbol by the sum of the pseudo-random sequences used in forming the transmitted sum.

4. The method of claim 2, comprising the steps of:

• transmitting the selected sum as a sub-symbol with zero-padded intervals;

• receiving the transmitted sub-symbol;

• inserting a cyclic prefix at the beginning of the received sub-symbol; · applying to the cyclic prefix a multiplication factor based on the common sub carrier set (r);

• demodulating the received sub-symbol; and

• dividing the demodulated sub-symbol by the sum of the pseudo-random sequences used in forming the transmitted sum. 5. The method of claim 4, comprising the steps of:

• changing the common subcarrier set after each transmitted sum according to a pattern; and

• sharing the pattern with the receiver.

6. The method of claim 3, comprising the steps of: · changing the pseudo-random sequences after each transmitted sum according to a pattern; and

• sharing the pattern with the receiver.

7. The method of claim 1, wherein the pseudo-random sequences applied in the first group of sub-symbols are real numbers, and the pseudo-random sequences applied in the second group of sub-symbols are imaginary numbers.