WO2011026266A1

WO2011026266A1 - The realization of minimum crest factor for multicarrier systems

Info

Publication number: WO2011026266A1
Application number: PCT/CN2009/073663
Authority: WO
Inventors: Yanyan Wu
Original assignee: Xi'an Jiaotong-Liverpool University
Priority date: 2009-09-01
Filing date: 2009-09-01
Publication date: 2011-03-10

Abstract

A method of reducing PAPR for a multiple carrier transmission systems is invented, including at the transmitter, pre-adjusting each subcarrier phase by an amount determined by a polynomial function of the subcarrier index with a set of predetermined coefficients, and at the receiver, recovering the predetermined coefficients from pilot subcarriers and reversing the pre-adjustments to recover the signal of each subcarrier. The coefficients of the polynomial function may be determined at the transmitter by a search method.

Description

The realization of minimum crest factor for multicarrier systems

Field of the invention

The present invention relates to Multiple Carrier (MC) systems, preferably Orthogonal Frequency Division Multiplexing (OFDM) systems, digital baseband design for transmitters and receivers.

Background

Multiple carrier transmission, in particular OFDM, has been adopted for many wireless systems, such as Worldwide Interoperability for Microwave Access (WiMax), 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE), Wireless Local-Area Networks (WLAN), and Digital Video Broadcasting (DVB). OFDM distributes the data over a large number of subcarriers spaced apart at precise frequencies in a particular relationship. The spacing is the minimum possible whilst maintaining orthogonality, and due to its feature of multiple narrow-band subcarriers, the data transmission on each subcarrier is at a lower rate which make it less subject to multipath delay spread. Therefore, OFDM is the most attractive multiple carrier scheme for high data rate transmission in future mobile radio systems.

The major drawback of multiple carrier systems is the high Peak to Average Power Ratio (PAPR) - also known as the Crest Factor - which is defined as the ratio of the peak value of the signal waveform to its Root Mean Square (RMS) value, often given in decibels. The main cause of large PAPRs is when phases in the subcarriers line up in a fashion results in constructively forming peaks in the time-domain signal. These large peaks demand linear and consequently in-efficient amplifier at the analogue front of the transmitter.

Many approaches to reduce PAPR or Crest Factor are known; some simpler methods (for example, clipping the amplitude of the signal) reduce orthogonality and hence introduce distortion. WO96/19055 teaches one method. Three representative prior art approaches to reduce the PAPR are SLM (Selective Mapping), PTS (Partial Transmitted Sequence) and Convex Optimisation. According to the SLM approach, transmission data blocks are partitioned into disjoint subblocks which are subsequently re-combined with a phase distortion, thereby to minimise the PAPR. According to the PTS approach, M statistically independent data sequences are generated by multiplying the data sequence containing the information to be transmitted with M random data sequences of the same length. The sequence with the lowest PAPR is transmitted. In the convex optimisation approach (using subgradient method), tone reservation method or constellation extension method, or their combination is used. The subgradient algorithm is applied to update the reserved tones or data-carrying tones to realise PAPR reduction.

Apart from drawbacks such as data rate loss due to either side information transmission or the reserved tones in the system, these prior art approaches treat the PAPR problem with phase rotations only to limited number of subcarriers or with limited rotations to all subcarriers, hence the crest factor can be achieved is local minima. The crest factors achieved using these approaches are therefore much higher than the minimum crest factor Kahane suggested (J.P. Kahane, "Sur les polynomes a coefficients unimodulaires", Bull. London Math. Soc, nol2, pp321-342, 1980).

Kahane teaches there exist of phases of a multiple carrier signal which yield crest factor approached 3dB for a real signal, and 1.5dB for a complex signal irrespective of the number of subcarriers. However Kahane' s proof uses a probabilistic argument, it remains unknown how one can directly construct these phases. To complicate the problem further, with a baseband modulation mapping such as Quadrature Phase Shift Keying (QPSK), the phase of the subcarrier signal cannot be selected voluntarily.

It is also known from Boyd (S. Boyd, "Multi-tone signals with low crest factor", IEEE transactions on circuits and systems, vol. CAS-33, No.10, October 1986) that for a multi-carrier signal, the crest factor is reduced if the phase of each of the subcarriers in the sequence is in a predetermined relationship to each other. Boyd teaches that a sequence due to Shapiro and Rudin and a sequence due to Newman can be shown numerically to give a low crest factor. In particular, with Newman phases, 4.6dB crest factor for real signal and 2.3dB crest factor for complex signal are achieved at least for a MC signal with up to a few hundred subcarriers.

GB2409135 describes a phase rotation scheme that introduces a systematic phase rotation to the original phases; the phase rotation is given by a function similar in the form to the "Newman" phase described by Boyd. The scheme provides a suboptimum solution for PAPR reduction of a multi-carrier signal, yet the crest factor achieved is well above the minim crest factor suggested by Kahane. Summary of the invention

One of the objectives of this invention is to provide a method to construct a sequence of phases that lead to minimum crest factor for a multiple carrier system with any digital baseband modulation such as QPSK or QAM. Another is that side information about phase distortion can be embedded in the pilot tones, hence no extra side information required for reception. Another is to provide such a scheme requiring compatible changes to existing OFDM systems.

The invention in various aspects is defined in the claims. It relies on the inventive realisation that phases of the subcarriers line up in a fashion that leads to the minimum crest factor can be expressed in a polynomial function of subcarrier number or index. Hence the phase adjustment for each subcarrier with the original starting phase of digital modulation, related to a polynomial function of the index of the subcarrier characterised by a set of polynomial coefficients, will give a significant improved performance in PAPR reduction. The order of the polynomial can be decided in advance depending on the approximation to the minimum CF expected and the number of subcarriers in the system.

Moreover, it is unnecessary to transmit these coefficient values since the coefficients can be derived from the pilot tones used in the MC system for synchronisation and channel estimation purpose, so that no supplementary information has to be transmitted in order be able to recover the transmitted data on the receiver side.

Additionally, the same crest factor can be obtained irrespective of an increase in the number of subcarriers.

Brief introduction of the drawings

Figure 1 is a block diagram of an OFDM transmitter according to an embodiment of the invention;

Figure 2 is a flow diagram showing the process of deriving a phase adjustment in the embodiment of Figure 1 ;

Figure 3 is a block diagram of an OFDM receiver according to the embodiment of Figure 1 ;

Figure 4 and Figure 5 demonstrate the performance of PAPR reduction of the invention in Figure 1, showing the Complementary Cumulative Distribution Function (CCDF) of PAPRs of 64QAM OFDM for 16 subcarriers and 8 subcarriers respectively.

Descriptions of embodiment

An embodiment of the invention will now be described with reference to the accompanying drawings.

Transmitter

Figure 1 illustrates a block diagram of an OFDM transmitter 1 according to an embodiment of the invention. It is conventional except for the phase adjustment described below, and suitable digital signal processing hardware is known and widely available. It may for example be implemented as one or more suitably programmed commercially available field-programmable gate array (FPGA), or as custom-designed integrated circuits.

Transmission binary data sequence 101 1 .. . is mapped into complex symbols in a baseband modulation mapping block 2 using QPSK (Quadrature Phase Shift Keying), or 64QAM (64-state Quadrature Amplitude Modulation) or any other suitable digital modulation technique.

Successive frames of complex symbols obtained by the digital modulation mapping are fed to a serial to parallel converter block 3 and thereby being multiplexed into N_c parallel data streams S₀ ^(l) (i)...S _Nc. ^l) at a lower data rate of 1/ N_c, where the superscript indicates i-th frame. Among the N_c streams there are pilot symbols (i.e. predetermined symbol carry data known to the receiver).

The parallel data streams are then fed to a phase adjustment block 4 where each symbol of the parallel data streams is multiplied by an exponential function with only an imaginary exponent given by a polynomial function of the subcarrier number or index, which has the effect of adding a corresponding phase to each symbol.

The phase adjustment for kth subcarrier is defined as m-order polynomial function of the subcarrier index k with a set of coefficients a_{l 5} a_2, ¾ (running from the first, k=0 to the total number N_c -1):

p (k ) = _e

a_m k - ) _{fof k = Q A N c} _ _l

Where the polynomial coefficients

«_; e [0, 1] for i = lK m

The order of the polynomial can be decided in advance depending on the approximation to the minimum CF expected and the number of subcarriers in the system. A set of coefficients values is selected afresh every OFDM symbol, based on the initial phases of digital modulation.

Subsequently, the data streams are IFFT-converted in block 5 for up-converting to a radio frequency carrier (not shown) for transmission.

The phase adjustment is therefore similar in schematic to that described in GB2409135. However, GB2409135 is describing a second order function of subcarrier index k, with only one linearly varied coefficient, whereas in the present embodiment, it is a polynomial function with a set of coefficients, preferably inversely varied. Note also in the present embodiment, the phase of each subcarrier signal is the sum of the original phase and the phase rotation introduced by the polynomial function, and the same set of polynomial coefficients are shared by all the subcarriers (including pilot tones).

The phases of the subcarrier signals produced by the present embodiment are therefore not in the relationship with that described in GB2409135.

Process of determining phase adjustments

The values of polynomial coefficients are the variables which govern the effectiveness of the phase adjustment applied by the embodiment. Each can take one of multiple different values, and a set of appropriate values is selected afresh every OFDM symbol, based on the initial phases of digital modulation, by the coefficients search block 6.

Block 6 is arranged to find a set of polynomial coefficients that would produce an expected crest factor (CF) for the output OFDM signal. It is operable to test different values of polynomial coefficients and to select an appropriate set of polynomial coefficients. It is also operable to test different order of the polynomial and to decide the order needed to achieve the expected CF.

In order to identify a set of values that would give the lowest CF, it is possible to perform an exhaustive search through a set of possible values of polynomial coefficients. For example, we may define the i-th order polynomial coefficient a_i such that

a_i = l/(N_c - S) where δ = 0,1...(N_c - 1)

This gives us Nc candidate values of a_i to test. Nonetheless other traditional algorithm such as subgradient search can also be applied. Referring to Figure 2, for the first set of test values (step 102), the CF or an equivalent indicator such as peak power is calculated, If the CF, or as indicated by the peak power, lies above or equal to a threshold value Th. (step 108), a different set of coefficients are selected among the candidate values and passed back to the phase adjustment block 4 (step 104). This would allow a next calculation of CF, or the equivalent indicator. The search would end if CF, or as indicated, is low enough to lie underneath a threshold value. The set of coefficients are then selected (step 110) for the phase adjustment purpose in block 4 to transmit the OFDM symbol.

The above search process can be repeated for different order of the polynomial for a random set of MC signals to obtain the performance curves as shown in Figure 4 and Figure 5. This would allow us to decide in advance the order of polynomial required to approximate certain CF, given the number of subcarrier in the system.

Receiver

Referring to Figure 3, a receiver comprises demodulation and down-conversion block (not shown), followed by a Fast Fourier Transform (FFT) block 12 which separates the signal into its separate subcarrier channels. At each OFDM symbol, the coefficients are calculated using the phases of the pilot symbols in coefficient calculation block 15. The phase recovery block 13 then recovers the original phase for each subcarrier using the known polynomial function according to the expression

ί

S_k = y_ke for = 0,A N_C - 1

The other channel corrections conventionally applied to OFDM signal processing are also applied as appropriate. The recovered signals are then converted by a parallel-to-serial convertor 14 back into a time-domain sequence which is output for decoding.

The receiver may be implemented as one or more suitably programmed commercially available FPGA, or as custom-designed integrated circuits.

Results of the embodiment

Phase adjustments with polynomial function of 1st order to 6th order are shown to reduce the crest factor to different levels, and to approximate the minimum crest factor gradually.

It is observed that using 6-order polynomial function for phase adjustment, the threshold can be reduced to below3 dB with the probability of 10-3 of the OFDM signal envelop exceeding it.

It should be noted that the invention is not limited to the above-described exemplary embodiment and it will be evident to a person skilled in the art that various modifications may be made without departing from the principle of the invention.

For example, the coefficients can be given in different granularity such that possible values for exhaustive search can be reduced or expanded. And although a search algorithm for finding the phase adjustment is described above, there may be a mathematical relationship between the initial phases of OFDM subcarriers and an appropriate set of values of the polynomial coefficients, which would allow them to be calculated directly rather than found by search. The present invention extends to such technique.

Equally, although the use of a set of coefficients to characterise the polynomial relationship is described above, it may be possible to employ only a subset of the coefficients for a suboptimum result. On the other hand, extra pilot tones can also be used to more accurately recover the polynomial coefficients. Alternatively, where the OFDM signal includes multiple pilot tones, the present invention may be applied separately to different groups of subcarriers each associated with different pilot tones.

Although transmission and reception are described, the invention may be practised using recording onto, and reproduction from, a recording medium.

These and any other variants apparent to person skilled are intended to be covered by the claims. For the avoidance of doubt, protection is sought for any and all novel subject matter contained herein.

Claims

1. A multicarrier transmitter apparatus comprises transforming means, for transforming an input signal into a plurality ofN_c subcarrier signals making up a multicarrier signal; PAPR reduction means, for reducing the ratio of peak to average power of the multi-carrier signal; and transmitting means, for transmitting the modulated signal. The multicarrier transmitter apparatus is characterised in that the PAPR reduction means performs, for each multicarrier (MC) symbol, a separate and different phase adjustment to the phase of each of the subcarrier signals, the phase adjustment being a polynomial function of the subcarrier number or index with a set of coefficients which are the same across all said subcarriers, and in that the PAPR reduction means derives the values of coefficients for each MC symbol.

2. The apparatus according to claim 1, wherein the PAPR reduction means derives the value of the coefficients by a process of testing the effect on the peak to average power ratio of a plurality of candidate values of the coefficients.

3. The apparatus according to claim 2, wherein the PAPR reduction means is operable to test, for each set of candidate coefficients, whether the peak to average power ratio lies below a predetermined threshold, and to select one set of candidate coefficients which allows such peak to average power ratio.

4. The apparatus according to claim 2, wherein the PAPR reduction means is operable to select a set of candidate coefficients which gives the lowest peak to average power ratio.

5. A multicarrier transmitter apparatus according to any preceding claim, in which the phase adjustment is performed based on a polynomial function of the subcarrier number or index.

6. The apparatus according to claim 5, wherein the order of the polynomial can be decided in advance depending on the approximation to the minimum CF expected, and the number of subcarriers in the system.

7. The multicarrier transmitter apparatus according to claim 5 and claim 6, wherein an m-order polynomial function for phase adjustment is given by p (k ) = β ^]π ^ ^{+ α}^ ^{+Κ α}^ for k = 0 ,A N _c - 1

Where the polynomial coefficients,

«_; e [0, 1] for i = lK m

8. A multicarrier transmitter apparatus according to any preceding claim, in which the modulation can be orthogonal FDM (OFDM).

9. The multicarrier transmitter apparatus according to any preceding claim, wherein the signal is modulated using PSK (Phase Shift Keying).

10. The multicarrier transmitter apparatus according to any preceding claim, wherein the signal is modulated using quadrature amplitude modulation (QAM).

11. A multicarrier receiver apparatus comprises downconverting and demodulation means, for obtaining baseband signal; demultiplexing means, for demultiplexing input signal made up of a plurality of N_c subcarrier signals; and phase correction means, for reversing the phase adjustments. The multicarrier receiver apparatus is characterised in that the phase correction means performs, for each MC symbol, a separate and different phase correction to the phase of each of the Nc subcarrier signals, the phase correction being a negation of said phase adjustment in preceding claims, and in that the correction means derives the values of the coefficients for each MC symbol from one or more of said subcarrier signals.

12. The apparatus according to claim 11, wherein the correction means derives the value of the coefficients only from one or more of said subcarrier signals, typically pilot subcarriers.

13. A method of reducing the peak-to-average power (PAPR) ratio of a multiple carrier signal comprising a plurality of N_c subcarrier signals; the method being characterised by adjusting the phase for each of the N_c subcarrier signals.

14. The method according to claim 13, wherein the phase adjustment is based on a polynomial function of the subcarrier number or index.

15. The method according to claim 13 and claim 14, wherein the order of the polynomial can be decided in advance depending on the approximation to the minimum CF expected, and the number of subcarriers in the system.

16. The method according to claim 13, claim 14 and claim 15 , wherein an m-order polynomial function for phase adjustment is given for k^th subcarrier as p ( k ) = _e J- (^ ₊ a ₂^ ₊A a _{m k} - ) _{for k = 0 A N c} _ _{

Where the polynomial coefficients,

a_i e [0 , 1] for i = lK m

17. The method according to claim 13, wherein the signal can be an orthogonal FDM (OFDM) signal.

18. The method according to claim 13, wherein the subcarriers signal is modulated using PSK (Phase Shift Keying).

19. The method according to claim 13, wherein the subcarriers signal is modulated using quadrature amplitude modulation (QAM).

20. The method according to claim 16, wherein the values of said coefficients are determined by exhaustive search through the candidate values.

21. The method according to claim 16, wherein the values of said polynomial coefficients are determined by iterative search method such as subgradient method.

22. The method according to claim 16, wherein the values of said polynomial coefficients are calculated directly.