GB2426901A

GB2426901A - FDM/OFDM with reduced peak to average power ratio

Info

Publication number: GB2426901A
Application number: GB0615460A
Authority: GB
Inventors: Yanyan Wu
Original assignee: Samsung Electronics Co Ltd
Current assignee: Samsung Electronics Co Ltd
Priority date: 2003-12-12
Filing date: 2003-12-12
Publication date: 2006-12-06
Anticipated expiration: 2023-12-12
Also published as: GB2426901B; GB2409135A; GB0615460D0; GB0328895D0; GB2409135B

Abstract

A method of reducing PAPR in an OFDM transmission, including at the transmitter, preadjusting each subcarrier phase by an amount determined by a quadratic function of the subcarrier index and a predetermined factor, and at the receiver, recovering the predetermined factor from a pilot subcarrier and reversing the pre-adjustments to recover the signal. The factor may be found at the transmitter by a search method.

Description

( 2426901 Frequency Division Multiplexing The present invention relates to

frequency division multiplexing ((FDM), preferably orthogonal frequency division multiplexing (OFDM)) systems, transmitters and receivers, and to methods of transmitting a signal in an orthogonal frequency division multiplexing (OFDM) system.

Orthogonal Frequency Domain Multiplexing (OFDM) is a multi- carrier modulation technique that has been adopted for many wireless systems, such as wireless local-area networks (WLAN) and digital video broadcasting (DVB). OFDM distributes the data over a large number of carriers 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 sub-carriers, the data transmission rate on each subcarrier is at a lower rate which is less subject to multi-path delay spread. Therefore, OFDM is one of the most attractive choices for high data rate transmission in future mobile radio systems, and is a study item in 3GPP.

Details of OFDM in the context of satellite broadcasting are disclosed in W096/1 9055. Use of OFDM with encoding is disclosed in "Evaluation of error correction block encoding for high speed HF Data" - Brayer, K. and Cardinale, 0.; IEEE Transactions on Communication Technology vol. COM No. 3, June 1967, "A combined coding and modulation approach for communication over dispersive channels" - Chase, D.; IEEE Transactions on Communications vol. COM - 21 No. 3, March 1973. More recent examples

V

are US 4881241, US 4884139, US 5191576, US 5197061, US 5228025, US 5274629, and US 5307376.

The main problem of OFDM is a 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 OFDM waveform to its Root Mean Square (RMS) value. In an OFDM system, the PAPR can be high because it is possible for the signals in each sub-carrier to be in phase, thus potentially giving rise to a peak value that is the sum of all sub-carrier signals. This can cause problems as regards the transmitter power amplifier efficiency. The implication of this, in the mobile radio scenario, can be a reduced handset battery life or adequate area coverage.

Many approaches to reducing Crest Factor or PAPR are known, but some simpler methods (for example, clipping the amplitude of some carriers) reduce orthogonality and hence introduce distortion. W096/19055 teaches one method. Other known methods include using broadband pulse shaping for each sub carrier, and Active Constellation Extension (ACE) for the outer constellation points.

Two representative prior art approaches to reduce the PAPR are SLM (Selective Mapping) and PTS (Partial Transmitted Sequence). According to the SLM approach, transmission data blocks are partitioned into disjoint sub- blocks 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 both approaches (and their combined versions), the receiver must have the knowledge about the random chosen phases used at the transmitter in order to recover the data. Thus the main drawback for both schemes is that phase factors have to be transmitted as coded side information. This results not only in a more complicated system but also a dependency of receiver performance on the correct decoding of the side information, which in turn means that it needs heavy error protection (and hence an increased number of side or overhead bits to be transmitted).

It is known, as a numerical observation, that for FDM (also known as multi-tone) signals, the crest factor is reduced if the phases of each of the subcan-iers in the sequence are in a predetermined relationship to each other (for example, a predetermined sequence relationship in which the phase is a function of the subcarrier number). Boyd (S. Boyd, "Multi-tone signals with low crest factor", IEEE transactions on circuits and systems, vol. CAS-33, No. 10, October 1986) teaches that a sequence due to Shapiro and Rudin and a sequence due to Newman (the latter having phases of the subcarriers in a quadratic relationship) can be shown numerically to give a low crest factor, at least for small numbers of subcarriers.

However, for a given baseband modulation mapping such as Quadrature Phase Shift Keying (QPSK), the phase of the signal cannot be selected voluntarily. It would of course be possible to apply to each subcarrier a phase rotation to bring them into one of these predetermined phase relationships, on each symbol. However, it would then be necessary to transmit the set of phase rotations to the receiver end, which would involve as much side data as the symbol itself. Further, the set of data representing the phase rotations would in turn require phase rotation in order to control the crest factor of the OFDM symbol used to transmit it, and so on. These relationships have therefore not led to any useful crest factor reduction scheme for use with real-world data.

One of the objects of the present invention is to provide a PAPR reduction scheme which does not require transmission of large amounts of side information, and preferably no side information. Another is to provide such a scheme requiring only low implementation complexity. Another is to provide such a scheme requiring minimal changes to existing OFDM systems, thereby reducing incompatibility.

The invention in various aspects is defined in the claims. It relies on the inventive realisation that the application of subcarrier phase corrections in a predetermined relationship, characterised by one (or perhaps a small number of) coefficients, will give an improved performance where the adjustments for each subcarrier are related to the index (or frequency) of the subcarrier. It has been found, for example, that using a Newman-type series of phase corrections which are a quadratic function of the subcarrier number and a single coefficient, that a good reduction in PAPR can be found by deriving a suitable coefficient value.

Moreover, it is unnecessary to transmit this coefficient value where the FDM signal includes a pilot tone (as is common in OFDM) since the coefficient can be derived from the pilot tone, so that no supplementary information has to be transmitted in order be able to recover the transmitted data on the receiver side.

Additionally, a minimum PAPR can be obtained irrespective of an increase in the number of sub-carriers.

An embodiment of the invention will now be described with reference to the accompanying drawings, of which 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 adjustments 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 is a graph showing the PAPRs of an OFDM system using a QPSK signal with eight sub-carriers with and without quadratic signal phase synthesis; and Figure 5 is a graph showing the PAPR against varying values of the phase relationship coefficient.

Transmitter Figure 1 illustrates a block diagram of an OFDM transmitter I according to an embodiment of the invention. It is conventional except for the phase synthesis 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 Digital Signal Processor chips, or as custom-designed integrated circuits.

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

Successive frames of N symbols from the modulation mapped transmission data streams are fed to a serial to parallel converter block 3 and thereby multiplexed into N parallel data streams s0. ..SNC.j. at a lower data rate of l/N. Among the N treams there are at least one pilot tone (i. e. a predetermined symbol known to the receiver and carrying no data) on one or more predtermined subcarriers.

The parallel data streams are then fed,to a quadratic phase synthesis block 4 where they undergo a phase synthesis process, by which each symbol is multiplied by a phase rotation function, which has the effect of adding a corresponding phase shift to each symbol.

These data streams are then frequency-converted and combined for transmission as described below.

The phase rotation functions Cm for the subcarriers are a quadratic function of the subcarrier number m, and a linear function of a coefficient p. The synthesis function is defined as a quadratic phase function of the number of the subcarrier in (running from the first, m=O to the total number N-l): j2,r_c_m 2 Cm(P) = e N for m = 0,... N -1 pE[0, N-1J The relationship between the phase rotations is therefore similar in form to the "Newman" phase relationship described in Boyd. However, Boyd is describing the relationship is between the phases of the signals on each subcarrier, whereas in the present embodiment correction factor by which the original phase of each subcarrier signal is added. The phases of the subcarrier signals produced by the present embodiment are therefore not in the relationship described by Boyd or Newman.

Process of determining phase adjustments The value of p is the variable which governs the effectiveness of the correction applied by the embodiment. It can take one of multiple different values, and an appropriate value is selected afresh every OFDM symbol, by the phase synthesis block 4.

A local CF calculation block 7 is provided. It is arranged to calculate the crest factor (CF) of the output OFDM symbol which would be produced, if a test value of p were employed. It is operable to test the CFs of several different test values of p and feed back the results to be used to select an appropriate one of the test values, in an iterative search process.

Referring to Figure 2, for the first test value (step 102) the calculation block calculates a CF value and passes the value back to the phase synthesis block 4 (step 104). The phase synthesis block 4 then tests (step 106) whether the CF value is low enough to lie underneath a threshold value Th. If not (step 108) the phase synthesis block selects a next test value of pand the CF calculation block 7 once more returns the corresponding CF value. The process continues until a value of CF which is low enough to lie underneath a threshold value Th is located. This value is then selected (step 110) to transmit the OFDM symbol.

Subsequently, each of the data streams is modulated with a different OFDM subcarrier frequency.(modulation block 5), combined (combiner block 6) and then up-converted to a radio frequency carrier (not shown) for transmission. The modulation may be achieved using the inverse Fast Fourier Transform (IFFT) since the frequencies of OFDM are in the harmonic relationship used by the IIFFT.

It would be possible to perform an exhaustive search for the value of p which gave the lowest CF, but we have found that in practice this is not necessary, as we have found that there are many values of p giving low CFs, distributed across the range of p values, as shown in Figure 5.

For example, if QPSK is employed, and if the PAPR threshold Th is set to be 7dB, the number of OFDM symbols is 50,000 and the number of subcarrier signals 64, an average of 2.791 JFFTs (Inverse Fast Fourier Transforms) are required to determine a value of p resulting in a PAPR below 7dB. If instead, 64QAM is employed, then the average number of IFFTs required is 2.736. Generally, we have found that the number of IFFTs required in the search process is about 4% of the number of sub- carriers.

Thus, the search process can be conducted computationally quickly.

Reciever Referring to Figure 3, a receiver comprises demodulation and down- conversion stages (not shown), followed by a Fast Fourier Transform (FFT) stage 15 which separates the signal into its separate subcarrier channels. At each OFDM symbol, the phase on the pilot channel (in this case channel 0) is measured by a phase measurement device 17. From the measured phase the value of p is calculated, by a phase synthesis block 14, which then calculates for each subcarrier a phase correction using the calculated value of p and the subcarrier number, according to the expression i2,r- Se m=k 0 m!=k This is discussed in greater detail in the Appendix below.

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

The receiver may be implemented as one or more suitably programmed commercially available Digital Signal Processor chips, or as customdesigned integrated circuits.

Results of the embodiment Figure 4 shows the PAPRs of an OFDM system using a QPSK signal with eight sub-carriers with and without quadratic signal phase synthesis.

Figure 4 shows that the PAPR is reduced when a quadratic signal phase synthesis is employed.

Appendix Referring to Figure 1, the synthesis function is defined as a quadratic phase function of the number of sub-carrier m as follows c(p)=e N for m =1,*** N-1 pE[0,N-lI p is chosen among [0, N -1] at the transmitter to obtain the lowest PAR.

The transmission block is a time sequence, given in brackets below: j2-O N-I j2r-1-I N-I j2,r-'-(N-I) cmSoze, . 7'J=O m=O m=O

II

The usual OFDM reception is applied. The reception of sub-carrier k gives r J2!L() 1 -j2,r---n 1 J2ff(m_k)n Yk =_[cmSe N Je N N, pm2 (m-k)n j2n-j2,r = S,,, N, e N, For the received signal 12 iv Y*= Se N, m=k 0 m!=k Ideally one sub carrier used as pilot will allow p to be identified at the receiver.

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

For example, although an iterative search for finding the phase adjustments is described above, there may be a mathematical relationship between the set of input bits making up OFDM symbol and an appropriate value of p, which would allow it to be calculated directly rather than found by search. The present invention extends to such techniques.

Equally, phase relationships other than the quadratic relationship described herein may be used (and may be appropriate particularly if a non- OFDM multi-tone signal is used). Equally, although the use of a single factor p to characterise the relationship is described above, it may be possible to employ more than one factor, where the OFDM signal includes multiple pilot tones (as is often the case). Multiple pilot tones can also be used to more accurately recover a single factor. Alternatively, where the OFDM signal includes multiple pilot tones, the present invention may be applied separately to different groups of subcarriers each associated with a different pilot tone.

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 the skilled person 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

L

Claims 1. A method of reducing PAPR in an OFDM transmission, including at the transmitter, pre-adjusting each subcarrier phase by an amount determined by a quadratic function of the subcarrier index and a predetermined coefficient, and at the receiver, recovering the predetermined coefficient from a pilot sulcarrier and reversing the preadjustments to recover the signal.
2. An orthogonal frequency division multiplexing (OFDM) transmitter, comprising: a signal transformer for transforming an input signal into a plurality of sub-carrier signals N; and a synthesizer for synthesizing the phase of each of the sub-carrier signals N using a quadratic phase synthesis function.
3. A method of generating a signal for transmission in an orthogonal frequency division multiplexing (OFDM) system, comprising: transforming an input signal into a plurality of sub-carrier signals N; and synthesizing the phase for each of the sub-carrier signals N using a quadratic phase synthesis function.
4. Frequency division multiplexing (FDM) modulator apparatus, comprising means for transforming an input signal into a plurality of sub- 4L carrier signals N making up a multi-carrier signal and means for reducing the ratio of peak to mean amplitude of the multi-carrier signal, characterised in that the peak to mean reduction means performs, for each FDM symbol, a separate and different phase adjustment to the phase of each of the sub-carrier signals N, the phase adjustments being a function of the subcarrier frequency or number, and of at least one coefficient which is the same across all said subcarriers, and in that the peak to mean reduction means derives the value of the coefficient for each FDM symbol.
5. Apparatus according to claim 4, wherein the peak to mean reduction means derives the value of the coefficient by a process of testing the effect on the peak to mean ratio of a plurality of candidate values of the coefficient, and selecting one of said candidate values.
6. Apparatus according to claim 5, wherein the peak to mean reduction means is operable to test, for each candidate value, whether the peak to mean ratio would lie below a predetennined threshold, and to select a candidate value which does lie therebelow.
7. Apparatus according to claim 5, wherein the peak to mean reduction means is operable to select the candidate value which would give rise to the lowest peak to mean ratio. 4'
8. FDM transmitter apparatus comprising a modulator according to any of claims 4 to 7, and means for transmitting the modulated signal.
9. Frequency division multiplexing (FDM) demodulator apparatus, comprising means for transforming a multiplexed input signal made up of a plurality of sub-carrier signals N into a time-domain output signal, and means for compensating the effect of peak to mean adjustment, characterised in that the compensating means performs, for each FDM symbol, a separate and different phase adjustment to the phase of each of the sub-carrier signals N, the phase adjustments being a function of the subcarrier frequency or number, and of at least one coefficient the same across all subcarners, and in that the compensating means derives the value of the coefficient for each FDM symbol from one or more of said sub- carrier signals.
10. Apparatus according to claim 9, in which the compensating means derives the value of the coefficient only from one or more of said subcarrier signals and not from any separately transmitted side information.
11. Apparatus according to claim 10, in which the compensating means derives the value of the coefficient from one or more pilot sub-carriers.
12. Apparatus according to any preceding claim, in which the modulation is orthogonal FDM (OFDM).
13. Apparatus according to any preceding claim, in which the phase adjustments are a quadratic function of the subcarrier number.
14. Apparatus according to claim 13, in which the coefficient is a secondorder coefficient.
15. Apparatus according to claim 14, wherein the quadratic phase synthesis function is j2,r---m 2 Cm(P) = e N for in = O,*. N -1 pE[O,N -1] where m is the subcarrier number and p is the coefficient.
16. Apparatus according to any preceding claim, wherein the signal is modulated using PSK (Phase Shift Keying).
17. Apparatus according to any preceding claim, wherein the signal is modulated using quadrature amplitude modulation (QAM).
18. An FDM signal, comprising, at each symbol, a plurality of subcarriers, characterised in that the phase of each subcarrier is adjusted by a separate and different phase adjustment, the phase adjustments being a function of the subcarrier frequency or number, and of at least one coefficient which is the same across all subcarriers, so that the peak to mean ratio of the multi-carrier ( signal is lower than that which would be exhibited by an otherwise identical signal in which said phase adjustments were not present.
19. A method of reducing the peak-to-average power (PAPR) ratio of a frequency division multiplexed signal comprising a plurality of subcarrier signals N; the method being characterised by: periodically adjusting the phase for each of the sub-carrier signals N using a phase synthesis function in which the phase for each subcarrier is a function of the subcarrier frequency or number, and of at least one coefficient which is the same across all subcarriers.
20. The method of claim 19, in which the signal is an orthogonal FDM (OFDM) signal.
21. The method of claim 19, in which the phase adjustments are a quadratic function of the subcarrier number.
22. The method of claim 21, in which the coefficient is a second-order coefficient.
23. The method of claim 22, wherein the quadratic phase synthesis function is j2,r Cm (p) = e N for ni = 0, N - I p [0, N -I] where m is the subcarrier number and p is the coefficient.
24. The method of claim 19, wherein the signal is modulated using PSK (Phase Shift Keying).
25. The method of claim 19, wherein the signal is modulated using quadrature amplitude modulation (QAM).
26. The method of claim 19, in which the value of said coefficient is determined by iterative search.