# Patent

## Title
Constellation rearrangement for ARQ transmit diversity schemes

## Abstract

An ARQ (re-) transmission method of transmitting data in a wireless communication system wherein data packets are transmitted from a transmitter to a receiver, using a first transmission and a second transmission based on a repeat request. The method comprises the steps of modulating data at the transmitter using a first signal constellation pattern to obtain a first data symbol. The first data symbol is transmitted as the first transmission to the receiver using a first diversity branch. Further, the data is modulated at the transmitter using a second signal constellation pattern to obtain a second data symbol. Then, the second data symbol is transmitted as the second transmission to the receive over a second diversity branch. Finally, the received first and second data symbol data symbol are diversity combined at the receiver. The invention further relates to a transmitter and a receiver embodied to carry out the method of the invention.

## Background
This is a divisional of application Ser. No. 12/490,096 (now abandoned) filed Jun. 23, 2009, which is a continuation of application Ser. No. 11/633,421 filed Dec. 5, 2006 now U.S. Pat. No. 7,567,622, which is a continuation of application Ser. No. 10/501,906 filed Dec. 6, 2004 now U.S. Pat. No. 7,154,961, which is a national stage of PCT/EP2002/011694 filed Oct. 18, 2002, the entire contents of each which are incorporated by reference herein.


The present invention relates generally to ARQ (re-) transmission techniques in wireless communication systems and in particular to a method, transceiver arid receiver using transmit diversity schemes wherein data packets are transmitted using a first and a second transmission based on a repeat request, and the bit-to-symbol mapping is performed differently for different transmitted diversity branches. The invention is particularly applicable to systems with unreliable and time-varying channel conditions resulting in an improved performance avoiding transmission errors.
There exist several well known transmit diversity techniques wherein one or several redundancy versions relating to identical data are transmitted on several (at least two) diversity branches “by default” without explicitly requesting (by a feedback channel) further diversity branches (as done in an ARQ scheme by requesting retransmissions). For example the following schemes are considered transmit diversity:

    
    
        Site Diversity: The transmitted signal originates from different sites, e.g. different base stations in a cellular environment.
        Antenna Diversity: The transmitted signal originates from different antennas, e.g. different antennas of a multi-antenna base station.
        Polarization Diversity: The transmitted signal is mapped onto different polarizations.
        Frequency Diversity: The transmitted signal is mapped e.g. on different carrier frequencies or on different frequency hopping sequences.
        Time Diversity: The transmitted signal is e.g. mapped on different interleaving sequences.
        Multicode Diversity: The transmitted signal is mapped on different codes in e.g. a CDMA (Code Division Multiple Access) system.
    
    


There are known several diversity combining techniques. The following three techniques are the most common ones:

    
    
        Selection Combining: Selecting the diversity branch with the highest SNR for decoding, ignoring the remaining ones.
        Equal Gain Combining: Combining received diversity branches with ignoring the differences in received SNR.
        Maximal Ratio Combining: Combining received diversity branches taking the received SNR of each diversity branch into account. The combining can be performed at bit-level (e.g. LLR) or at modulation symbol level.
    
    


Furthermore, a common technique tor error detection/correction is based on Automatic Repeat reQuest (ARQ) schemes together with Forward Error Correction (FEC), called hybrid ARQ (HARQ). If an error is detected within a packet by the Cyclic Redundancy Check (CRC), the receiver requests the transmitter to send additional information (retransmission) to improve the probability to correctly decode the erroneous packet.
In WO-02/067491 A1 a method for hybrid ARQ transmissions has been disclosed which averages the bit reliabilities over successively requested retransmissions by means of signal constellation rearrangement.
As shown therein, when employing higher order modulation formats (e.g. M-PSK, M-QAM with log2(M)>2), where more than 2 bits are mapped onto one modulation symbol, the bits have different reliabilities depending on the chosen mapping. This leads for most FEC (e.g. Turbo Codes) schemes to a degraded decoder performance compared to an input of more equally distributed bit reliabilities.
In conventional communication systems the modulation dependent variations in bit reliabilities are not taken into account and, hence, usually the variations remain after combining the diversity branches at the receiver.
The object of the invention is to provide an ARQ (re-) transmission method, a transmitter and a receiver which show an improved performance with regard to transmission errors. This object is solved by a method, transmitter and receiver as set forth in the independent claims,
The invention is based on the idea to improve the performance at the receiver by applying different signal constellation mappings to the available distinguishable transmit diversity branches and ARQ (re-) transmissions. The invention is applicable to modulation formats, where more than 2 bits are mapped onto one modulation symbol, since this implies a variation in reliabilities for the hits mapped onto the signal constellation. The variations depend on the employed mapping and on the actually transmitted content of the bits.
Depending on the employed modulation format and the actual number of bits mapped onto a single modulation symbol, for a given arbitrary number (N>1) of available diversity branches and required retransmissions the quality of the averaging process is different. Averaging in the sense of the present invention is understood as a process of reducing the differences in mean combined bit reliabilities among the different bits of a data symbol. Although if might be that only after using several diversity branches or paths a perfect averaging with no remaining differences is achieved, averaging means in the context of the document any process steps in the direction of reducing the mean combined bit reliability differences. Assuming on average an equal SNR for all available diversity branches and ARQ transmissions, for 16-QAM 4 mappings (4 diversity branches) would be needed to perfectly average out the reliabilities for all bits mapped on any symbol. However, not always the number of available transmit diversity branches and/or the number of ARQ transmissions is sufficient to perform a perfect averaging. Hence, the averaging should then be performed on a best effort basis as shown in the example below.
The present invention will be more, readily understood from the following detailed description of preferred embodiments with reference to the accompanying figures which show:



BRIEF DESCRIPTION OF THE DRAWINGS 
FIG. 1 an example for a 16-QAM signal constellation;
FIG. 2 an example for a different mapping of a 16-QAM signal constellation;
FIG. 3 two further examples of 16-QAM signal constellations;
FIG. 4 an exemplary embodiment of a communication system according to the present invention;
FIG. 5 details of a table for storing a plurality of signal constellation patterns; and
FIG. 6 shows the communication system according to the present invention with an interleaver/inverter section.



DETAIL DESCRIPTION OF THE DRAWINGS
The method described here performs a combined averaging of bit reliabilities considering the transmit diversity branches. The following detailed description is shown for a square 16-QAM with Gray mapping. However, without loss of generality the shown example is extendable to other M-QAM and M-PSK (with log2(M)>2) formats. Moreover, the examples are shown for transmit diversity and HARQ schemes transmitting an identical bit-sequence on both branches and all HARQ transmissions (single redundancy version scheme). Then again, an extension to a transmit diversity and HARQ scheme transmitting only partly identical bits on the diversity branches and HARQ transmissions can be accomplished. An example for a system using multiple redundancy versions is described in copending EP 01127244, filed on Nov. 16, 2001. Assuming a Turbo encoder, the systematic bits can be averaged on a higher level as compared to the parity bits.
Although the below examples give details of an embodiment with the special case of hybrid ARQ (HARQ), it should be noted that the inclusion of an FEC code is not necessary for the present invention to show performance gains. However the highest performance gains can be achieved with the use of HARQ.
The following example describes a method with two diversity branches and HARQ.
1st Transmission:
Assuming a transmit diversity scheme with two generated diversity branches, which are distinguishable at the receiver (e.g. by different spreading or scrambling codes in a CDMA system) and a transmission of the same redundancy version, usually the received diversity branches are combined at the receiver before applying the FEC decoder. A common combining technique is the maximal ratio combining, which can be achieved by adding the calculated log-likelihood-ratios LLRs from each individual received diversity branch.
The log-likelihood-ratio LLR as a soft-metric for the reliability of a demodulated bit b from a received modulation symbol r=x÷jy is defined as follows:




  
    
      
        
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As can be seen from FIG. 1 (bars indicate rows/columns for which the respective bit equals 1), the mappings of the in-phase component bits and the quadrature component bits on the signal constellation are orthogonal (for M-PSK the LLR calculation cannot be simplified by separating into complex components, however the general procedure of bit-reliability averaging is similar). Therefore, it is sufficient to focus on the in-phase component bits i1 and i2. The same conclusions apply then for q1 and q2.
Assuming that Mapping 1 from FIG. 1 is applied for the bit-to-symbol mapping for the 1st diversity branch, the log-likelihood-ratio LLR of the most significant bit (MSB) i1 and the least significant bit (LSB) i2 yields the following equations for a Gaussian channel:




  
    
      
        
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where x denotes the in-phase component of the normalized received modulation symbol r and K is a factor proportional to the signal-to-noise ratio. Under the assumption of a uniform signal constellation (x1=3x0) equations (2) and (3) can be fairly good approximated approximated, as shown in S. Le Goff, A. Glavieux, C. Berrou, “Turbo-Codes and High Spectra Efficiency Modulation,” IEEE SUPERCOMM/ICC '94, Vol. 2, pp. 645-649, 1994, and Ch. Wengerter, A. Golitschek Edler von Elbwart, E. Seidel, G. Velev, M. P. Schmitt, “Advanced Hybrid ARQ Technique Employing a Signal Constellation Rearrangement,” IEEE Proceedings of VTC 2002 Fall, Vancouver, Canada, September 2002, by

LLR(i1) ̃−4Kx0x  (4)

LLR(i2) ̃−4Kx0(2x0−|x|)  (5)

The mean LLR for i1 and i2 for a given transmitted modulation symbol yields the values given in Table 1 (substituting 4Kx02 by Λ). Mean, in this sense, refers to that the mean received value for a given transmitted constellation point, exactly matches this transmitted constellation point. Individual samples of course experience noise according to the parameter K. However, for a Gaussian channel the mean value of the noise process is zero. In case of transmitted modulation symbols 0q11q2 and 1q11q2 where q1 and q2 are arbitrary, the magnitude of the mean LLR (11) is higher than of the mean LLR (i2). This means that the LLR for the MSB i1 depends on the content of the LSB i2; e.g. in FIG. 1 i1 has a higher mean reliability in case the logical value far i2 equals 1 (leftmost and rightmost columns). Hence, assuming a uniform distribution of transmitted modulation symbols, on average 50% of the MSBs i1 have about three times the magnitude in LLR of i2.







TABLE 1







Mean LLRs for bits mapped on the in-phase component


of the signal constellation for Mapping 1 in


FIG. 1 according to equations (4) and (5).










Symbol
Mean value
Mean
Mean


(i1q1i2q2)
of x
LLR (i1)
LLR (i2)





0q10q2
 x0
−4Kx02 = −Λ
−4Kx02 = −Λ


0q11q2
 x1
−12Kx02 = −3Λ
4Kx02 = Λ


1q10q2
−x0
4Kx02 = Λ
−4Kx02 = −Λ


1q11q2
−x1
12Kx02 = 3Λ
4Kx02 = Λ









If now adding a 2nd transmit diversity branch transmitting e.g. an identical bit sequence prior art schemes would employ an identical mapping to the 1st diversity branch. Here, it is proposed to employ a 2nd signal constellation mapping (Mapping 2) according to FIG. 2, which yields the mean LLRs given in Table 2.







TABLE 2







Mean LLRs for bits mapped on the in-phase component


of the signal constellation for Mapping 2 in FIG. 2.












Symbol
Mean value
Mean
Mean



(i1q1i2q2)
of x
LLR (i1)
LLR (i2)







0q10q2
 x0
−Λ
−3Λ



0q11q2
 x1
−Λ
 3Λ



1q10q2
−x0
 Λ
 −Λ



1q11q2
−x1
 Λ
 Λ










Comparing now the soft-combined LLRs of the received diversity branches applying the constellation rearrangement (Mapping 1+2) and applying the identical mappings (Mapping 1+1, prior art), it can be observed from Table 3 that the combined mean LLR values with applying the constellation rearrangement have a more uniform distribution (Magnitudes: 4×4Λ and 4×2Λ instead of 2×6Λ and 6×2Λ). For most FEC decoders (e.g. Turbo Codes and Convolutional Codes) this leads to a better decoding performance. Investigations have revealed that in particular Turbo encoding/decoding systems exhibit a superior performance. It should be noted, that the chosen mappings are non exhaustive and mere combinations of mappings fulfilling the same requirements can be found.







TABLE 3







Mean LLRs (per branch) and combined mean LLRs for bits


mapped on the in-phase component of the signal constellation


for the diversity branches when employing Mapping 1


and 2 and when employing 2 times Mapping 1.












Constellation
Prior Art




Rearrangement
No Rearrangement


Transmit

(Mapping 1 + 2)
(Mapping 1 + 1)












Diversity
Symbol
Mean
Mean
Mean
Mean


Branch
(i1q1i2q2)
LLR (i1)
LLR (i2)
LLR (i1)
LLR (i2)





1
0q10q2
 −Λ
 −Λ
 −Λ
−Λ



0q11q2
−3Λ
 Λ
−3Λ
 Λ



1q10q2
 Λ
 −Λ
 Λ
−Λ



1q11q2
 3Λ
 Λ
 3Λ
 Λ


2
0q10q2
 −Λ
−3Λ
 −Λ
−Λ



0q11q2
 −Λ
 3Λ
−3Λ
 Λ



1q10q2
 Λ
 −Λ
 Λ
−Λ



1q11q2
 Λ
 Λ
 3Λ
 Λ


Combined
0q10q2
−2Λ
−4Λ
−2Λ
−2Λ 


1 + 2
0q11q2
−4Λ
−4Λ
−5Λ
2Λ



1q10q2
 2Λ
−2Λ
 2Λ
−2Λ 



1q11q2
 4Λ
 2Λ
 6Λ
2Λ









2nd and Further Transmissions:

In case the 1st transmission has not been successfully decoded the receiver requests a retransmission (2nd transmission). Assuming for 2nd transmission also 2 transmit diversity branches are available, the 2 additional mappings (mapping 3 and mapping 4 in FIG. 3) are employed to further improve the averaging of the bit reliabilities as shown in Table 4.In this example (assuming an equal SNR for all received signals) the averaging is performed perfectly after receiving 2 transmit diversity branches times 2 transmissions (possibility to employ 4 different mappings—sufficient for 16-QAM). Table 4 compares the LLRs with and without applying the proposed Constellation Rearrangement. Having a closer look at the combined LLRs, it can be seen that with application of the Constellation Rearrangement the magnitude for all bit reliabilities results in 6Λ.
It should be noted again, that the chosen mappings are non exhaustive and more combinations of mappings fulfilling the same requirements can be found.







TABLE 4







Mean LLRs (per branch) and combined mean LLRs for bits mapped on the


in-phase component of the signal constellation for the diversity branches


and (re-) transmissions when employing Mappings 1 to 4 and when


employing 4 times Mapping 1.












Constellation
Prior Art




Rearrangement
No Rearrangement




(Mapping
(Mapping


Transmit

1 + 2 + 3 + 4)
1 + 1 + 1 + 1)













Diversity
Transmission
Symbol
Mean
Mean
Mean
Mean


Branch
Number
(i1q1i2q2)
LLR (i1)
LLR (i2)
LLR (i1)
LLR (i2)





1
1
0q10q2
−Λ
−Λ
−Λ
−Λ




0q11q2
−3Λ 
 Λ
−3Λ 
 Λ




1q10q2
 Λ
−Λ
 Λ
−Λ




1q11q2
3Λ
 Λ
3Λ
 Λ


2
1
0q10q2
−Λ
−3Λ 
−Λ
−Λ




0q11q2
−Λ
3Λ
−3Λ 
 Λ




1q10q2
 Λ
−Λ
 Λ
−Λ




1q11q2
 Λ
 Λ
3Λ
 Λ


3
2
0q10q2
−Λ
−Λ
−Λ
−Λ




0q11q2
−Λ
 Λ
−3Λ 
 Λ




1q10q2
 Λ
−3Λ 
 Λ
−Λ




1q11q2
 Λ
3Λ
3Λ
 Λ


4
2
0q10q2
−3Λ 
−Λ
−Λ
−Λ




0q11q2
−Λ
 Λ
−3Λ 
 Λ




1q10q2
3Λ
−Λ
 Λ
−Λ




1q11q2
 Λ
 Λ
3Λ
 Λ


Combined

0q10q2
−6Λ 
−6Λ 
−4Λ 
−4Λ 


1 + 2 + 3 + 4

0q11q2
−6Λ 
6Λ
−12Λ 
4Λ




1q10q2
6Λ
−6Λ 
4Λ
−4Λ 




1q11q2
6Λ
6Λ
12Λ 
4Λ









If the constellation rearrangement is performed by applying different mapping schemes, one would end up in employing a number of different mappings as given in FIG. 1, FIG. 2 and FIG. 3. If the identical mapper (e.g. FIG. 1) should be kept for all transmit diversity branches, e.g. mapping 2 can be obtained from mapping 1 by the following operations:

    
    
        exchange positions of original bits i1 and i2 
        exchange positions of original bits q1 and q2 
        logical bit inversion of original bits 11 and q1 
    
    


Alternatively, those bits that end in positions 1 and 2 can also be inverted (resulting In a different mapping with an identical bit-reliability characteristics). Accordingly, mapping 2 can be obtained from mapping 1, using an interleaver/inverter section 14. (see FIG. 6) which performs interleaving and/or inverting of the bits.
Therefore, the following table provides an example how to obtain mappings 1 to 4 (or mappings with equivalent bit reliabilities for i1, i2, q1 and q2); where the bits always refer to the first transmission, and a long dash above a character denotes logical bit inversion of that bit:







TABLE 5







Alternative implementation of the Constellation Rearrangement


by interleaving (intra-symbol interleaving) and logical


inversion of bits mapped onto the modulation symbols.









Interleaver and Inverter


Mapping No.
functionality





1
i1q1i2q2


2
ī2 q2ī1 q1 or i2q2ī1 q1


3
ī2 q2i1q1 or i2q2i1q1


4
i1q1ī2 q2 or ī1 q1ī2 q2









Generally at least 2 different mappings should be employed for N>1 diversity branches, where the order and the selection of the mappings is irrelevant, as long as the bit-reliability averaging process, meaning the reduction in differences in bit reliabilities) is maintained.
Preferred realizations in terms of number of employed mappings

    
    
        M-QAM
        
            Employing log2(M) different mappings
            Employing log2(M)/2 different mappings
        
        
        M-PSK
        
            Employing log2(M) different mappings
            Employing log2(M)/2 different mappings
            Employing 2log2(M) different mappings
        
        
    
    


The applied signal constellation mappings for modulation at the transmitter and demodulation at the receiver need to match for each individual transmit diversity branch. This can be achieved by appropriate signaling of parameters indicating the proper mapping or combination of mappings to be applied for the diversity branches and HARQ transmissions. Alternatively the definition of the mappings to be applied for transmit diversity branches and HARQ transmissions may be system predefined.
FIG. 4 shows an exemplary embodiment of a communication system according to the present invention. More specifically, the communication system comprises a transmitter 10 and a receiver 20 which communicate through a communication channel consisting of a plurality of diversity branches 40A, 40B and 40C. Although three diversity branches are illustrated in the figure, it becomes clear to a person skilled in the art that an arbitrary number of branches may be chosen. From a data source 11, data packets are supplied to a FEC encoder 12, preferably a FEC Turbo encoder, where redundancy bits are added to correct errors. The bits output from the FEC encoder are subsequently supplied to a mapping unit 13 acting as a modulator to output symbols formed according to the applied modulation scheme stored as a constellation pattern in a table 15. Subsequently the data symbols are applied to a transmission unit 30 for transmission over the branches 40A-C. The receiver 20 receives the data packets by the receiving unit 35. The bits are then input into a demapping unit 21 which acts as a demodulator using the same signal constellation pattern stored in the table 15 which was used during the modulation of these bits.
The demodulated data packets received over one diversity branch are stored in a temporary buffer 22 for subsequent combining in a combining unit 23 with the data packets received over at least one other diversity branch.
A retransmission is launched by an automatic repeat request issued by an error detector (not shown) and communicated by a communication section 57 of receiver 20 to a receiving section 55 of transmitter 10 with the result that an identical data packet is transmitted from transmitter 10. In combining unit 23, the previously received erroneous data packets are soft-combined with the retransmitted data packets. Then a decoder decodes the bits and outputs a measure for the transmission quality, e.g. the bit-error rate BER.
As illustrated in FIG. 5, table 15 stores a plurality of signal constellation patterns #0 . . . #n which are selected for the individual transmissions over the individual diversity branches and HARQ transmissions according to a predetermined scheme. The scheme, i.e. the sequence of signal constellation patterns used for modulating/demodulating are either pre-stored in the transmitter and the receiver or are signaled by transmitter to the receiver prior to usage.

## Claims

1. An automatic repeat request (ARQ) transmission method in a wireless communication system wherein data packets are transmitted from a transmitter to a receiver, using a first transmission and a second transmission based on a repeat request, the method comprising:
modulating said data packets at the transmitter using a first mapping to obtain first data symbols;
modulating said data packets at the transmitter using a second mapping to obtain second data symbols;
performing the first transmission by transmitting the first data symbols and the second data symbols over a plurality of diversity branches to the receiver;
performing the second transmission by transmitting third data symbols after modulation of said data packets using a third mapping and fourth data symbols after modulation of said data packets using a fourth mapping, over the plurality of diversity branches to the receiver;
demodulating the received data packets at the receiver using the first to fourth mappings respectively; and
diversity combining the demodulated data packets received over the plurality of diversity branches.

2. A transmitter for an automatic repeat request (ARQ) transmission of data packets using a first transmission and a second transmission based on a repeat request received from a receiver, the transmitter comprising:
a mapping unit for modulating said data packets using a first mapping to obtain first data symbols and for modulating said data packets using a second mapping to obtain second data symbols; and
a transmission unit for performing the first transmission by transmitting the first data symbols and the second data symbols over a plurality of diversity branches,
wherein the transmission unit is configured for performing the second transmission by transmitting third data symbols after modulation of said data packets using a third mapping and fourth data symbols after modulation of said data packets using a fourth mapping, over the plurality of diversity branches.

3. The transmitter according to claim 2, further comprising an encoder for encoding data bits using a forward error correction encoding scheme prior to modulation.

4. The transmitter according to claim 3, wherein the employed encoding scheme is a Turbo coding scheme.

5. The transmitter according to claim 2, wherein the mapping unit employs a higher order modulation scheme including at least one of M-PSK and M-QAM with log2(M)>2 wherein data bits mapped onto the data symbols have different bit reliabilities depending on the chosen mapping.

6. The transmitter according to claim 2, wherein a modulation scheme is 16 QAM and a number of log2(M) mappings are used.

7. The transmitter according to claim 2, wherein the mappings for the plurality of diversity branches are selected such that differences in magnitude among combined bit reliabilities are reduced after a bit combining of the data packets.

8. The transmitter according to claim 2, further comprising a memory for pre-storing the first to fourth mappings.

9. The transmitter according to claim 2, wherein the used mappings are signaled to the receiver.

10. The transmitter according to claim 3, wherein the transmission unit transmits parameters indicating a combination of signal constellation mappings to be applied for the plurality of diversity branches.

11. A receiver for an automatic repeat request (ARQ) reception of data packets using a first reception and a second reception based on a repeat request transmitted from the receiver, the receiver comprising:
a reception unit for performing the first reception by receiving said data packets modulated using a first mapping and a second mapping over a plurality of diversity branches, wherein the reception unit is configured for performing the second reception by receiving said data packets modulated using a third mapping and a fourth mapping over the plurality of diversity branches;
a demapping unit for demodulating the received data packets. using the first to fourth mappings respectively; and
a combining unit for diversity combining the demodulated data packets.

12. The receiver according to claim 11, further comprising a decoder for decoding the combined data symbols using a forward error correction decoding scheme after the diversity combining.

13. An automatic repeat request (ARQ) transmission method to transmit data packets using a first transmission and a second transmission based on a repeat request received from a receiver, comprising:
modulating said data packets using a first mapping to obtain first data symbols;
modulating said data packets using a second mapping to obtain second data symbols;
performing the first transmission by transmitting the first data symbols and the second data symbols over a plurality of diversity branches to the receiver; and
performing the second transmission by transmitting third data symbols after modulation of said data packets using a third mapping and fourth data symbols after modulation of said data packets using a fourth mapping, over at least one of the plurality of diversity branches to the receiver.

14. An automatic repeat request (ARQ) reception method to receive data packets using a first reception and a second reception based on a repeat request from the receiver, comprising:
performing the first reception by receiving said data packets modulated using a first mapping and a second mapping over a plurality of diversity branches;
performing the second reception by receiving said data packets modulated using a third mapping and a fourth mapping over the plurality of diversity branches;
demodulating the received data packets using the first to fourth mappings respectively; and
diversity combining the demodulated data packets.