Abstract:
An apparatus and method for transmitting and receiving a bit stream. On the transmission side, coded bits (Y.sub.t) and an interleaved version of the coded bits (X.sub.t) are separately modulated and transmitted. On the reception side, a priori output probabilities produced by a probability generator ( 34 ) are combined ( 112 ) and then input to a SISO decoder ( 111 ). Combined a posteriori output probabilities ( 115 ) produced by the SISO decoder are split ( 113 ) and then fed back to the probability generator.

Description:
This application is a Divisional of application Ser. No. 10/037,179, filed Oct. 23, 2001, now U.S. Pat. No. 7,120,213 which claims priority under 35 USC 119(e)(1) of copending U.S. provisional application No. 60/244,043 filed on Oct. 27, 2000. This application contains subject matter related to subject matter disclosed in U.S. Ser. No. 09/925,077 filed on Aug. 8, 2001, which is incorporated herein by reference. 

   FIELD OF THE INVENTION 
   The invention relates generally to wireless communications and, more particularly, to wireless communications that utilize turbo coding and transmit diversity. 
   BACKGROUND OF THE INVENTION 
   Each of the documents listed below is referred to herein by the corresponding number enclosed in square brackets to the left of the document. Each of these documents is also incorporated herein by reference.
     [1] Y. Liu, M. P. Fitz, and O. Y. Takeshita, “Qpsk space-time turbo codes,” in IEEE ICC, June 2000.   [2] X. Li and J. A. Ritcey, “Bit-interleaved coded modulation with iterative decoding,” using soft feedback, “ Electronic Letters , vol. 34, pp. 942-943, 4 Mar. 1998.   [3] X. Li and J. A. Ritcey, “Bit-interleaved coded modulation with iterative decoding,” in  IEEE ICC , vol. 2, pp. 858-863, June 1999.   [4] X. Li and J. A. Ritcey, “Trellis-coded modulation with bit interleaving and iterative decoding,”  IEEE Journal on Selected Areas in Communications , vol. 17, pp. 715-724, April 1999.   [5] X. Li and J. A. Ritcey, “Bit-interleaved coded modulation with iterative decoding,”  IEEE Communications Letters , vol. 1, pp. 169-171, November 1997.   [6] V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-Time Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction,” in  IEEE Transactions on information theory , vol. 44, No. 2, pp. 744-765, March 1998.   [7] A. R. Hammons and H. E. Gamal, “On the Theory of Space-Time Codes for PSK Modulation,” in  IEEE Transactions on information theory , vol. 2, No. 2, pp. 524-542, March 2000.   

   Coding and interleaving techniques are often used in wireless communication systems to improve the communication performance.  FIG. 1  illustrates an example of a conventional wireless communication system described in [1]. This example implements turbo coding by using two convolutional coders (CC). One of the convolutional coders receives at its input the data stream that is to be transmitted, and the other convolutional coder receives at its input an interleaved (see  10 ) version of the data stream. The outputs of the convolutional coders are then modulated using QPSK (Quadrature Phase Shift Keying) and transmitted by respective transmit antennas. At the receiver, the signal from the antenna is input to a probability generator which generates symbol (or bit) probabilities. These symbol probabilities are fed to soft-input, soft-output (SISO) decoders that iterate to get estimates of the transmitted symbols (or bits). The SISO decoders use knowledge of the trellis of the convolutional coders to produce the estimates. 
     FIG. 2  illustrates an example of a conventional wireless communication system described in [2] and [3]. The system of  FIG. 2  uses a single convolutional coder and an interleaver  21  before modulation and transmission by a single antenna. At the receiver, the signal from the antenna is demodulated and de-interleaved (see  22 ), and is then input to a SISO decoder. The a posteriori symbol probabilities output from the SISO decoder are interleaved (see  23 ) and fed back into the demodulator to get a better estimate of the symbol probabilities. This loop is iterated over. Systems similar to the one illustrated in  FIG. 2  have also been suggested in [4] and [5], but those systems implement hard decoding decisions instead of soft decisions. 
     FIG. 8  illustrates an example of a conventional wireless communication system described in [6]. In this example, bits are encoded with a single encoder, and separate sets of the encoded bits are applied to respective modulators in separate branches. The modulators perform constellation mapping, and the separate branches permit transmit diversity. Special care is exercised in order to provide a full diversity stream. At the receiving end, conventional Viterbi decoding is performed. The work in [6] was followed by the work in [7], wherein it is demonstrated that, for all BPSK constellations, it is very easy to achieve diversity, and that coding advantage should be a primary optimization goal. 
   It is desirable in view of the foregoing to provide for improved performance in wireless communication systems that utilize turbo coding and transmit diversity. 
   According to the invention, coded bits and an interleaved version of the coded bits are separately modulated and transmitted. On the receiver side, a priori output probabilities produced by the probability generator are combined and then input to a SISO decoder, and combined a posteriori output probabilities produced by the SISO decoder are split and then fed back to the probability generator. This advantageously permits the probability generator to produce an improved estimate of the received symbols. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  illustrates a conventional wireless communication system which utilizes interleaving, turbo coding and transmit diversity. 
       FIG. 2  illustrates a conventional wireless communication system that utilizes turbo coding, interleaving and feedback of a posteriori probabilities from a SISO decoder. 
       FIG. 3  diagrammatically illustrates exemplary embodiments of wireless communication systems which utilize turbo coding, interleaving, transmit diversity and a posteriori probability feedback according to the invention. 
       FIG. 4  diagrammatically illustrates exemplary embodiments of the probability generator of  FIG. 3 . 
       FIG. 5  illustrates exemplary operations which can be performed by the receiver of  FIG. 3 . 
       FIG. 6  diagrammatically illustrates further exemplary embodiments of wireless communication systems which utilize interleaving, turbo coding, transmit diversity and a posteriori probability feedback according to the invention. 
       FIG. 7  illustrates exemplary simulation results for the systems of  FIGS. 1 ,  3  and  6 . 
       FIG. 8  illustrates a conventional wireless communication system which utilizes a single encoder and transmit diversity. 
       FIG. 9  diagrammatically illustrates exemplary embodiments of a wireless communication transmission apparatus which utilizes a single encoder according to the invention. 
       FIG. 10  diagrammatically illustrates exemplary embodiments of a wireless communication receiving apparatus that is cooperable with the wireless communication transmission apparatus of  FIG. 9 . 
       FIG. 11  illustrates exemplary operations which can be performed by the wireless communication receiving apparatus of  FIG. 10 . 
       FIG. 12  illustrates exemplary simulation results which compare the performance of the system of  FIGS. 9 and 10  to the performance of the conventional system of  FIG. 8 . 
   

   DETAILED DESCRIPTION 
   Referring again to  FIG. 1 , the symbol Z t  received by the antenna of the receiver  12  at time t can be expressed as a function of the corresponding symbols or bits X t  and Y t  produced by the respective convolutional coders of the transmitter  11 , and the fading characteristics of the respective wireless communication channels through which X t  and Y t  are transmitted to the receiver  12 . The fading characteristics (or coefficients) are illustrated by fading parameters α and β in  FIG. 1 . Accordingly, the symbol value received by the antenna of the receiver  12  can be expressed as follows
 
 Z   t   =αX   t   +βY   t   +n   t ,  (1)
 
where n t  represents noise in the wireless communication channels. At  13 , the probability generator  15  produces, for all possible values C X  that X t  can assume at time t, the following probability
 
 P ( X   t   =C   X   |Z   t   =C   Z )  (2)
 
Expression (2) above represents the probability that X t =C X  given that the received symbol or bit value Z t =C Z . At  14 , the probability generator  15  produces similar probabilities for all possible values C y  of Y t , namely
 
 P ( Y   t   =C   Y   |Z   t   =C   Z )  (3)
 
   Taking the probability defined in Expression (2) above as an example, and applying Bayes&#39; Rule, Expression (2) can be written as follows
 
 P ( Z   t   =C   Z   |X   t   =C   X ) P ( X   t   =C   X )/ P ( Z   t   =C   Z )  (4)
 
   In practice, for an iterative loop, the probability given by Expression (2) is generated under the assumption that nothing is known in advance about the statistics of X t . This is called the extrinsic probability and ensures that only “new” information is used to generate data that will be fed back. Therefore, P(X t =C x ) can be eliminated from Expression (4). The denominator of Expression (4) can also be eliminated because it merely represents the probability that Z t =C Z  at time t, which is merely a constant value that operates only as a scaling factor. Thus, eliminating the aforementioned extrinsic factor and the aforementioned scaling factor from Expression (4) leaves
 
 P ( Z   t   =C   Z   |X   t   =C   X )  (5)
 
   Using known probability theory, Expression (5) can be rewritten as follows 
   
     
       
         
           
             
               
                 
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   Referring again to Equation (1) above, the leftmost probability of Expression (6) can be rewritten as follows
 
 P ( n   t   =C   Z   −αC   X   −βC   Y )  (7)
 
   Substituting Expression (7) into Expression (6) gives 
   
     
       
         
           
             
               
                 
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   Thus, Expression (2) above can be rewritten as Expression (8) above. 
   The noise n t  in Expression 8 can be modeled as a Gaussian random variable, and the fading parameters α and β can be readily estimated. Thus, given that the received symbol Z t =C Z  is known, values of the leftmost probability in Expression 8 can be easily calculated for all possible values of C X  and C Y . The values of the rightmost probability of Expression (8) are provided according to the invention as the a posteriori output probabilities from a SISO decoder, as described in more detail below. 
   Using reasoning analogous to that given above for rewriting Expression (2) as Expression (8), Expression (3) above can be rewritten as follows 
   
     
       
         
           
             
               
                 
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   As mentioned above with respect to Expression (8), the leftmost probability of Expression (9) can be easily calculated for a known value of C Z  and all possible values of C X  and C Y . Also analogous to the discussion of Expression (8) above, the values of the rightmost probability of Expression (9) are provided according to the invention as a posteriori output probabilities of a SISO decoder. 
   Referring now to  FIG. 3 , in exemplary wireless communication system embodiments according to the invention, a receiver  31  includes a probability generator  34  coupled to an antenna which receives symbol Z t  from a transmitter that employs transmit diversity, for example the transmitter  11  of  FIG. 1 . The probability generator  34  calculates the values of the leftmost probability in Expressions (8) and (9). At its input  47 , the probability generator receives (as feedback) from SISO decoder  35  the values of the rightmost probability of Expression (9). At its input  48 , the probability generator  34  receives (as feedback) from the SISO decoder  36  the values of the rightmost probability of Expression (8). Having calculated the values of the leftmost probability of Expressions (8) and (9), and having received the values of the rightmost probabilities of Expressions (8) and (9) from the SISO decoders  36  and  35 , respectively, the probability generator  34  performs the summation of Expression (8) to produce at its output  45  the values of the probability of Expression (2), and also performs the summation of Expression (9) to produce at its output  46  the values of the probability of Expression (3). 
   The outputs  45  and  46  provide a priori output probabilities to the SISO decoders  35  and  36 . The decoder  35  operates with respect to X t  and the decoder  36  operates with respect to Y t . The SISO decoders  35  and  36  use their respective a priori output probabilities to produce respective a posteriori input probabilities. The a posteriori input probabilities produced by SISO decoder  35  are interleaved at  38  (corresponding to the interleaver in the transmitter  11 ) and the results are provided as a priori input probabilities to the SISO decoder  36 . Similarly, the a posteriori input probabilities produced by the SISO decoder  36  are de-interleaved at  37  (again corresponding to the interleaver of the transmitter  11 ) and the results are provided as a priori input probabilities to the SISO decoder  35 . The a posteriori input probabilities produced by the SISO decoder  35  are also provided to a decision maker which can use conventional techniques to decide the input symbol (as seen by the corresponding coder  16 ) based on the a posteriori input probabilities. 
   The output probabilities provided to (a priori) and produced by (a posteriori) the SISO decoder  35  represent respective probabilities that the symbol X t  as output from the convolutional coder  16  has respective ones of a plurality of possible values. Similarly, the input probabilities provided to (a priori) and produced by (a posteriori) SISO decoder  35  represent respective probabilities that the symbol that was input to the convolutional coder  16  to produce X t  has respective ones of a plurality of possible values. The SISO decoder  36  functions analogously with respect to the symbol Y t  and the convolutional coder  17 . Each SISO decoder uses the a priori probabilities (input and output) provided thereto together with knowledge of the trellis used by the corresponding convolutional coder to produce corresponding a posteriori probabilities (output and input). In some embodiments, each coder  16  and  17  uses the same trellis. 
     FIG. 4  diagrammatically illustrates exemplary embodiments of the probability generator  34  of  FIG. 3 . A fading parameter estimator  42  provides estimates α′ and β′ of the fading parameters α and β of  FIG. 3  using, for example, any desired conventional technique. A calculation apparatus  41  receives these estimated fading parameters, and also has access (e.g. from look-up table values) to the probability of the noise parameter n t , which can be modeled, for example, as a Gaussian random variable. The calculation apparatus  41  knows the value of C Z  (simply the received value) in Expressions (8) and (9), and thus can calculate the values of the leftmost probability in Expressions (8) and (9) using the estimated fading parameters α′ and β′. Thus, the calculation apparatus  41  produces at  49  the values of the leftmost probability of Expressions (8) and (9). These values are input to combiners  43  and  44 . 
   The combiner  43  receives at  47  the a posteriori output probabilities produced by SISO decoder  35 , and the combiner  44  receives at  48  the a posteriori output probabilities produced by SISO decoder  36 . The values received at  47  represent the values of the rightmost probability in Expression (9) and the values received at  48  represent the values of the rightmost probability in Expression (8). The combiner  43  operates to combine the values that it receives at  49  and  47  in the manner shown in Expression (8), namely multiplying the values together and summing the resulting products over all possible values of C Y . Similarly, the combiner  44  combines the values that it receives at  49  and  48  as shown by Expression (9) above, namely multiplying the values together and summing the resulting products over all possible values of C X . The combiner  43  produces at  46  the values of the probability shown in Expression (3), and the combiner  44  produces at  45  the values of the probability shown in Expression (2). 
   It should be clear that the probability generator  34  can easily account for the scaling factor described above with respect to Expression (4) by suitably normalizing the probability values that it generates, although such normalizing is not explicitly shown in the drawings. 
     FIG. 5  illustrates exemplary operations which can be performed by the receiver embodiments of  FIGS. 3 and 4 . At  51 , initial a priori output probabilities are produced for the SISO decoders. This can be done, for example, by the probability generator  34  calculating the values of the leftmost probabilities of Expressions (8) and (9) and summing these values without multiplying by the rightmost probabilities of Expressions (8) and (9) (which rightmost probabilities are not yet available as feedback from the SISOs).  FIG. 5  assumes that the SISO decoder  35  is selected to operate first and begin the iterative process. However, the SISO  36  could also be selected to operate first and begin the iterative process, and this possibility is therefore indicated by the parenthetical expressions in  FIG. 5 . The following textual description of  FIG. 5  assumes the aforementioned example of beginning with SISO  35 . 
   At  52 , SISO  35  uses the initial a priori output probabilities to produce a posteriori input probabilities. At  53 , interleaving is applied to the a posteriori input probabilities from SISO  35 . At  54 , SISO  36  uses the initial (for the first iteration) a priori output probabilities and the interleaved a posteriori input probabilities of SISO  35  to produce a posteriori input and output probabilities. At  55 , de-interleaving is applied to the a posteriori input probabilities from SISO  36 . At  56 , the a posteriori output probabilities from SISO  36  are used to produce a priori output probabilities for SISO  35 . At  57 , the SISO  35  uses its a priori output probabilities and the de-interleaved a posteriori input probabilities of SISO  36  to produce a posteriori input and output probabilities. At  58 , the a posteriori output probabilities from SISO  35  are used to produced a priori output probabilities for SISO  36 . The operations at  53 - 58  are then repeated for any desired number of iterations. 
     FIG. 6  diagrammatically illustrates further exemplary embodiments of a wireless communication system according to the invention. In the system of  FIG. 6 , the transmitter  61  is similar to the transmitter  11  of  FIGS. 1 and 3 , but includes interleavers  63  and  64  at the outputs of the convolutional coders. Thus, the receiver  62  includes a de-interleaver  65  and an interleaver  66  to account for the operations of the interleaver  63 , and also includes a de-interleaver  67  and an interleaver  68  to account for the operation of the interleaver  64 . Aside from the operations of the interleavers and de-interleavers illustrated at  63 - 68 , the wireless communication system of  FIG. 6  can operate in generally the same fashion as the wireless communication system of  FIG. 3 , that is, generally as described above with respect to  FIG. 5 . 
     FIG. 7  illustrates exemplary simulation results for the systems of  FIG. 1  ( 71 ),  FIG. 3  ( 72 ), and  FIG. 6  ( 73 ). As shown in  FIG. 7 , the  FIG. 3  system at  72  performs better (in terms of frame error rate FER) than the  FIG. 1  system at  71 , showing gains of about 2 dB at higher SNRs. The  FIG. 3  system also exhibits a noticeable increase in slope, so the gains can be expected to be even larger at higher SNRs. The  FIG. 6  system at  73  provides an additional performance gain of about 1 dB at the higher SNRs, and also exhibits an increase in slope as compared to the system of  FIG. 1  at  71 . 
     FIG. 9  diagrammatically illustrates pertinent portions of exemplary embodiments of a wireless communication transmitter apparatus according to the invention. As shown in  FIG. 9 , the input bits received from a communication application are encoded by a single convolutional coder  91 , and the encoded bits are interleaved by an interleaver  92 . The symbols or bits X t  produced by the interleaver  92  and the symbols or bits Y t  produced by the encoder  91  are then modulated (for example using QPSK) and transmitted by respective transmit antennas. 
     FIG. 10  diagrammatically illustrates pertinent portions of exemplary embodiments of a wireless communication receiver apparatus that is capable of receiving the wireless communication signals transmitted by the wireless communication transmitter apparatus of  FIG. 9 . The apparatus of  FIG. 10  includes a probability generator  34  which can be, for example, identical to the probability generator  34  described above with respect to  FIGS. 3-6 . The a priori output probability values produced at  45  by the probability generator  34  are applied to a de-interleaver  110  to account for the interleaver  92  in the transmitter apparatus of  FIG. 9 . The a priori output probability values produced at  46  by the probability generator  34  are applied to a combiner  112  along with the output of the de-interleaver  110 . 
   The combiner  112  is operable for combining the probability values at  46  with the probability values output by the de-interleaver  110 . In some exemplary embodiments, the combiner is simply a multiplier which multiplies the input probability values by one another. The combiner  112  thus outputs combined a priori output probability values which represent combinations of the a priori output probability values input to the combiner  112 . The combined a priori output probability values at  114  are provided to a SISO decoder  111 . The SISO decoder  111  uses the combined a priori output probability values  114  to produce combined a posteriori input and output probabilities. The combined a posteriori input probabilities are provided to a decision maker which decides the symbol values, and the combined a posteriori output probabilities are provided at  115  to a splitter  113 . 
   The splitter  113  is operable for splitting each of the combined a posteriori output probability values at  115  into its constituent probability values. The splitter output values  116 , corresponding to probability values  46 , are provided to input  48  of the probability generator  34 , and the splitter output values  117 , corresponding to the probability values at  45 , are applied to an interleaver  92  (same as in  FIG. 9 ) whose output is provided to the input  47  of the probability generator  34 . In some exemplary embodiments, the splitter  113  is a marginal probability calculator which uses conventional techniques to extract, from the combined probability values at  115 , constituent marginal probability values corresponding to the probability values at  45  and  46 . 
   The decision maker can also utilize, for example, a splitter such as shown at  113  to split each of the combined a posteriori input probabilities into its constituent probability values. These constituent probability values can then be used in conventional fashion to make the symbol decisions. 
     FIG. 11  illustrates exemplary operations which can be performed by the wireless communication receiver apparatus of  FIG. 10 . At  120 , the probability generator  34  produces first and second sets of initial a priori output probabilities. At  121 , de-interleaving is applied to the second set of a priori output probabilities. At  122 , the first set of a priori output probabilities is combined with the de-interleaved second set of a priori output probabilities to produce combined a priori output probabilities. At  123 , the SISO decoder uses the combined a priori output probabilities to produce combined a posteriori input and output probabilities. At  124 , the combined a posteriori output probabilities are split into first and second sets of a posteriori output probabilities. At  125 , interleaving is applied to the second set of a posteriori output probabilities and, at  126 , the first set and the interleaved second set of a posteriori output probabilities are used by the probability generator  34  to produce the next iteration of the second and first sets of a priori output probabilities, respectively. Thereafter, the operations at  121 - 126  are repeated for any desired number of iterations. 
     FIG. 12  illustrates simulation results which compare the performance of the conventional system of  FIG. 8  with the performance of the system of  FIGS. 9-11  according to the invention. In particular, the performance of the conventional system of  FIG. 8  is illustrated at  130  and the performance of the system of  FIGS. 9-11  is illustrated at  131  (first iteration),  132  (second iteration) and  133  (fifth iteration). The performance illustrated at  131 ,  132  and  133  was obtained using random interleaving in the transmitter of  FIG. 9  and the receiver of  FIG. 10 . 
   It will be apparent to workers in the art that any wireless communication system that utilizes a space-time turbo code, or any kind of turbo code, can benefit from the present invention. Advantageously, the added complexity of the a posteriori output probability feedback loops is relatively small compared to the complexity of a SISO block. It will also be apparent to workers in the art that the embodiments of  FIGS. 3-6  and  9 - 11  can be implemented, for example, by suitable modifications in hardware, software, or a combination of hardware and software, in conventional wireless communication transmitters and receivers. 
   Although exemplary embodiments of the invention are described above in detail, this does not limit the scope of the invention, which can be practiced in a variety of embodiments.