# Patent

## Title
Communication systems and methods

## Abstract

In accordance with embodiments, a communication system includes a first device and a second device in communication with the first device. The second device has at least a first pair and a second pair of antennas. The second device spreads a communication bit by a predetermined spreading factor and forms a first set of spatial block codes in frequency domain based on the spread communication bit. The first set of spatial block codes being consecutively transmitted on one of the first and second pairs of antennas.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application claims priority to the U.S. Provisional Application Ser. No. 60/976,948, by Hua Xu et al., entitled “4-TX TRANSMIT DIVERSITY DESIGN FOR PHICH CHANNEL IN LTE DOWNLINK,” filed on Oct. 2, 2007, which is hereby incorporated herein by reference as if reproduced in its entirety.


STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
Not applicable.
REFERENCE TO A MICROFICHE APPENDIX
Not applicable.
BACKGROUND
For open-loop fading channel, diversity is often considered the only choice to mitigate the fading effects and improve the system reliability. While forward error correction (FEC) coding provides valuable time diversity, for a slow fading environment, space diversity/polarization proves to be more effective. The objective of the so-called space-time codes is to maximize the diversity.
There are basically two kinds of space-time codes: trellis codes and block codes. While trellis codes provide additional coding gain, they have drawbacks, namely: the decoder is more complex (since these codes work on the QAM symbols), and it is difficult to concatenate trellis space-time codes with powerful soft-decoding FEC codes, such as Turbo codes and convolutional codes. Space-time block codes (STBCs) do not provide coding gain, but they are simple to decode (especially for complex orthogonal design codes), and they can be combined with other soft-decoding FEC codes. It is for these reasons that STBCs are more practical and are widely adopted by numerous standards.
The best known STBC was invented by Alamouti and Tarokh (U.S. Pat. No. 6,185,258) where the code matrix is presented as in Table 1 below.









TABLE 1






Time t
Time (t + T)







Antenna 1
S1
S2


Antenna 2
−S2*
S1*









The Alamouti code has several properties, which facilitate space diversity implementations. The signals are orthogonal; hence full diversity is achieved at the receiver side. The transmit power is balanced between the two antennas and the two time slots; hence a low cost power amplifier can be used (reducing the modem cost). Further, the code rate is 1; hence no throughput is sacrificed. Further, its maximum likelihood decoder is very simple, which makes the cost of an optimal decoder negligible.
Unfortunately, it was proven later that there are no such orthogonal codes existing for a system with more than two transmitter antennas. Therefore, the focus was shifted to the following two approaches: designing orthogonal STBC codes with a code rate smaller than 1; and designing quasi-orthogonal STBC codes to maintain the property of code rate 1. While the first approach sacrifices the system throughput, the second approach sacrifices signal quality due to a loss of orthogonality. There are several variations of codes that follow the two approaches described above, with focus on other areas such as power balancing and code rate manipulation. However, the Alamouti is still preferred for many implementations.
Table 2 is an example of an STBC for 4 antenna applications (Code-A). Code-A is an orthogonal code having code rate 3/4. Maintaining orthogonality as in Code-A helps maintain diversity order and signal quality.











TABLE 2






Time t
Time (t + T)
Time (t + 2T)
Time (t + 3T)







Antenna 1
S1
−S2*
−S3*
X


Antenna 2
S2
S1*
x
S3*


Antenna 3
S3
x
S1*
−S2*


Antenna 4
x
−S3
S2
S1









With Code-A, each received signal has a diversity order of 4. However, one weakness of Code-A is its code rate loss, which must be compensated in FEC codes. In other words, due to the rate loss in STBC, the code rate in FEC must be higher. Higher code rates can cause problems for the powerful trellis codes, whose coding gain loss becomes significant when punctuation becomes excessive. Further, Code-A does not achieve full power balance across the transmit antennas.
Table 3 contains a second example of STBC for 4 antenna applications (Code-B). Code-B is a non-orthogonal code having code rate 1. Maintaining the throughput as in Code-B helps prevent loss of coding gain at the 1-EC stage.











TABLE 3






Time t
Time (t + T)
Time (t + 2T)
Time (t + 3T)







Antenna 1
S1
−S2*
S3
−S4*


Antenna 2
S2
S1*
S4
S3*


Antenna 3
S3
−S4*
S1
−S2*


Antenna 4
S4
S3
S2
S1*









Since Code-B is not an orthogonal code, its determinant suffers from mutual interference. Defining the equivalent channel matrix Q as




  
    Q
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  ,




then {right arrow over (r)}=Q s, where {right arrow over (r)}=[r1 r2* r3 r4*]T, and {right arrow over (s)}=[s1 s2 s3 s4]T. The determinant of Q is given by |Q|=A2−B2, where A=|h1|2+|h2|2+|h3|2+|h4|2, and B=2(Re(h1h3)+Re(h2h4)). The element of B2 represents the loss due to the loss of orthogonality. Since B2≧0, it always contributes negatively to the code performance.

An example application of STBC is the Long Term Evolution (LTE) protocol, which defines a physical hybrid automatic repeat request (ARQ) indicator channel (PHICH) to transmit ACK/NACK bits. In general, the LTE protocol requires ACK/NACK bits to be spread and multiplexed together using code-division multiplexing (CDM), and to be repeated three times. The spreading factor (SF) selection for PHICH is non-trivial and has various consequences related to the spreading gain, ease of implementation, power balancing and other issues.
SUMMARY
In accordance with embodiments, a communication system comprises a first device and a second device in communication with the first device. The second device has at least a first pair and a second pair of antennas. The second device spreads a communication bit by a predetermined spreading factor and forms a first set of spatial block codes in frequency domain based on the spread communication bit. The first set of spatial block codes being consecutively transmitted on one of the first and second pairs of antennas.
In accordance with embodiments, a communication device comprises a transmitter with a control module. The communication device also comprises a first pair and second pair of antennas coupled to the transmitter. The control module causes a first set of spatial block codes, formed in frequency domain and corresponding to a spread communication bit, to be mapped for consecutive transmission on one of the first and second pairs of antennas.
In accordance with embodiments, a method comprises spreading a communication bit based on a predetermined spreading factor. The method further comprises forming a set of spatial block codes in frequency domain based on the spread communication bit and transmitting the set of spatial block codes consecutively over a pair of antennas.
These and other features will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings and claims.



BRIEF DESCRIPTION OF THE DRAWINGS
For a more complete understanding of this disclosure, reference is now made to the following brief description, taken in connection with the accompanying drawings and detailed description, wherein like reference numerals represent like parts.
FIG. 1 illustrates a communication system in accordance with embodiments of the disclosure;
FIG. 2 illustrates a communication device in accordance with embodiments of the disclosure;
FIGS. 3A-3B illustrate ACK/NACK mappings in accordance with embodiments of the disclosure;
FIGS. 4A-4B illustrate PHICH mappings that apply the ACK/NACK mappings of FIGS. 3A and 3B across OFDM symbols to balance power in accordance with embodiments of the disclosure; and
FIG. 5 illustrates a method in accordance with embodiments of the disclosure.



DETAILED DESCRIPTION
It should be understood at the outset that although an illustrative implementation of one or more embodiments are provided below, the disclosed systems and/or methods may be implemented using any number of techniques, whether currently known or in existence. The disclosure should in no way be limited to the illustrative implementations, drawings, and techniques illustrated below, including the exemplary designs and implementations illustrated and described herein, but may be modified within the scope of the appended claims along with their full scope of equivalents.
Disclosed herein is a communication technique. In at least some embodiments, communication bits are spread and a set (two or more) of spatial block codes is formed in frequency domain for each spread communication bit. Each set of spatial block codes is transmitted consecutively over a pair of antennas. For example, in accordance with embodiments, a first set of spatial block codes is transmitted consecutively over a first pair of antennas, a second set of spatial block codes is transmitted consecutively over a second pair of antennas, and a third set of spatial block codes is transmitted consecutively over the first pair of antennas and so forth. The spatial block codes may be spatial frequency block codes (SFBC) and/or spatial time block codes (STBC). In some embodiments, the communication technique disclosed herein may be understood to be a modified SFBC+FSTD (frequency shift transmit diversity) scheme.
In accordance with some embodiments, devices that employ the communication technique have at least four transmit antennas (two pairs) and use a spreading factor of four. In such embodiments, the communication technique maintains orthogonality of communication bits while exploiting spatial transmit diversity with the four transmit antennas. Such embodiments also benefit from the spreading gain and facilitate the ability to use the simple and robust Alamouti decoder for decoding spatial block codes. Power imbalances on each transmit antenna can be mitigated by appropriately mapping spatial block codes to the different antennas.
The communication technique disclosed herein was designed for transmitting repeated ACK/NACK bits over PHICH channels in accordance with the LTE protocol. Accordingly, the disclosure discusses this application of the communication technique. However, embodiments are not limited to any particular application.
FIG. 1 illustrates a communication system 100 in accordance with embodiments of the disclosure. As shown, the communication system 100 comprises devices 102 and 104 in communication with each other. As an example, the device 102 may correspond to user equipment (UE) and the device 104 may correspond to a base station.
The device 104 comprises a control module 110 that controls the preparation and transmission of at least some communications bits 106. In accordance with at least some embodiments, the control module 110 comprises a spreader 112 that receives communication bits as input and spreads the communication bits based on a predetermined spreading factor. For ACK/NACK bits, the spreading factor is preferably equal to four. The control module 110 also comprises a SFBC block 114 that receives the spread communication bits from the spreader 112 and that forms a set of SFBCs for each spread communication bit. Each set of SFBCs includes as least two SFBCs. The control module 110 also comprises an antenna mapper 116 that maps each set of SFBCs to a pair of antennas for transmission to the device 102. In accordance with embodiments, the antenna mapper 116 selectively maps each set of SFBCs for consecutive transmission on different pairs of antennas.
As shown, the antenna mapper 116 comprises a power balancer 118, which mitigates power imbalances on different antennas by mapping different sets of SFBCs for consecutive transmission on different pairs of antennas as evenly as possible. Examples of such mappings will be described in greater detail for FIGS. 3A-3B and 4A-4B.
FIG. 2 illustrates a communication device 200 in accordance with embodiments of the disclosure. The communication device 200 provides a high level overview of various components involved in communications. As shown, the communication device 200 comprises a baseband processor 202 coupled to transmit (TX) circuitry 204 and receive (RX) circuitry 206. The TX circuitry 204 and RX circuitry 206 couple to a plurality of antennas 212A-212N (e.g., at least four antennas). The baseband processor 202 also couples to a control system 210 and an interface 208.
As an example, the communication device 200 may correspond to a base station or a user equipment device. In general, the RX circuitry 206 receives radio frequency signals bearing information from a remote transmitter. The RX circuitry 206 may include a low-noise amplifier and a filter, which operate to amplify received signals and remove broadband interference from received signals. The RX circuitry 206 also performs downconversion and digitization operations on received signals.
The baseband processor 202 processes digitized received signals to extract information or data bits conveyed in the received signal. This processing typically involves demodulation, decoding, and error correction operations. Accordingly, the baseband processor 202 is generally implemented in one or more digital signal processors (DSPs) and/or application-specific integrated circuits (ASICs). The received information can be utilized by the device 200 itself and/or transmitted to another device.
For transmissions, the baseband processor 202 receives digitized data (e.g., voice, data, or control information) from the interface 208 as directed by the control system 210 and encodes the data for transmission. The encoded data is output to the TX circuitry 204, which modulates the encoded data by a carrier signal having one or more desired transmit frequencies. In at least some embodiments, the TX circuitry 204 uses orthogonal frequency-division multiplexing (OFDM) modulation, which divides the transmission band into multiple, orthogonal carrier waves. Each carrier wave is modulated according to the digital data to be transmitted. Because OFDM divides the transmission band into multiple carriers, the bandwidth per carrier decreases and the modulation time per carrier increases. Since the multiple carriers are transmitted in parallel, the transmission rate for the digital data, or symbols, on any given carrier is lower than when a single carrier is used. The TX circuitry 204 may also amplify the modulated carrier signal to an appropriate level for transmission and deliver the modulated carrier signal to the appropriate antennas 212A-212N.
In accordance with embodiments, the communication device 200 employs the control module 110 of FIG. 1 and/or its components. For example, the components/operations of the control module 110 may be incorporated into the control system 210 or may be distributed among other components of the communication device 200.
As previously mentioned, the communication technique disclosed herein is suitable for transmitting ACK/NACK repetitions over PHICHs according to the LTE protocol. FIG. 3A illustrates an ACK/NACK mapping 300A in accordance with embodiments of the disclosure. In the mapping 300A, three repetitions of ACK/NACK bits are mapped between antennas 1-4. More specifically, each ACK/NACK repetition is spread based on a spreading factor equal to four and is represented by two SFBCs. A first set of SFBCs, corresponding to the first ACK/NACK repetition, is transmitted consecutively on antennas 1 and 3. A second set of SFBCs, corresponding to the second ACK/NACK repetition, is transmitted consecutively on antennas 2 and 4. A third set of SFBCs, corresponding to the third ACK/NACK repetition, is transmitted consecutively on antennas 1 and 3.
FIG. 3B illustrates another ACK/NACK mapping 300B in accordance with embodiments of the disclosure. In the mapping 300B, three repetitions of ACK/NACK bits are mapped between antennas 1-4. Each ACK/NACK repetition has been spread based on a spreading factor equal to four and is represented by two SFBCs. A first set of SFBCs, corresponding to the first ACK/NACK repetition, is transmitted consecutively on antennas 2 and 4. A second set of SFBCs, corresponding to the second ACK/NACK repetition, is transmitted consecutively on antennas 1 and 3. A third set of SFBCs, corresponding to the third ACK/NACK repetition, is transmitted consecutively on antennas 2 and 4.
To support the mappings 300A and 300B, four orthogonal vectors wiεC4×1, i=1, 2, 3, 4 are generated and the vector a=b1w1+b2w2+b3w3+b4w4 is formed to send four ACK/NACK bits bi, i=1, 2, 3, 4. For the mappings 300A and 300B, four resource elements (REs) are needed to transmit one repetition for the four ACK/NACK bits (i.e., a total of 12 REs are needed to transmit three repetitions as in the mappings 300A and 300B). Advantageously, the structure of space-time code keeps the orthogonality during the transmission and, therefore, the four ACK/NACK bits can be decoded without introducing any cross-interference.
In the mappings 300A and 300B, power is not balanced across each of antennas 1-4. Specifically, more power is transmitted across antennas 1 and 3 for the mapping 300A (compared to antennas 2 and 4) because antennas 1 and 3 transmit two ACK/NACK repetitions while antennas 2 and 4 transmit one ACK/NACK repetition. Likewise, more power is transmitted across antennas 2 and 4 for the mapping 300B (compared to antennas 1 and 3) because antennas 2 and 4 transmit two ACK/NACK repetitions while antennas 1 and 3 transmit one ACK/NACK repetition.
To mitigate power imbalances, the mappings 300A and 300B can be used together. Preferably, the mappings 300A and 300B can be implemented evenly across a plurality of PHICHs. For example, in some embodiments, odd numbered PHICHs implement mapping 300A and even numbered PHICHs implement mapping 300B. Alternatively, odd numbered PHICH groups implement mapping 300A and even numbered PHICH groups implement mapping 300B, where each PHICH group refers to a number of PHICHs multiplexed on the same RE by orthogonal coding. Additionally, if there are multiple PHICHs or PHICH groups in each OFDM symbol, the mappings 300A and 300B can be applied in an alternating manner across OFDM symbols to balance power. The ACK/NACK mappings 300A and 300B of FIGS. 3A-3B are exemplary only and are not intended to limit embodiments of the invention to a particular mapping or application of the communication technique.
FIGS. 4A-4B illustrate PHICH mappings 400A and 400B that apply the ACK/NACK mappings 300A and 300B of FIGS. 3A and 3B across OFDM symbols to balance power. In the PHICH mapping 400A of FIG. 4A, there are two OFDM symbols 402A and 402B, each containing repetitions of a number of PHICHs. More specifically, OFDM symbol 402A contains a first repetition of PHICH-1 and PHICH-2 (labeled as PHICH-1(1) and PHICH-2(1) respectively), a second repetition of PHICH-3 and PHICH-4 (labeled as PHICH-3(2) and PHICH-4(2) respectively), and a third repetition of PHICH-1 and PHICH-2 (labeled as PHICH-1(3) and PHICH-2(3) respectively). The OFDM symbol 402B contains a first repetition of PHICH-3 and PHICH-4 (labeled as PHICH-3(1) and PHICH-4(1) respectively), a second repetition of PHICH-1 and PHICH-2 (labeled as PHICH-1(2) and PHICH-2(2) respectively), and a third repetition of PHICH-3 and PHICH-4 (labeled as PHICH-3(3) and PHICH-4(3) respectively). To balance power across the antennas being used, the PHICH mapping 400A applies the mappings 300A and 300B to different PHICHs in an alternating manner as shown.
In the PHICH mapping 400B of FIG. 4B, there are three OFDM symbols 404A, 404B, and 404C, each containing one repetition of a number of PHICHs. More specifically, the OFDM symbol 404A contains a first repetition of PHICH-1, PHICH-2 and PHICH-3 (labeled as PHICH-1(1), PHICH-2(1), and PHICH-3(1) respectively). The OFDM symbol 404B contains a second repetition of PHICH-1, PHICH-2 and PHICH-3 (labeled as PHICH-2(2), PHICH-3(2), and PHICH-1(2) respectively). The OFDM symbol 404C contains a third repetition of PHICH-1, PHICH-2 and PHICH-3 (labeled as PHICH-3(3), PHICH-1(3), and PHICH-2(3) respectively). To balance power across the antennas being used, the PHICH mapping 400B applies the mappings 300A and 300B to different PHICHs in an alternating manner as shown. The PHICH mappings 400A and 400B of FIGS. 4A-4B are exemplary only and are not intended to limit embodiments of the communication technique to a particular mapping or application. For example, if each OFDM symbol corresponds to a single PHICH, the mappings 300A and 300B can similarly be alternated over corresponding OFDMs to mitigate power imbalances.
In at least some embodiments, the communication technique involves various operations in accordance with the 3GPP protocol. In such embodiments, the control module 110 described previously performs such operations. For example, a block of symbols d(0), . . . , d(Msymb−1) to be transmitted should be first aligned with resource element group size, resulting in a block of symbols d(0)(0), . . . , d(0)(c·Msymb−1), where c=1 for normal cyclic prefix; and c=2 for extended cyclic prefix. For normal cyclic prefix, d(0)(i)=d(i), for i=0, . . . , Msymb−1. For extended cyclic prefix,




  
    
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The block of symbols d(0)(0), . . . , d(0)(c·Msymb−1) are mapped to layers and precoded, resulting in a block of vectors y(i)=[y(0) . . . y(P-1)(i)]T, i=0, . . . , c·Msymb−1, where y(p)(i) represents the signal for antenna port p, p=0, . . . , P−1, and the number of antenna ports for cell-specific reference signals Pε{1, 2, 4}. The layer mapping and precoding operation depends on the cyclic prefix length and the number of antenna ports used for transmission of the PHICH. The PHICH is transmitted on the same set of antenna ports as the physical broadcast channel (PBCH).
For transmission on four antenna ports (P=4), layer mapping follows Table 4 below. In Table 4, the number of layers is equal to the number of antenna ports.









TABLE 4





Number
Number of 
Codeword-to-layer mapping


of layers
code words
i = 0, 1, . . . , Msymblayer − 1







4
1
x(0)(i) = d(0)(4i) Msymblayer = Msymb(0)




x(1)(i) = d(0)(4i + 1)




x(2)(i) = d(0)(4i + 2)




x(3)(i) = d(0)(4i + 3)









with Msymb(0)=c·Msymb and precoding by





  
    
      
        
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                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    
                      -
                      1
                    
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    
                      -
                      j
                    
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    
                      -
                      1
                    
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    
                      -
                      j
                    
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
              
              ]
            
          
          ⁡
          
            [
            
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            0
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            1
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            2
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            3
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            0
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            1
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            2
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            3
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        Equation
        ⁢
        
          
        
        ⁢
        1
      
    
  




if (i+nPHICHgroup) mod 2=0 for normal cyclic prefix, or (i+└nPHICHgroup/2┘) mod 2=0 for extended cyclic prefix, where nPHICHgroup is the PHICH group number and i=0, 1, 2, and by





  
    
      
        
          [
          
            
              
                
                  
                    y
                    
                      (
                      0
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      4
                      ⁢
                      i
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      1
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      4
                      ⁢
                      i
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      2
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      4
                      ⁢
                      i
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      3
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      4
                      ⁢
                      i
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      0
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      1
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      1
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      1
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      2
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      1
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      3
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      1
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      0
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      2
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      1
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      2
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      2
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      2
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      3
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      2
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      0
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      3
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      1
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      3
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      2
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      3
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      3
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      3
                    
                    )
                  
                
              
            
          
          ]
        
        =
        
          
            
              1
              
                2
              
            
            ⁡
            
              [
              
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    
                      -
                      1
                    
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    
                      -
                      j
                    
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    
                      -
                      1
                    
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    
                      -
                      j
                    
                  
                  
                    0
                  
                
              
              ]
            
          
          ⁡
          
            [
            
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            0
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            1
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            2
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            3
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            0
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            1
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            2
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            3
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        Equation
        ⁢
        
          
        
        ⁢
        2
      
    
  




otherwise for i=0, 1, 2. The value j is the repetition index of each bit (e.g., 3 repetitions) and nPHICHgroup is the PHICH number (or PHICH group number) as in FIGS. 4A and 4B. Equation 1 corresponds to mapping a first repetition to a pair of antennas (e.g., antennas 1 and 3 as in FIG. 3A). Equation 2 corresponds to mapping a second repetition to a pair of antennas (e.g., antennas 2 and 4 as in FIG. 3A). Thus, in accordance with some embodiments, the mappings provided by Equations 1 and 2 are applied alternatively to different pairs of antennas to achieve the communication technique.

FIG. 5 illustrates a method 500 in accordance with embodiments of the disclosure. As shown, the method 500 comprises spreading a communication bit based on a predetermined spreading factor (block 502). In at least some embodiments, the spreading factor is equal to four. At block 504, the method 500 comprises forming a set of SFBCs based on the spread communication bit. At block 506, the set of SFBCs are consecutively transmitted over a pair of antennas.
In at least some embodiments, the method 500 comprises additional steps. For example, the method 500 may include forming an additional set of SFBCs corresponding to a repetition of the spread communication bit and transmitting the additional set of SFBCs consecutively over a different pair of antennas. Additionally or alternatively, the method 500 may include mapping separate sets of SFBCs corresponding to repetitions of the spread communication bit and transmitting each set of SFBCs consecutively over different pairs of antennas in an alternating manner. Additionally or alternatively, the method 500 may include selectively mapping three sets of SFBCs corresponding to three repetitions of ACK/NACK bits, transmitting the first and third sets of SFBCs on a first pair of antennas, and transmitting the second set of SFBCs on a second pair of antennas. Additionally or alternatively, the method 500 comprises selectively applying different ACK/NACK mappings to a PHICH mapping to balance power for a plurality of antennas.
While several embodiments have been provided in the present disclosure, it should be understood that the disclosed systems and methods might be embodied in many other specific forms without departing from the spirit or scope of the present disclosure. The present examples are to be considered as illustrative and not restrictive, and the intention is not to be limited to the details given herein. For example, the various elements or components may be combined or integrated in another system or certain features may be omitted, or not implemented.
In addition, techniques, systems, subsystems, and methods described and illustrated in the various embodiments as discrete or separate may be combined or integrated with other systems, modules, techniques, or methods without departing from the scope of the present disclosure. Other items shown or discussed as coupled or directly coupled or communicating with each other may be indirectly coupled or communicating through some interface, device, or intermediate component whether electrically, mechanically, or otherwise. Other examples of changes, substitutions, and alterations are ascertainable by one skilled in the art and could be made without departing from the spirit and scope disclosed herein.

## Claims

1. A communication system, comprising:
a first device; and
a second device in communication with the first device, the second device having at least a first pair and a second pair of antennas,
wherein the second device spreads a communication bit by a predetermined spreading factor and forms a first set of spatial block codes in frequency domain based on the spread communication bit, the first set of spatial block codes being consecutively transmitted on one of the first and second pairs of antennas, and
wherein the second device forms a separate set of spatial block codes for each repetition of the spread communication bit, each separate set of spatial block codes being consecutively transmitted over the first and second pairs of antennas in an alternating manner.

2. The communication system of claim 1 wherein the communication bit corresponds to an ACK/NACK bit.

3. The communication system of claim 1 wherein the predetermined spreading factor is four.

4. The communication system of claim 1 wherein the first pair of antennas corresponds to a first and third antenna position and wherein the second pair of antennas corresponds to a second and fourth antenna position.

5. The communication system of claim 1 wherein the spatial block codes comprise at least one of spatial frequency block codes (SFBC) and spatial time block codes (STBC).

6. A communication device, comprising:
a transmitter with a control module; and
a first pair and second pair of antennas coupled to the transmitter;
wherein the control module causes a first set of spatial block codes, formed in frequency domain and corresponding to a spread communication bit, to be mapped for consecutive transmission on one of the first and second pairs of antennas and
wherein the control module selectively maps three sets of spatial block codes corresponding to three repetitions of the spread communication bit, the first and third sets of spatial block codes being mapped for transmission on the first pair of antennas and the second set of spatial block codes being mapped for transmission on the second pair of antennas.

7. The communication device of claim 6 wherein the control module selectively maps the first and third sets of spatial block codes for transmission on the second pair of antennas and maps the second set of spatial block codes for transmission on the first pair of antennas.

8. The communication device of claim 6 wherein the control module applies a spreading factor of four to the communication bit.

9. The communication device of claim 6 wherein the control modules selectively applies different ACK/NACK mappings to a PHICH mapping to balance power across the first and second pairs of antennas.

10. A method, comprising:
spreading a communication bit based on a predetermined spreading factor;
forming a set of spatial block codes in frequency domain based on the spread communication bit;
transmitting the set of spatial block codes consecutively over a pair of antennas;
forming an additional set of spatial block codes corresponding to a repetition of the spread communication bit; and
transmitting the additional set of spatial block codes consecutively over a different pair of antennas.

11. The method of claim 10 further comprising,
mapping separate sets of spatial block codes corresponding to repetitions of the spread communication bit; and
transmitting each set of spatial block codes consecutively over different pairs of antennas in an alternating manner.

12. The method of claim 10 further comprising selectively applying different ACK/NACK mappings to a PHICH mapping to balance power for a plurality of antennas.

13. A communication device, comprising:
a transmitter with a control module; and
a first pair and second pair of antennas coupled to the transmitter;
wherein the control module causes a first set of spatial block codes, formed in frequency domain and corresponding to a spread communication bit, to be mapped for consecutive transmission on one of the first and second pairs of antennas, and
wherein the control module selectively maps a block of symbols, d(0)(0), . . . , d(0)(c·Msymb−1), to the first and second pairs of antennas according to













Number
Number of 
Codeword-to-layer mapping


of layers
code words
i = 0, 1, . . . , Msymblayer − 1







4
1
x(0)(i) = d(0)(4i) Msymblayer = Msymb(0)




x(1)(i) = d(0)(4i + 1)




x(2)(i) = d(0)(4i + 2)




x(3)(i) = d(0)(4i + 3)









with Msymb(0)=c·Msymb and precoding by




  
    
      
        
          [
          
            
              
                
                  
                    y
                    
                      (
                      0
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      4
                      ⁢
                      i
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      1
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      4
                      ⁢
                      i
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      2
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      4
                      ⁢
                      i
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      3
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      4
                      ⁢
                      i
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      0
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      1
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      1
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      1
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      2
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      1
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      3
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      1
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      0
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      2
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      1
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      2
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      2
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      2
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      3
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      2
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      0
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      3
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      1
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      3
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      2
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      3
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      3
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      3
                    
                    )
                  
                
              
            
          
          ]
        
        =
        
          
            
              1
              
                2
              
            
            ⁡
            
              [
              
                
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    
                      -
                      1
                    
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    
                      -
                      j
                    
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    
                      -
                      1
                    
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    
                      -
                      j
                    
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
              
              ]
            
          
          ⁡
          
            [
            
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            0
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            1
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            2
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            3
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            0
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            1
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            2
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            3
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        Equation
        ⁢
        
          
        
        ⁢
        1
      
    
  




if (i+nPHICHgroup) mod 2=0 for normal cyclic prefix, or (i+└nPHICHgroup/2┘) mod 2=0 for extended cyclic prefix, where nPHICHgroup is the PHICH group number and i=0, 1, 2, and by




  
    
      
        
          [
          
            
              
                
                  
                    y
                    
                      (
                      0
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      4
                      ⁢
                      i
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      1
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      4
                      ⁢
                      i
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      2
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      4
                      ⁢
                      i
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      3
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      4
                      ⁢
                      i
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      0
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      1
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      1
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      1
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      2
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      1
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      3
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      1
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      0
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      2
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      1
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      2
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      2
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      2
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      3
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      2
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      0
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      3
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      1
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      3
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      2
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      3
                    
                    )
                  
                
              
            
            
              
                
                  
                    y
                    
                      (
                      3
                      )
                    
                  
                  ⁡
                  
                    (
                    
                      
                        4
                        ⁢
                        i
                      
                      +
                      3
                    
                    )
                  
                
              
            
          
          ]
        
        =
        
          
            
              1
              
                2
              
            
            ⁡
            
              [
              
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    
                      -
                      1
                    
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    
                      -
                      j
                    
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    
                      -
                      1
                    
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    j
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                
                
                  
                    0
                  
                  
                    0
                  
                  
                    1
                  
                  
                    0
                  
                  
                    0
                  
                  
                    0
                  
                  
                    
                      -
                      j
                    
                  
                  
                    0
                  
                
              
              ]
            
          
          ⁡
          
            [
            
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            0
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            1
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            2
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Re
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            3
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            0
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            1
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            2
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
              
                
                  
                    Im
                    ⁡
                    
                      (
                      
                        
                          x
                          
                            (
                            3
                            )
                          
                        
                        ⁡
                        
                          (
                          i
                          )
                        
                      
                      )
                    
                  
                
              
            
            ]
          
        
      
    
    
      
        Equation
        ⁢
        
          
        
        ⁢
        2
      
    
  



otherwise for i=0, 1, 2, where i is the repetition index of each bit.

14. The communication device of claim 13 wherein the block of symbols are mapped to the first and second pairs of antennas by alternatively applying Equations 1 and 2.

15. The communication device of claim 13 wherein the block of symbols comprises ACK/NACK repetitions.

16. A communication device, comprising:
a transmitter with a control module; and
a first pair and second pair of antennas coupled to the transmitter;
wherein the control module causes a first set of spatial block codes, formed in frequency domain and corresponding to a spread communication bit, to be mapped for consecutive transmission on one of the first and second pairs of antennas, and
wherein the control module causes separate sets of spatial block codes for each repetition of the spread communication bit to be mapped for consecutive transmission on the first and second pairs of antennas in an alternating manner.

17. A method, comprising:
spreading a communication bit based on a predetermined spreading factor;
forming a set of spatial block codes in frequency domain based on the spread communication bit;
transmitting the set of spatial block codes consecutively over a pair of antennas;
selectively mapping three sets of spatial block codes corresponding to three repetitions of ACK/NACK bits,
transmitting the first and third sets of spatial block codes on a first pair of antennas; and
transmitting the second set of spatial block codes on a second pair of antennas.