### Table 4.4: Optimum q-state 1 b/s/Hz BPSK 4-space-time codes.

### TABLE I TOTAL EDGE COUNT FOR MAP EQUALIZATION FOR A SPACE-TIME TRELLIS CODED SYSTEM (STTC) AND FOR THE PROPOSED SYSTEM (RSM), FOR SEVERAL VALUES OF ISI LENGTH D, NUMBER OF TRANSMIT ANTENNAS N, AND BPSK MODULATION.

### Table 1: System Parameters of BPSK with space-time transmit diversity

"... In PAGE 3: ....5 Numerical Results................................................................................................31 Table1 : System Parameters of BPSK with space-time transmit diversity.... ..."

### Table 4: Optimum q-state 1 b/s/Hz BPSK 4-space-time codes. A quot;y quot; denotes that the code is catastrophic.

2002

"... In PAGE 11: ...CP (L). These values are listed in Table 2. In cases where the codes which provide best ; AP (L) and CP (L) are catastrophic, the best non-catastrophic codes are also presented. n gt; 2 Cases Some optimum (maximum diversity and coding gain) space-time codes using 3 or 4 transmit antennas and BPSK modulations are provided in Table 3 and Table4 . The search- ing procedure for these cases is similar to that for the n = 2 cases.... ..."

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### Table 2: System Parameters of MQAM with space-time transmit diversity

"... In PAGE 3: ...able 1: System Parameters of BPSK with space-time transmit diversity......................40 Table2 : System Parameters of MQAM with space-time transmit diversity.... In PAGE 40: ... BER performance of MQAM with or without STTD under Rayleigh fading channel is presented in [46]. Table2 shows the system parameters that are used here ... ..."

### Table 3: Optimum q-state 1 b/s/Hz BPSK 3-space-time codes. A quot;y quot; denotes that the code is catastrophic.

2002

"... In PAGE 11: ...CP (L). These values are listed in Table 2. In cases where the codes which provide best ; AP (L) and CP (L) are catastrophic, the best non-catastrophic codes are also presented. n gt; 2 Cases Some optimum (maximum diversity and coding gain) space-time codes using 3 or 4 transmit antennas and BPSK modulations are provided in Table3 and Table 4. The search- ing procedure for these cases is similar to that for the n = 2 cases.... In PAGE 11: ... In each case, the selected code satis ed the su cient conditions for maximum diversity gain while simultaneously pro- viding maximum values of , AP (L) and CP (L). These values are listed in Table3 and Table 4. A 16-state QPSK space-time code using 3 transmit antennas is given in Table 5.... ..."

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### Table 1. Space-time characteristics of possible legislative drafting systems

2004

### Table 1. Optimum a20 -state 1 b/s/Hz QPSK 2-space-time codes over a40a6a41 for quasi-static fading.

2001

"... In PAGE 1: ... We use the systematic approach [4] with minor modifica- tions to search for the 1 b/s/Hz optimum 2-space-time trel- lis codes for rapid fading and quasi-static fading cases. In Table1... ..."

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### Table 1: Optimum q-state 2 b/s/Hz 4-PSK space-time codes (ePmin from [6]).

2002

"... In PAGE 8: ... As previously discussed q = 2(Q?1)R with Q = 2 or 3 if the number of states is 4 or 16, while [9] q = 2(Q?2)R+1 with Q = 2 or 3 if the number of states is 8 or 32. Our results for this case are summarized in Table1 . Besides providing ; AP (L) and CP (L), for convenience we provide the \e ective product distance quot;, ePmin, from [6] in Table 1.... In PAGE 8: ... Our results for this case are summarized in Table 1. Besides providing ; AP (L) and CP (L), for convenience we provide the \e ective product distance quot;, ePmin, from [6] in Table1 . To help the reader understand the process taken to arrive at Table 1, we describe some of the details.... In PAGE 8: ... Besides providing ; AP (L) and CP (L), for convenience we provide the \e ective product distance quot;, ePmin, from [6] in Table 1. To help the reader understand the process taken to arrive at Table1 , we describe some of the details. In particular, we found that there are 1840 di erent 4-state codes (not counting4 permutations of the columns of G) which satis ed the su cient conditions for maximum diversity gain while simultaneously providing the highest coding gain, = 2, of any codes satisfying the su cient conditions for maximum diversity gain.... In PAGE 8: ... The 4 state case was atypical in this respect, it being the only case where we could not nd optimum codes, with the largest possible diversity and coding gain, which satis ed the su cient conditions for maximum diversity. From these 288 codes, we selected one of the 24 codes with largest AP (2), CP (2) and AP (3) to put in Table1 . By examining the slope of the FER performance 4In the count of 1840 given, several of the codes counted could be considered to be equivalent.... In PAGE 9: ... All of the 96 codes provided the same AP (3) of 5:76, and 24 of them gave best CP (3) of 6:24. Thus we selected the rst one we encountered with CP (3) = 6:24 to put in Table1 . We were also able to show that any codes satisfying the necessary conditions for maximum diversity could not provide = p32 without yielding AP (3) lt; 5:76.... In PAGE 9: ... We were also able to show that any codes satisfying the necessary conditions for maximum diversity could not provide = p32 without yielding AP (3) lt; 5:76. For the 32-state case we found that the maximum coding gain is = 6 and one such code with best CP (3) = 6:33 and best CP (4) = 8:72 is put in Table1 . Further this code satis es the su cient conditions for maximum diversity gain.... In PAGE 9: ... Further this code satis es the su cient conditions for maximum diversity gain. We note that a few of our calculations concerning the cases in Table1 di er from those in [1] and [4]. The coding gain for the 8-state case from [1] is = p12 based on our calculations, as opposed to = p20 as stated in [1].... In PAGE 11: ... We conjecture it achieves near optimum (if not optimum) coding gain. 5 Probability of Frame Error Performance Figure 1 shows the frame error rate of the space-time codes listed in Table1 for cases with 2 transmit and 2 receive antennas. Figure 1 illustrates the gain achieved by increasing the constraint length of the codes.... In PAGE 11: ... Figures 2 through 4 compare the performance of our codes and those from [1, 4, 6]. Clearly, the codes in Table1 are better than the codes from [1, 4, 6] when judged in terms of frame error rate. In all our simulations, each frame consists of 130 transmissions from of each transmit antenna (` = 130).... In PAGE 14: ... We discuss the signi cance of augmenting with AP (L) and CP (L), using the cases in Figure 2 as an example. Consider the 4 state code GT = 0 B @ 2 0 1 2 2 2 2 1 1 C A (9) given in Table1 . Recall this code provides a coding gain of p8.... ..."

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### TABLE I Opt q-state 2 b/s/Hz 4-PSK 2-space-time codes (2 tr ant).

2000

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