### TABLE II Best found asymptotic gains (in dB) with respect to Gray mapping for 2m-QAM constellations and nmap dimensions

2005

Cited by 4

### TABLE II Best found asymptotic gains (in dB) with respect to Gray mapping for 2m-QAM constellations and nmap dimensions

2005

### Table 3.2: Best found asymptotic gains (in dB) with respect to Gray mapping for 2m-QAM constellations and nmap dimensions

2004

### Table 1: Critical values of for M-QAM.

1998

"... In PAGE 4: ...roof. The details mimic the real-valued case given in [7]. In summary, C is a lower bound on dither amplitude for which the convex set F exists, while ZF and OE are lower bounds on for which CMA-like local neighborhoods around zero- forcing and open-eye equalizers exist, respectively. Table1 quanti- fies the values of f C; ZF; OEg for M-QAM alphabets. Note that the constant ZF may be less than C, in which case there would exist isolated CMA-like neighborhoods around the ZF solutions (i.... ..."

Cited by 4

### Table 1: Critical values of for M-QAM.

1998

"... In PAGE 4: ...roof. The details mimic the real-valued case given in [7]. In summary, C is a lower bound on dither amplitude for which the convex set F exists, while ZF and OE are lower bounds on for which CMA-like local neighborhoods around zero- forcing and open-eye equalizers exist, respectively. Table1 quanti- fies the values of f C; ZF; OEg for M-QAM alphabets. Note that the constant ZF may be less than C, in which case there would exist isolated CMA-like neighborhoods around the ZF solutions (i.... ..."

Cited by 4

### TABLE III. BANDWIDTH AND POWER EFFICIENCY OF M- QAM SIGNALS [1]

### Table 1: Conversion factor from average energy to peak energy for M-QAM. In this investigation we use 64-QAM as the maximum modulation level, thus transmitting six bits per symbol when the channel is as its best. When the channel de-

1999

"... In PAGE 3: ... A tight upper bound on the symbol error probability for M-QAM modulation is given by [6]: PM 1 ? quot; 1 ? 2Q s 3Eav (M ? 1)N0 !#2 : (1) Here the average symbol energy Eav, the noise power, N0, and the modulation format, M, are assumed to be known. The Gaussian cumulative distribution function, Q(x), can be calculated according to: Q(x) = 1 ? erf( x p2) 2 ; (2) where erf(x) is the error function: erf(x) = 2 p Z x 0 e?t2dt: (3) By solving (1) for Eav N0 and using (2) and (3), we get the SNIR required for a certain symbol error probability, PM, and a given M: Eav N0 2(M ? 1) 3 herf?1 p1 ? PM i2 : (4) Furthermore, since we measure and predict the average signal energy, whereas the constraints1 have to be applied to the maximum signal energy, the value Eav has to be modified by a factor M, according to Table1 , yielding Emax = M Eav. M 2 4 16 64 M 1 1 p9=5 p7=3 Table 1: Conversion factor from average energy to peak energy for M-QAM.... ..."

Cited by 1

### Table 1: Conversion factor from average energy to peak energy for M-QAM. In this investigation we use 64-QAM as the maximum modulation level, thus transmitting six bits per symbol when the channel is as its best. When the channel de-

"... In PAGE 3: ... A tight upper bound on the symbol error probability for M-QAM modulation is given by [6]: a0 a1 a3a20a5a22a21 a23 a5a22a21a25a24a27a26a29a28a31a30 a32a27a33a35a34a37a36 a38a40a39 a21a41a5a13a42a44a43a46a45a48a47a50a49a31a51a53a52 (1) Here the average symbol energy a33 a34a37a36 , the noise power, a43 a45 , and the modulation format, a39 , are assumed to be known. The Gaussian cumulative distribution function, a26 a38a55a54 a42 , can be calculated according to: a26 a38a56a54 a42a58a57 a5a22a21a60a59a8a61a44a62 a38a35a63 a64 a51 a42 a24 a65 (2) where a59a8a61a44a62 a38a56a54 a42 is the error function: a59a8a61a44a62 a38a55a54 a42a66a57 a24 a67 a68a70a69 a63 a45a72a71 a9a74a73a55a75a77a76a27a78 a52 (3) By solving (1) for a79a81a80a83a82 a84a86a85 and using (2) and (3), we get the SNIR required for a certain symbol error probability, a0a86a1 , and a given a39 : a33a35a34a37a36 a43 a45a88a87 a24 a38a40a39 a21a89a5a90a42 a32 a91 a59a92a61a93a62 a9a81a94a35a95a97a96 a5a22a21a25a0a86a1a99a98a101a100 a51 a52 (4) Furthermore, since we measure and predict the average signal energy, whereas the constraints1 have to be applied to the maximum signal energy, the value a33a35a34a37a36 has to be modified by a factor a102 a1 , according to Table1 , yielding a33a104a103a22a34 a63 a57 a102 a1a4a105 a33a35a34a37a36 . a39 2 4 16 64 a102 a1 a5 a5 a96 a106a108a107 a18 a96 a109a110a107 a32 Table 1: Conversion factor from average energy to peak energy for M-QAM.... ..."