Effective signal interference plus noise ratio estimation for multi-order modulation

This application claims the benefit of U.S. provisional patent application Ser. No. 61/038,569, filed Mar. 21, 2008, the disclosure of which is hereby incorporated herein by reference in its entirety.

This invention relates to determining an effective signal interference plus noise ratio estimation associated with the transmission of data, and in particular to determining an effective signal interference plus noise ratio estimation associated with the transmission of data transmitted at multiple modulation orders.

In certain technologies, such as orthogonal frequency division multiplexing (OFDM), a communications channel between two devices is implemented through multiple subcarriers. Each subcarrier of a channel may have a different signal-to-interference-plus-noise ratio (SNR) associated with the subcarrier at a particular instant in time. Methodologies have been introduced that map the instantaneous SNR of multiple subcarriers into an effective channel SNR associated with the channel. The effective channel SNR can be used, for example, to determine a block-error probability (BLEP) for a given particular channel state. The BLEP may be used to determine an appropriate modulation and coding scheme (MCS) for use on the channel to optimize throughput of the channel. Determining an effective channel SNR is also useful in system level simulations.

It is common today to code information bits with forward error correction bits and send the data in a forward error correction (FEC) block. The effects of noise and interference may prevent a receiver from decoding an FEC block. Thus, it is necessary to periodically retransmit a FEC block. The retransmitted FEC block may be combined with the original FEC block, and if the combined FEC block cannot be properly decoded, additional FEC blocks will be requested until the FEC block can be decoded. Some retransmission technologies, such as Adaptive Hybrid Automatic Repeat Request (A-HARQ) for example, allow the modulation order of a retransmitted FEC block to differ from the modulation order used to transmit the original FEC block. It may be desirable for the transmitter to send the retransmitted FEC block at a particular SNR to increase the likelihood that the combined FEC block can be decoded. Thus, it would be helpful to determine an effective channel SNR associated with the transmission of two FEC blocks of data at different modulation orders. However, the known methodologies for determining an effective channel SNR cannot determine an effective channel SNR associated with transmissions at different modulation orders. With increased interest in the use of A-HARQ for emerging telecommunication technologies, there is a need for a mechanism for determining an effective channel SNR associated with data transmitted at different modulation orders.

The present invention determines an effective signal-to-interference-plus-noise ratio (ESINR) associated with the transmission of modulation symbols at different modulation orders. The transmissions can be separate transmissions that are combined together, such as in Adaptive Hybrid Automatic Repeat Request (A-HARQ) retransmissions of forward error correction (FEC) blocks, or the transmissions can be a single transmission of a single data block using different modulation orders, such as spatial multiplexing in a multiple-input and multiple-output (MIMO) transmission.

A base modulation is determined, such as a binary phase shift keying modulation, which is associated with a base modulation order, such as one. A normalization factor is determined to normalize the soft-bit energy of a bit represented by a modulation symbol of the base modulation order to determine a base modulation symbol signal-to-interference-plus-noise ratio (SNR). A SNR bit factor (SBF) for each of Q number of bits per symbol associated with a second modulation order that is different from the base modulation order, such as a binary phase shift keying modulation order, is determined. The SBF is determined based on the soft-bit energy associated with bits represented by modulation symbols of the second modulation order, and through normalization of the soft-bit energy via the normalization factor. SBFs may be determined for multiple different modulation orders. An ESINR can be calculated using the SBFs of the modulation orders by which the different modulation symbols were modulated. The calculated ESINR is in terms of a base modulation symbol SNR, and may be used in system level simulations to determine block error probabilities, for example. The ESINR may be used in A-HARQ to determine an appropriate modulation and coding scheme for a retransmission of an FEC block.

Those skilled in the art will appreciate the scope of the present invention and realize additional aspects thereof after reading the following detailed description of the preferred embodiments in association with the accompanying drawing figures.

The accompanying drawing figures incorporated in and forming a part of this specification illustrate several aspects of the invention, and together with the description serve to explain the principles of the invention.

FIG. 1 is a block diagram illustrating subcarriers in an orthogonal frequency division multiplexing (OFDM) transmission system;

FIG. 2 is a block diagram illustrating particular data transmissions in the system illustrated in FIG. 1 ;

FIG. 3 is a high-level block diagram of a modulation order mapper according to one embodiment of the invention;

FIG. 4 is a constellation diagram associated with a quadrature phase shift keying (QPSK) modulation order;

FIG. 5 is a constellation diagram associated with a 16-quadrature amplitude modulation (16QAM) modulation order

FIG. 6 is a block diagram illustrating a mapping of modulation symbol signal-to-interference-plus-noise ratios (SNRs) to base modulation symbol SNRs according to one embodiment of the invention; and

FIG. 7 is a block diagram illustrating a modulation order mapping in accordance with one embodiment of the invention.

The embodiments set forth below represent the necessary information to enable those skilled in the art to practice the invention and illustrate the best mode of practicing the invention. Upon reading the following description in light of the accompanying drawing figures, those skilled in the art will understand the concepts of the invention and will recognize applications of these concepts not particularly addressed herein. It should be understood that these concepts and applications fall within the scope of the disclosure and the accompanying claims.

The present invention relates to determining an effective signal to interference plus noise ratio (ESINR) associated with transmission of modulation symbols at different modulation orders. The present invention can be used in system level simulation, or by a scheduler in a base station, for example, to determine a particular modulation and coding scheme (MCS) for use in the retransmission of a forward error correction (FEC) block to determine an ESINR associated with the combined transmissions of an FEC block at different modulation orders.

As used throughout the specification, the phrase “modulation order” will refer to a modulation technique by the number of different symbols that can be transmitted by the modulation technique. For example, the binary phase shift keying (BPSK) modulation technique has an order of two because two different symbols can be transmitted using BPSK. As another example, the 16-quadrature amplitude modulation (16QAM) technique has an order of sixteen because sixteen different symbols can be transmitted using 16QAM.

FIG. 1 is a block diagram illustrating subcarriers in an orthogonal frequency division multiplexing (OFDM) transmission system 10 . A base station, such as a Long Term Evolution (LTE) enhanced Node B (eNodeB) 12 , includes a scheduler 14 adapted to determine a particular MCS for use in a transmission of data to a receiver, such as a user equipment (UE) 16 . The scheduler 14 can have a control system 18 including hardware and software suitable for carrying out the operations of the scheduler 14 , and can be coupled to a coder 20 and a modulator 22 suitable for coding and modulation operations. The UE 16 also has a control system 24 which may include a combination of hardware and software for implementing a variety of functionality in the UE 16 , which may comprise, for example, a cellular phone. The UE 16 includes a demodulator 26 and a decoder 28 for demodulating and decoding data transmitted by the eNodeB 12 to the UE 16 . Although not shown, it will be appreciated that the eNodeB 12 also has a demodulator and decoder for processing data sent to the eNodeB 12 by the UE 16 and that the UE 16 similarly has a modulator and coder for use in providing data to the eNodeB 12 . Modulation and coding techniques are well known to those skilled in the art and will not be discussed herein.

The eNodeB 12 may have a plurality of different channels 30 A, 30 B from which to choose to send data to the UE 16 . Each channel 30 A, 30 B is made up of multiple subcarriers 32 . For example, the channel 30 A is made up of subcarriers 32 A- 32 C, and the channel 30 B is made up of subcarriers 32 D- 32 F. Each subcarrier 32 may have a different signal-to-interference-plus-noise ratio (SNR) associated with it. Because the SNR is not flat across the subcarriers 32 , a process has been developed, referred to herein as an Effective SIR Mapping (ESM) process, that maps the SNRs associated with the subcarriers 32 that compose a channel 30 to an instantaneous ESINR associated with the respective channel 30 . The ESM process is described in detail in “System-level evaluation of OFDM—further considerations,” R1-031303, RAN WG1 #35, the entirety of which is hereby incorporated herein by reference. The SNR associated with a subcarrier 32 differs based on the modulation order used on the subcarrier 32 . The ESM process proposes the following equation for determining the ESINR on a channel 30 using BPSK modulation over multiple subcarriers 32 :

γ eff = - ln ⁡ ( 1 N ⁢ ∑ k = 1 N ⁢ ⅇ - γ k ) ,

where γ eff is the ESINR associated with the channel 30 , N is the number of subcarriers 32 , and γ k is the SNR on each subcarrier 32 .

For higher order modulations, the ESM process proposes the use of the following generalized formula:

γ eff = - βln ⁡ ( 1 N ⁢ ∑ i = 1 N ⁢ ⅇ γ i β ) ,

where β is an experimentally derived value based on a particular MCS. Thus, the ESM process requires a different β for each different MCS, and fails to address the determination of a single ESINR associated with the transmission of data over subcarriers 32 using different modulation orders.

FIG. 2 is a block diagram illustrating exemplary data transmissions in the system 10 illustrated in FIG. 1 . The eNodeB 12 transmits a FEC block 34 A to the UE 16 . By FEC block, it is meant that a combination of information bits and FEC bits are transmitted as a block of data, as is understood by those skilled in the art. The FEC block 34 A is transmitted by the eNodeB 12 using 16QAM modulation. Assume that the decoder 28 is unable to decode the FEC block 34 A and the UE 16 sends a NAK 36 to the eNodeB 12 to indicate that the FEC block 34 A should be retransmitted. Assume further that the eNodeB 12 uses an Adaptive Hybrid Automatic Repeat Request (A-HARQ) process for retransmitting FEC blocks. A-HARQ is known to those skilled in the art and will not be described in detail herein, other than to note that FEC blocks retransmitted using A-HARQ are frequently combined with previously transmitted FEC blocks in order to increase the likelihood of successful decoding of the FEC block.

Using A-HARQ, the eNodeB 12 may send an FEC block 34 B, which is a retransmission of the information bits in the FEC block 34 A with additional error correction bits, using a different MCS than the eNodeB 12 used to transmit the FEC block 34 A. However, the eNodeB 12 may want to ensure that the FEC block 34 B is sent at a certain MCS that will result in a particular block error probability (BLEP) for the combined transmissions of the FEC block 34 A and the FEC block 34 B so that the combined transmissions are likely to be properly decoded by the decoder 28 . In order for the eNodeB 12 to determine a BLEP associated with the combined transmissions of the FEC block 34 A and the FEC block 34 B, the eNodeB 12 may determine a combined ESINR associated with the transmissions of both FEC blocks 34 A, 34 B. However, the ESM process described previously provides no mechanism for determining an ESINR associated with the transmission of data at different modulation orders.

The present invention provides a modulation order mapper that enables the determination of an ESINR associated with the transmission of data at different modulation orders. While described above in terms of A-HARQ retransmissions in an OFDM system, the ability to determine an ESINR associated with the transmission of data using different modulation orders may be useful in a wide variety of situations, such as during system level simulations. Moreover, while the discussion herein will, for the purposes of illustration, associate a modulation symbol SNR with a particular subcarrier in an OFDM system, the principles herein are not limited to determining an ESINR from different modulation orders from different subcarriers, but rather can be used on a modulation symbol by modulation symbol basis, such as for use in a technology that enables different modulation orders to be used to transmit data within the same FEC block.

FIG. 3 is a high-level block diagram of a modulation order mapper 50 according to one embodiment of the invention. The modulation order mapper 50 maps the modulation symbol SNR associated with symbols of different modulation orders to a BPSK modulation symbol SNR such that an ESINR calculation 52 can determine an ESINR 54 associated with data transmitted at different modulation orders.

The present invention, as described herein, uses the soft-bit energy associated with bits in a modulation symbol to determine a SNR bit factor (SBF) for each bit of a respective modulation symbol. The SBF is then used to map the modulation symbol SNR of a respective modulation symbol to a BPSK modulation symbol SNR. Once all modulation symbol SNRs are mapped to the BPSK modulation symbol SNR, the ESINR can be calculated. According to one embodiment of the invention, a SNR ratio per bit for BPSK modulation is determined based on the soft-bit energy associated with a BPSK symbol. The soft-bit energy associated with a bit of a modulation symbol may be determined by log likelihood ratio (LLR) principles. LLR concepts are known to those skilled in the art and will not be described in detail herein. When demodulating in an equalized domain, an LLR calculation can be simplified to the following equation:

L ⁡ ( b ) = - γ symbol ⁡ ( min s ∈ S 0 ⁢ ( ( x - s x ) 2 + ( y - s y ) 2 ) - min s ∈ S 1 ⁢ ( ( x - s x ) 2 + ( y - s y ) 2 ) ) ,

where γ symbol is the SNR of the received QAM symbol, x is the real part of a QAM signal being transmitted, y is the imaginary part of the QAM signal being transmitted, S 0 is the constellation set that has b=0, and S 1 is the constellation set that has b=1. Assuming no noise in the signal, L(b) equals the square of the minimum distance between the constellation point and the two constellation sets S 0 or S 1 , (depending on whether the bit under consideration has a value of ‘1’ or ‘0’), weighted by γ symbol , which can be treated as the received bit energy. While the present invention used a Max-Log soft-demapping algorithm to determine the soft-bit energy associated with the modulation symbol bits as described herein, the invention is not limited to any particular soft-demapping algorithm.

Note that for BPSK symbol modulation, a single bit, b(i), is mapped to a complex-valued modulation symbol x=I+jQ according to Table 1.

Again, assuming no noise, the demapped soft-bit energy can be determined from the square of the minimum distance between the two constellation sets S 0 and S 1 . The square of the minimum distance between each of the constellation sets in a BPSK symbol equals 4, and thus:

E BPSK, soft-bit =4

Note that for either BPSK constellation point, I 2 +Q 2 =1, e.g., (1/√{square root over (1)}) 2 +(1/√{square root over (2)}) 2 =1), and thus the energy associated with a BPSK constellation point equals 1. By defining a normalization variable θ=4, the per-bit SNR (frequently represented herein by the Greek symbol gamma, i.e., γ) is normalized back to the BPSK symbol SNR, such that γ BPSK, per-bit =γ BPSK, symbol , as illustrated in the following equation:

γ BPSK , per - bit = E BPSK , soft - bit θ ⁢ γ BPSK , symbol = γ BPSK , symbol .

The normalization variable θ will be used, as described herein, to normalize soft-demapped bits from high-order QAMs, so that such soft-demapped bits will appear as a series of BPSK modulation symbols. By mapping different modulation symbol SNRs to a base modulation symbol SNR, an ESINR in terms of the base modulation can be determined from symbols associated with multiple modulation orders. The ESINR can be used, for example, to determine a block error rate performance from an additive white Gaussian noise (AWGN) curve that is based on the base modulation order.

A SBF is then determined for each of the Q bits that are represented by a respective modulation symbol. For example, Q=2 for quadrature phase shift keying (QPSK) modulation, and a SBF will be determined for each of the two bits that may be represented by a QPSK modulation symbol. For 16QAM modulation, Q=4, and a SBF will be determined for each of the four bits that may be represented by a 16QAM modulation symbol. The SBFs associated with a respective modulation order can then be applied, as described herein, to the SNR associated with a respective modulation symbol of the same modulation order to map the modulation symbol SNR to the BPSK modulation order SNR for use in determining an ESINR. Examples for determining SBFs associated with QPSK and 16QAM will be described herein, and such examples will enable those skilled in the art to determine SBFs associated with higher order modulations.

FIG. 4 is a constellation diagram associated with a QPSK modulation order. The pairs of bits that may be represented by a particular QPSK modulation symbol are shown in FIG. 4 as constellation points 60 A- 60 D, and are referred to in Table 2 as b(i) and b(i+1). The pairs of bits b(i) and b(i+1) are mapped to a complex-valued modulation symbol x=I+jQ according to Table 2.

In order to determine a SBF for each of the Q=2 bits associated with a QPSK modulation symbol, the soft-bit energy associated with each bit of each constellation point 60 A- 60 D is determined. In the example of QPSK modulation, there are a total of eight bits (i.e., two bits for each constellation point 60 , and four constellation points 60 A- 60 D). The soft-bit energy for each bit is determined by the square of the minimum distance between the constellation point 60 associated with the respective bit, and the closest constellation point 60 wherein the same bit position (e.g., b(i) or b(i+1)) has a different value than the respective bit. For example, to determine the soft-bit energy associated with bit 64 in the constellation point 60 A, the closest constellation point 60 having a bit in the same bit position of the bit 64 (i.e., b(i+1)) is determined. Notably bit 68 at the b(i+1) position in the constellation point 60 B has the same value, ‘0’, as the bit 64 . However, bit 70 and bit 74 in constellation points 60 D and 60 C, respectively, each have a value that is different from bit 64 . It should be apparent that the constellation point 60 C is closer to the constellation point 60 A than the constellation point 60 D. Thus, the soft-bit energy of the respective bit 64 can be calculated as the square of the minimum distance between the constellation point 60 A and the constellation point 60 C is determined according to the following equation:

While not expressly illustrated herein, notably, the soft-bit energy for each of the bits 62 - 76 is two in accordance with the above equation. Thus, for any bit in any constellation point 60 associated with the QPSK modulation order, the soft-bit energy is 2. Soft-bit energies are then assigned to each of the Q bits associated with a modulation symbol in proportion to the occurrence of the soft-bit energies among the total of all bits of all constellation points. Since, in the example of QPSK, each of the eight total bits of all constellation points have a soft-bit energy of 2, each of the Q=2 bits will be assigned a soft-bit energy of 2.

The SBF of each of the Q=2 bits is then determined by normalizing the SNR of the soft demapped energy to the SNR of the BPSK symbol, according to the following equation:

γ QPSK , per - bit = E QPSK , soft - bit β ⁢ γ QPSK , symbol ⁢

⁢ SBF = 1 2 ⁢ γ QPSK , symbol . ( 1 )

Such normalization makes each QPSK bit equivalent to a BPSK symbol, e.g., each QPSK symbol can be viewed as two separate BPSK symbols, with each BPSK symbol having an SNR of ½γ QPSK, symbol .

FIG. 5 is a constellation diagram associated with a 16QAM modulation order. In 16QAM modulation, Q=4 because each 16QAM modulation symbol can represent four bits. The 16 different sequences of bits that may be represented by a particular 16QAM modulation symbol are shown in FIG. 5 as constellation points 78 A- 78 P. The sequence of bits b(i), b(i+1), b(i+2), and b(i+3) are mapped to a complex-valued modulation symbol x=I+jQ according to Table 3.

In order to determine a SBF for each of the Q=4 bits associated with a 16QAM modulation symbol, the soft-bit energy associated with each bit of each constellation point 78 A- 78 P is determined. There are a total of 64 bits (i.e., four bits for each constellation point 78 , and 16 constellation points 78 A- 78 P). The soft-bit energy for each bit is determined by the square of the minimum distance between the constellation point 78 associated with the respective bit, and the closest constellation point 78 wherein the same bit position (e.g., b(i), b(i+1), b(i+2), or b(i+3)) has a different value than the respective bit, as described above with respect to determining the soft-bit energies of each bit in each QPSK constellation point.

Determining the soft-bit energies for each of the 64 bits in accordance with formula 1, above, results in 48 of the 64 bits having a soft-bit energy of ⅖ and 16 of the 64 bits having a soft-bit energy of 8/5. Thus, ¾ of the 64 bits have a soft-bit energy of ⅖ and ¼ of the 64 bits have a soft-bit energy of 8 / 5 . Consequently, ¾ of the L=4 bits are assigned a soft-bit energy of ⅖ and ¼ of the L=4 bits are assigned a soft-bit energy of 8/5, because in any four-bit sequence associated with a 16QAM modulation symbol, the probability is that ¾ of the bits (i.e., three of the four bits), will have a soft-bit energy of ⅖ and ¼ of the bits (i.e., one of the four bits) will have a soft-bit energy of 8/5.

The SBF of each of the Q=4 bits is determined by normalizing the SNR of the soft demapped energy of each of the Q=4 16QAM bits to the SNR of the BPSK symbol, according to the following equation:

For 64QAM modulation, Q=6 because each 64QAM modulation symbol can represent six bits. The sequence of bits b(i), b(i+1), b(i+2), b(i+3), b(i+4) and b(i+5) are mapped to a complex-valued modulation symbol x=I+jQ according to Table 4.

In order to determine a SBF for each of the Q=6 bits associated with a 64QAM modulation symbol, the soft-bit energy associated with each bit of each constellation point is determined. There are a total of 384 bits (i.e., six bits for each of 64 constellation points). The soft-bit energy for each bit is determined by the square of the minimum distance between the constellation point associated with the respective bit, and the closest constellation point wherein the same bit position (e.g., b(i), b(i+1), b(i+2), b(i+3), b(i+4) b(i+5)) has a different value than the respective bit, as described above with respect to determining the soft-bit energies of each bit in each QPSK constellation point.

Determining the soft-bit energies for each of the 384 bits in accordance with formula 1, above, results in four separate soft-bit energies occurring in with the following probability, as shown in Table 5.

Notably for every 12 64QAM modulated bits (i.e., every two 64QAM symbols), seven of the bits have a soft-bit energy of 2/21, three of the bits have a soft-bit energy of 8/21, one of the bits has a soft bit energy of 1 8/21, and one of the bits has a soft-bit energy of 3 2/21. Because Q=6 and the probability for certain soft-bit energies, for example soft bit energies of 1 8/21 and 3 2/21, have less than a ⅙ probability of occurring in a 64QAM symbol, Q can be set to 12 and two 64QAM symbols can be demapped at the same time. If it is not feasible to demap two 64QAM symbols at the same time, the 64QAM symbol may be demapped individually but alternately assigned one of two SBF groups such that each of the six bits from a respective 64QAM symbol is assigned an SBF in accordance with one of the two SBF groups. One example of such grouping is:

The SBF of each of the Q=12 bits can be determined by normalizing the SNR of the soft demapped energy of each of the Q=12 64QAM bits to the SNR of the BPSK symbol, according to the following equation:

FIG. 6 is a block diagram illustrating a mapping of modulation symbol SNRs to base modulation symbol SNRs according to one embodiment of the invention. A modulation order mapper 80 A maps a QPSK modulation symbol SNR to two BPSK modulation symbol SNRs, each having a SBF of ½. A modulation order mapper 80 B maps a 16QAM modulation symbol SNR to four BPSK modulation symbol SNRs, three of which have a SBF of 1/10 and one of which has a SBF of ⅖. A modulation order mapper 80 C maps two 64QAM modulation symbol SNRs to 12 BPSK modulation symbol SNRs, seven of which have a SBF of 1/42, three of which have a SBF of 2/21, one of which has a SBF of 9/42, and one of which has a SBF of 8/21. While the modulation order mappers 80 A- 80 C have been illustrated separately, it will be understood by one skilled in the art that the modulation order mappers 80 A- 80 C could be implemented as a single modulation order mapper 80 if desired.

While SBFs have been illustrated throughout the specification in fractional form for purposes of illustration, it will be understood that the SBFs may be shown in any numeric form, such as decimal form, and that the actual value of the SBF may deviate from the value illustrated herein a certain amount if desired. For example, recall that a 16QAM modulation symbol SNR can be mapped to four BPSK modulation symbol SNRs, using SBFs of ⅖ and 8/5. Alternately, such SBFs could be expressed in decimal form as 0.40 and 1.6, respectively. Moreover, an SBF, such as the SBF 0.40, could be designated as any number in a range of numbers, such as, for example, a number in a range from about 0.30 to about 0.50, depending on a desired level of accuracy, without departing from the invention herein.

FIG. 7 is a block diagram illustrating a modulation order mapping in accordance with one embodiment of the invention. Assume that a system level simulation simulates the transmission of a first FEC block of data on a channel 82 having three subcarriers 84 A- 84 C, each of which carries QPSK modulation symbols. Assume the first FEC block was not decoded properly, and a second FEC block containing the same information bits is transmitted using A-HARQ on a channel 86 having three subcarriers 88 A- 88 C, each of which carries 16QAM modulation symbols. The modulation order mapper 80 maps each subcarrier channel 84 A- 84 C QSPK symbol SNR into two BSPK symbol SNRs, each having an SBF of ½. The modulation order mapper 80 maps each subcarrier channel 88 A- 88 C 16QAM symbol SNR into four BSPK symbol SNRs, three of which have an SBF of 1/10, and one of which has an SBF of ⅖. The ESINR can be calculated through the use of equation 90, wherein N is the total number of equivalent BPSK symbols (i.e., 18 in the example illustrated in FIG. 7 ), L is the number of subcarriers being demapped (e.g., six in the example illustrated in FIG. 7 ), M k is the number of bits in the modulation symbol (before mapping) associated with the k th subcarrier channel, SBF k,b is the SBF associated with the b th bit in the k th modulation symbol, and γ k is the SNR of the k th modulation symbol.

While the invention has been illustrated and discussed in the context of subcarriers, the invention is not limited to different modulations on different subcarriers and can be used in any context where it is desired to determine an ESINR associated with multiple modulation symbols of different modulation orders. The invention can be used, for example, to determine an ESINR of a single transmission containing multiple symbols of different modulation orders, such as may occur via the use of multiple-input and multiple-output (MIMO) technology. In such context, the ESINR may be calculated via the following equation:

E ⁢ ⁢ SIN ⁢ ⁢ R = - ln ⁡ ( 1 N ⁢ ∑ k = 1 L ⁢ ∑ b = 1 M k ⁢ ⅇ - SBF k , b ⁢ γ k ) ,

wherein N is the total number of BPSK equivalent symbols, L is the number of QAM symbols in the FEC block, M k is the number of bits in the k th QAM symbol, SBF k,b is the SBF associated with the b th bit in the k th QAM symbol, and γ k is the SNR of the k th QAM symbol.

While the invention has been described in the context of mapping higher modulation orders to a BPSK modulation order, those of skill in the art will recognize that other modulation orders, such as a QPSK modulation order, may be used as a base modulation order, if appropriate in the context of the respective application.

Those skilled in the art will recognize improvements and modifications to the preferred embodiments of the present invention. All such improvements and modifications are considered within the scope of the concepts disclosed herein and the claims that follow.