Method and apparatus for determining power allocation in a MIMO communication system

[0001] The present invention relates generally to data communication, and more specifically to a novel and improved method and apparatus for determining allocation of bin energy at each antenna in a multiple-input multiple-output (MIMO) communication system.

[0002] A multi-channel communication system provides increased transmission capacity over other types of communication systems for various types of communication such as voice and data. Such a multi-channel system may be a multiple-input multiple-output (MIMO) communication system, an orthogonal frequency division modulation (OFDM) system, a MIMO system that utilizes OFDM, or some other type of system. A MIMO system incorporates multiple transmit antennas and multiple receive antennas to exploit spatial diversity. Spatial diversity may be used to support a number of spatial subchannels, each of which may be used to transmit data. An OFDM system effectively partitions the operating frequency band into a number of frequency subchannels (or frequency bins), each of which is associated with a respective subcarrier on which data may be modulated. A multi-channel communication system thus supports a number of “transmission” channels, each of which may correspond to a spatial subchannel in a MIMO system, a frequency subchannel in an OFDM system, or a spatial subchannel of a frequency subchannel in a MIMO system that utilizes OFDM.

[0003] The transmission channels of a multi-channel communication system typically experience different link conditions (e.g., due to different fading and multipath effects) and may achieve different signal-to-noise-plus-interference ratios (SNRs). Consequently, the transmission capacities (i.e., the information bit rates) that may be supported by the transmission channels for a particular level of performance may be different from channel to channel. As such, determining the power level allocation to each channel may be difficult. Adjusting power allocated to one channel may cause interference for another channel. Moreover, the link conditions typically vary over time. Therefore, in a time varying system, the determination of power allocation is increasingly difficult in a multi-channel communication system.

[0004] To this end as well as others, there is a need for techniques to effectively and efficiently determine power allocation to each channel in a multi-channel communication system.

[0005] In a MIMO communication system with limited power for each transmit antenna, a method, apparatus, and a processor provide for determining bin energy level allocation to each OFDM frequency bin at each transmit antenna. An estimate of a solution vector including elements of the allocation bin energy level to each OFDM frequency bin at each antenna is determined. An error function based on the determined solution vector is also determined. An error magnitude is determined based on the determined error function. The error magnitude is compared to an error threshold. The processor accepts the estimate of the solution vector with the elements of the allocation bin energy level when the error magnitude is less than the error threshold.

[0011] Various aspects, embodiments, and features of the invention may be applied to any multi-channel communication system in which multiple transmission channels are available for data transmission. Such multi-channel communication systems include multiple-input multiple-output (MIMO) systems, orthogonal frequency division modulation (OFDM) systems, MIMO systems that utilize OFDM, and others. The multi-channel communication systems may also implement code division multiple access (CDMA), time division multiple access (TDMA), frequency division multiple access (FDMA), or some other multiple access techniques. Multiple access communication systems can support concurrent communication with a number of terminals (i.e., users).

[0012] FIG. 1 is a diagram of a multiple-input multiple-output (MIMO) communication system 100 for operation in accordance with various aspects and embodiments of the invention. MIMO system 100 employs multiple (NT) transmit antennas and multiple (N_R) receive antennas for data transmission. MIMO system 100 is effectively formed for a multiple access communication system having a base station (BS) 104 that concurrently communicates with a number of terminals (T) 106. In this case, base station 104 employs multiple antennas and represents the multiple-input (MI) for downlink transmissions and the multiple-output (MO) for uplink transmissions. The downlink (i.e., forward link) refers to transmissions from the base station to the terminals, and the uplink (i.e., reverse link) refers to transmissions from the terminals to the base station.

[0013] A MIMO system employs multiple (N_T) transmit antennas and multiple (N_R) receive antennas for data transmission. A MIMO channel formed by the N_T transmit and N_R receive antennas may be decomposed into N_C independent channels, with N_C≦min {N_T, N_R}. Each of the N_C independent channels is also referred to as a spatial subchannel of the MIMO channel and corresponds to a dimension. In one common MIMO system implementation, the NT transmit antennas are located at and associated with a single transmitter system, and the N_R receive antennas are similarly located at and associated with a single receiver system. A MIMO system may also be effectively formed for a multiple access communication system having a base station that concurrently communicates with a number of terminals. In this case, the base station is equipped with a number of antennas and each terminal may be equipped with one or more antennas.

[0014] An OFDM system effectively partitions the operating frequency band into a number of (N_F) frequency subchannels (i.e., frequency bins). At each time slot, a modulation symbol may be transmitted on each of the N_P frequency subchannels. Each time slot corresponds to a particular time interval that may be dependent on the bandwidth of the frequency subchannel.

[0015] A multi-channel communication system may be operated to transmit data via a number of transmission channels. For a MIMO system not utilizing OFDM, there is typically only one frequency subchannel and each spatial subchannel may be referred to as a transmission channel. For a MIMO system utilizing OFDM, each spatial subchannel of each frequency subchannel may be referred to as a transmission channel. For an OFDM system not utilizing MIMO, there is only one spatial subchannel for each frequency subchannel and each frequency subchannel may be referred to as a transmission channel.

[0016] The transmission channels in a multi-channel communication system typically experience different link conditions (e.g., due to different fading and multipath effects) and may achieve different signal-to-noise-plus-interference ratios (SNRs). Consequently, the capacity of the transmission channels may be different from channel to channel. This capacity may be quantified by the information bit rate (i.e., the number of information bits per modulation symbol) that may be transmitted on a transmission channel for a particular level of performance (e.g., a particular bit error rate (BER) or packet error rate (PER)). Since the link conditions typically vary with time, the supported information bit rates for the transmission channels also vary with time.

[0017] To more fully utilize the capacity of the transmission channels, channel state information (CSI) descriptive of the link conditions may be determined (typically at the receiver system) and provided to the transmitter system. The transmitter system may then process (e.g., encode, modulate, and allocate power) data such that the transmitted information bit rate for each channel matches the transmission capacity of the channel. CSI may be categorized as either “full CSI” or “partial CSI”. Full CSI includes sufficient characterization (e.g., the amplitude and phase) across the entire system bandwidth for the propagation path between each transmit-receive antenna pair in a N_R×N_T MIMO matrix (i.e., the characterization for each transmission channel). Partial CSI may include, for example, the SNRs of the transmission channels.

[0018] Various techniques may be used to process data prior to transmission over multiple transmission channels. In one technique, data for each transmission channel may be coded, modulated and allocated a power level based on the channel's CSI. By coding, modulating and allocating power separately for each transmission channel, the coding, modulation and the allocated power may be optimized for the SNR achieved by each channel. In one implementation of such a technique, a fixed base code is used to encode data, and the coded bits for each transmission channel are then punctured (i.e., selectively deleted) to obtain a code rate supported by that channel. In this implementation, the modulation scheme for each transmission channel is also selected based on the channel's code rate and SNR. This coding and modulation implementation is described in further detail in U.S. patent application Ser. No. 09/776,075, entitled “CODING SCHEME FOR A WIRELESS COMMUNICATION SYSTEM,” filed Feb. 1, 2001, assigned to the assignee of the present application and incorporated by reference herein. For this first technique, substantial implementation complexity is typically associated with having a different code rate and modulation scheme for each transmission channel. Moreover, the power allocation to different channels may involve several iterations since power from one channel is considered as interference for another channel at the receiving antennas. In accordance with various aspects of the invention, techniques are provided to determine the power allocation to different channels in an efficient and effective manner by determining bin energy and total energy at each antenna across all bins.

[0019] For a MIMO system utilizing OFDM and having full-CSI available, the transmitter system has knowledge of the complex-valued gain of the transmission path between each transmit-receive antenna pair of each frequency subchannel. This information may be used to render the MIMO channel orthogonal for each frequency subchannel, so that each eigen-mode (i.e., spatial subchannel) of each frequency subchannel may be used for an independent data stream. For a MIMO system utilizing OFDM and having partial-CSI available, the transmitter has limited knowledge of the transmission channels. Independent data streams may be transmitted on corresponding transmission channels over the available transmit antennas, and the receiver system uses a particular linear or non-linear processing technique (i.e., equalization) to separate out the data streams. The equalization provides an independent data stream corresponding to each transmission channel (i.e., each transmit antenna and/or each frequency subchannel), and each of these data streams has an associated SNR.

[0020] If the set of SNRs for the transmission channels is available at the transmitter system, this information may be used to select the proper coding and modulation scheme and distribute the total available transmit power. Similar processing may be performed if the channel gains are available at the transmitter system. In an embodiment, a common coding scheme (e.g., a particular Turbo code of a particular code rate) and a common modulation scheme (e.g., a particular QAM constellation) are used for all selected transmission channels.

[0021] In a MIMO OFDM system with N_T transmit antennas and N_R receive antennas, the received signals in the n-th frequency bin at the output of the N_R receive antennas may be expressed as:
r(n)=H(n)x(n)+z(n);1≦n≦N_P,  Eq (1)
where r(n) is the received symbol vector (i.e., the N_R×1 vector output from the MIMO channel, as derived from the receive antennas) in the n-th OFDM frequency bin; H(n) is the N_R×N_T complex-valued channel coefficient matrix, representing the channel response at the frequency associated with the n-th OFDM frequency bin; x(n) is the transmitted symbol vector in the n-th OFDM frequency bin (i.e., the N_T×1 vector input into the MIMO channel); and z(n) is an N_R×1 vector representing noise plus interference in the n-th OFDM frequency bin. The received symbol vector r(n) includes N_R modulation symbols associated with OFDM frequency bin n, from N_R signals received via N_R receive antennas at a specific time slot. Similarly, the transmitted symbol vector x(n) includes N_T modulation symbols associated with OFDM frequency bin n, in N_T signals transmitted via N_T transmit antennas at a specific time slot.
The channel coefficient matrix H(n) can be further written as:
H(n)=[h₁(n)h₂(n) . . . h_NT(n)]  Eq (2)
where the vectors h₁(n) contain the channel coefficients associated with the i-th transmit antenna at the frequency associated with the n-th OFDM frequency bin.

[0022] The transmission channels in a multi-channel communication system typically experience different link conditions and achieve different SNRs. Some channel conditions associated with increased channel attenuation result in lower received SNRs, while other channel conditions associated with decreased channel attenuation result in higher received SNRs. It is well-known in information theory that, in multi-channel communication systems with limited available transmit power, capacity is maximized by distributing the available power among the channels using a procedure known as water-pouring as described by [1] Robert G. Gallager, in Information Theory and Reliable Communication, published by John Wiley and Sons, Inc., 1968, incorporated by reference herein, and hereinafter known as [1]. In MIMO OFDM communication systems, where the transmitter has full CSI, the transmitter is capable of performing beam forming across the set of transmit antennas, and there is a limit on total combined transmit power from all transmit antennas, the capacity can be maximized by allocating the total transmit power amongst all of the spatial subchannels of all of the frequency subchannels according to the water-pouring procedure in [1]. This procedure, when applied to a single frequency in a MIMO system, is described, for example, by [2] I. Emre Telatar, in “Capacity of Multi-antenna Gaussian Channels,” European Transactions on Telecommunications, vol. 10, pp 585-595, Nov/Dec, 1999, incorporated by reference herein, and hereinafter known as [2]. In a publication [3] by Daniel Perez Palomar, Javier R. Fonollosa, Miguel A. Lagunas, “Capacity results on frequency-selective Rayleigh MIMO channels,” IST Mobile Comm SUMMIT 2000, pp 491-496, Galway, Ireland, Oct. 1-4, 2000, incorporated by reference herein, and hereinafter known as [3], water-pouring across frequencies and eigen-modes in a MIMO system are described.

[0023] However, in MIMO OFDM communication systems where there are per-antenna transmit power limitations, or it is not possible to perform beam forming across the set of transmit antennas, it is necessary to find an optimal allocation of available transmit power across the frequency subchannels at each transmit antenna, since in these cases it is not possible to directly control the allocation of transmit power to eigen-modes. In these cases, the water-pouring solution described in [1] cannot be used because of the coupling between the MIMO spatial subchannels on each frequency subchannel when eigen-mode decomposition is not available to render the frequency subchannels orthogonal.

[0024] FIG. 2 depicts a flow diagram of a process 200 to determine the allocation bin energy level to each OFDM frequency bin at each antenna and total energy across all bins and antennas in accordance with various embodiments of the invention. The OFDM frequency bins may range from 1 to N_F (1≦n≦N_F). The number of transmit antennas may range from 1 to any number N_T (1≦m≦N_T). The objective of the procedure is to compute values of the bin energies, ε_m(n);1≦m≦N_T;1≦n≦N_F, and water-pouring parameters B_m;1≦m≦N_T, which satisfy the water-pouring equations: $\begin{array}{cc}\max \left[\left(B_m-\frac{1}{{\Gamma }_m\left(n\right)}\right),0\right]-{\varepsilon }_m\left(n\right)=0;1\le m\le N_T;1\le n\le N_F\sum _{n=1}^{N_F}{\varepsilon }_m\left(n\right)-E_m=0;1\le m\le N_T& \mathrm{Eq}\left(3\right)\end{array}$
where E_m is the maximum energy available for transmission of a single OFDM symbol at antenna m, and Γ_m(n) is defined by the following: $\begin{array}{cc}{\Gamma }_m\left(n\right)={{\underset{\_}{h}}_m^H\left(n\right)\left[N_0\underset{\_}{I}+\sum _{\underset{l\ne m}{l=1}}^{n_{Lx}}{\varepsilon }_m\left(n\right){\underset{\_}{h}}_l\left(n\right){\underset{\_}{h}}_l^H\left(n\right)\right]}^{-1}{\underset{\_}{h}}_m\left(n\right)& \mathrm{Eq}\left(4\right)\end{array}$
In the following description of the iterative procedure for finding values of the bin energies, ε_m(n); 1≦m≦N_T;1≦n≦N_F, and water-pouring parameters B_m;1≦m≦N_T, which satisfy the water-pouring equations in Eq (3), the following N_T(N_F+1)×1 vector, x, is defined with elements:
x_{(m−1)(NF+1)+n}=ε_m(n);1≦m≦N_T; 1≦n≦N_F
x_m(NF+1)=B_m; 1≦m≦N_T  Eq (5)
and the following N_T(N_F+1)×1 vector function, F(x), is defined with elements: $\begin{array}{cc}\begin{array}{c}{F}_{\left(m-1\right)\left(N_F+1\right)+n}\left(\underset{\_}{x}\right)=\max \left[\left(x_{m\left(N_F+1\right)}-\frac{1}{{\Gamma }_m\left(n\right)}\right),0\right]-\\ x_{\left(m-1\right)\left(N_F+1\right)+n};1\le m\le N_T;\\ 1\le n\le N_F\end{array}{F}_{m\left(N_F+1\right)}\left(\underset{\_}{x}\right)=\sum _{n=1}^{N_F}{x}_{\left(m-1\right)\left(N_F+1\right)+n}-E_m;1\le m\le N_T& \mathrm{Eq}\left(6\right)\end{array}$

[0025] The solution vector, x, is the vector whose values satisfy F(x)=0, where 0 is a N_T(N_F+1)×1 vector of zeros.

[0026] In process 200, steps 201 through 206 establish an initial guess at the solution vector. Subsequent steps, 207 through 217, are iterated until a solution vector is reached such that the error is smaller than some specified error criterion: ∥F(x)∥²<E_max. These steps are a method of applying the Newton-Raphson method for solving non-linear equations to the solution of the present problem. A reference [4] by William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian T. Flannery, Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, 1992, incorporated by reference herein, and hereinafter known as [4], may be helpful for understanding of Newton-Raphson. This solution also requires calculation of the Jacobian, J(x), of F(x), which is a matrix of partial derivatives of F(x) with respect to the elements of x. The elements of the Jacobian matrix J(x) are given in the following: $\begin{array}{cc}\frac{\partial F_{\left(m-1\right)\left(N_F+1\right)+n}\left(\underset{\_}{x}\right)}{\partial x_{\left(i-1\right)\left(N_F+1\right)+j}}=0;1\le j\ne n\le N_F;1\le m,i\le N_T\frac{\partial F_{m\left(N_F+1\right)}\left(\underset{\_}{x}\right)}{\partial x_{\left(m-1\right)\left(N_F+1\right)+j}}=1;1\le j\le N_F;1\le m\le N_T\frac{\partial F_{\left(m-1\right)\left(N_F+1\right)+n}\left(\underset{\_}{x}\right)}{\partial x_{m\left(N_F+1\right)}}=\{\begin{array}{c}1;x_{m\left(N_F+1\right)}-\frac{1}{{\Gamma }_m\left(n\right)}>0\\ 0;x_{m\left(N_F+1\right)}-\frac{1}{{\Gamma }_m\left(n\right)}\le 0;1\le n\le N_F;\\ 1\le m\le N_T\end{array}\hspace{1em}\frac{\partial F_{m\left(N_F+1\right)}\left(\underset{\_}{x}\right)}{\partial x_{m\left(N_F+1\right)}}=0;1\le m\le N_T\frac{\partial F_{\left(m-1\right)\left(N_F+1\right)+n}\left(\underset{\_}{x}\right)}{\partial x_{\left(m-1\right)\left(N_F+1\right)+n}}=-1;1\le n\le N_F;1\le m\le N_T\frac{\partial F_{\left(m-1\right)\left(N_F+1\right)+n}\left(\underset{\_}{x}\right)}{\partial x_{\left(i-1\right)\left(N_F-1\right)+n}}=\hspace{1em}\{\begin{array}{cc}-\frac{\partial }{\partial x_{\left(i-1\right)\left(N_F+1\right)+n}}\left(\frac{1}{{\Gamma }_m\left(n\right)}\right);& x_{m\left(N_F+1\right)}-\frac{1}{{\Gamma }_m\left(n\right)}>0\\ 0;& x_{m\left(N_F+1\right)}-\frac{1}{{\Gamma }_m\left(n\right)}\le 0\\ & 1\le i\ne m\le N_T;\\ & 1\le m\le N_F\end{array}\hspace{1em}& \mathrm{Eq}\left(7\right)\end{array}$
where $\begin{array}{cc}\frac{\partial }{\partial x_{\left(i-1\right)\left(N_F+1\right)+n}}\left(\frac{1}{{\Gamma }_m\left(n\right)}\right)=\frac{{{{\underset{\_}{h}}_m^H\left(n\right)\left[N_0\underset{\_}{I}+\sum x_{\left(l-1\right)\left(N_F+1\right)+n}{\underset{\_}{h}}_l\left(n\right){\underset{\_}{h}}_l^H\left(n\right)\right]}^{-1}{\underset{\_}{h}}_l\left(n\right)}^2}{{\left({\Gamma }_m\left(n\right)\right)}^2}& \mathrm{Eq}\left(8\right)\end{array}$

[0027] At step 201, initially, an equal energy level is allocated to each bin of the OFDM frequency bins at each transmit antenna, i.e., ${\varepsilon }_m\left(n\right)=\frac{E_m}{N_F};1\le m\le N_T;1\le n\le N_F.$
At step 202, signal to noise ratio of each OFDM frequency bin n, 1≦n≦N_F at each antenna m, 1≦m≦N_T, represented by Γ_m(n), is calculated in accordance with Eq (4), using the values of ε_m(n) calculated in step 201.

[0028] At step 203, a set of bin energies, ε_m(n) for each transmit antenna m; 1≦m≦N_T, and OFDM frequency bin, n; 1≦n≦N_F, and the water-pouring parameter, B_m, for each transmit antenna, m; 1≦m≦N_T, are calculated, to satisfy the water-pouring equations given in Eq (3) using the values of Γ_m(n) calculated in step 202. The values of B_m and ε_m(n) may be calculated in accordance with a process depicted in FIG. 3.

[0029] At step 204, an initial solution vector, x_old, is calculated in accordance with the relationship described in Eq (5), using the values of B_m and ε_m(n) calculated in step 203.

[0030] At step 205, an error function F(x_old) is calculated in accordance with the relationship described in Eq (6), using the initial solution vector, x_old, calculated in step 204.

[0031] At step 206, an error magnitude E_old is calculated. The error magnitude E_old may be equal to the square of the magnitude of the error function F(x_old): E_old=∥F(x_old)∥². At step 207, the Jacobian, J(x_old), is calculated in accordance with the relationship described in Eq (7) and Eq (8). The Jacobian of a nonlinear function may be used to solve a system of nonlinear equations in a large matrix. At step 208, a correction vector ∂x and a step multiplier α may be determined. The correction vector is computed by solving the equation ∂x=−(J(x_old))⁻¹F(x_old) for the correction vector ∂x. The value of the step multiplier, α, may be determined in such a way as to ensure that the error magnitude, E_new, associated with the update of the solution vector is smaller than E_old.

[0032] One way of determining the value of the step multiplier is $\alpha =\min \left(1,\frac{1}{\max \left(\underset{\_}{\partial x}\right)}\right),$
where max (|∂x|) is the magnitude of the element of ∂x with the largest magnitude.

[0033] At step 209, a new solution vector x_new is calculated based on the old solution vector x_old and the correction factor ∂x and the step multiplier α. The new solution vector x_new may be calculated according to x_new=x_old+α∂x. At step 210, a new error magnitude E_new is calculated based on the new solution vector x_new. At step 211, E_new is compared to a maximum error magnitude, E_max, allowed for the system. The value for E_max may be pre-selected. If at step 211, the value of E_new is less than the E_max, the solution vector x_new holds acceptable values for set of bin energies, ε_m(n); 1≦m≦N_T;1≦n≦N_F, and water-pouring parameters B_m;1≦m≦N_T. If the value of E_new is more than the allowable E_max, the calculated values are erroneous to an unacceptable degree.

[0034] At step 212, the value of E_new is compared to the value of E_old. If the value of E_new is less than the value of E_old, at step 213, the old solution vector x_old is set to equal the new solution vector x_new, and the value of E_old is set equal to the value of E_new. At step 217, the value for the error function F(x_old) is calculated based on the value of solution vector x_old determined at step 213. From step 217, the process loops back to step 207. At step 207, after looping back from step 217, Jacobian of x_old is determined based on the value of F(x_old) determined at step 217.

[0035] At step 212, if the value of E_new is more than the value of E_old, the process loops to step 214. At step 214, the value of step multiplier a is compared to a minimum value of the step multiplier α_min. If the step multiplier a is greater than the minimum value, at step 215, a new value for step multiplier α is determined. The new value in accordance with an embodiment is less than the old value by a factor “k” greater than one. The process loops back to step 209 to calculate a new x_new based on the new step multiplier α. At step 214, if the step multiplier α is less than the minimum value, the value of x_new is set for the value of x_old, and a large value is set for E_old at step 216. From step 216, the process loops back to step 207. The process may be repeated many times until the error magnitude is less than a maximum error magnitude at step 211. The last value of the solution vector x_new holds the set of bin energies, ε_m(n); 1≦m≦N_T; 1≦n≦N_F, and the water-pouring parameters B_m; 1≦m≦N_T.

[0036] The initial guess for the values of the bin energies, ε_m(n); 1≦m≦N_T;1≦n≦N_F, and the water-pouring parameters, B_m;1≦m≦N_T, calculated in step 203 may be calculated in accordance with a process depicted in flow chart 300 shown in FIG. 3. This process is repeated once for each transmit antenna m, 1≦m≦N_T. The total energy, E_m, available for an OFDM symbol at a transmit antenna m is known. Each OFDM symbol may have a number N_F of frequency bins. At step 301, the value of B_m is initially set equal to the value of the total energy, E_m, available at each antenna. At step 302, a vector G_m(n),1≦n≦N_F is created from the values of Γ_m(n),1≦n≦N_F calculated in step 202 of process 200, by sorting them in order of descending magnitude. The first value, G_m(1), of vector G_m(n),1≦n≦N_F holds the largest value of Γ_m(n),1≦n≦N_F, and the last value, G_m(N_F), of vector G_m(n),1≦n≦N_F holds the smallest value of Γ_m(n),1≦n≦N_F. At step 303, an index vector, I_m(n), may be defined to cross reference common elements between the vectors G_m(n),1≦n≦N_F) and Γ_m(n),1≦n≦N_F such that Γ_m(I_m(n))=G_m(n). At step 304, a variable S_m, associated with an antenna m, m,1≦m≦N_T, is set to zero. At step 305, the elements of the sorted bin energy vector e_m(n),1≦n≦N_F are set to zero for OFDM frequency bin n,1≦n≦N_F. An iterative loop 399 may begin at step 306 and end at step 307. Iterative loop 399 runs for a variable l from 1 to N_F. At step 399a S_m is updated according to $S_m=S_m+\frac{1}{G_m\left(l\right)}.$
At step 399b, a variable B_temp is set according to $B_{\mathrm{temp}}=\frac{E_m+S_m}{l}.$
At step 399c, if $B_{\mathrm{temp}}-\frac{1}{G_m\left(l\right)}$
is greater than zero, B_m is set to B_temp at step 399ci. At step 399cii, a loop 388 begins for all values i=1 to l. At step 388-1, e_m(i) is set according to $e_m\left(i\right)=B_m-\frac{1}{G_m\left(i\right)}.$
The loop 388 ends at step 399ciii. At step 399c, if $B_{\mathrm{temp}}-\frac{1}{G_m\left(l\right)}$
is less than or equal to zero, then iterative loop 399 ends. Once the process is completed at step 307, the initial guess for the bin energies, ε_m(i), are set according to ε_m(I_m(n))=e_m(n),1≦n≦N_F for all OFDM frequency bins n,1≦n≦N_F. The values determined for B_m and ε_m(n),1≦n≦N_F in this process are used in the process flow 200 at step 203.

[0037] FIG. 4 is a diagram of a MIMO communication system 400 capable of operating in accordance with various aspects and embodiments of the invention. System 400 includes a first system 410 (e.g., base station 104 in FIG. 1) in communication with a second system 450 (e.g., terminal 106). System 400 may be operated to employ a combination of antenna, frequency, and temporal diversity to increase spectral efficiency, improve performance and enhance flexibility. At system 410, a data source 412 provides data (i.e., information bits) to a transmit (TX) data processor 414, which (1) encodes the data in accordance with a particular encoding scheme, (2) interleaves (i.e., reorders) the encoded data based on a particular interleaving scheme, and (3) maps the interleaved bits into modulation symbols for one or more transmission channels selected for data transmission. The encoding increases the reliability of the data transmission. The interleaving provides time diversity for the coded bits, permits the data to be transmitted based on an average SNR for the selected transmission channels, combats fading, and further removes correlation between coded bits used to form each modulation symbol. The interleaving may further provide frequency diversity if the coded bits are transmitted over multiple frequency subchannels. In an aspect, the coding, and symbol mapping may be performed based on control signals provided by a controller 434. A TX channel processor 420 allocates the power level for each selected transmission channel, and provides a stream of modulation symbols for each transmission channel, one modulation symbol per time slot. The allocated transmit power for each selected transmission channel is to achieve a desired SNR at the receiver system. In an aspect, the power allocation may be performed based on control signals provided by a controller 434. The set of bin energies, ε_m(n); 1≦m≦N_T;1≦n≦N_F, and the total energy at each antenna across all bins, E_m, are basis for the channel power allocation. The modulator 422 modulates each signal for transmission from an antenna.

[0038] At a receiver system 450, a number of receive antennas 452 receive the transmitted signals and provide the received signals to respective demodulators (DEMOD) 454. Each demodulator 454 performs processing complementary to that performed at modulator 422. The modulation symbols from all demodulators 454 are provided to a receive (RX) channel/data processor 456 and processed to recover the transmitted data streams. RX channel/data processor 456 performs processing complementary to that performed by TX data processor 414 and TX channel processor 420 and provides decoded data to a data sink 460.

[0039] At system 410, the transmitted feedback signal is received by antennas 424, demodulated by demodulators 422, and provided to a RX data processor 432. RX data processor 432 performs processing complementary to that performed by TX data processor 462 and recovers the reported CSI, which is then provided to controller 434.

[0040] Controller 434 uses the reported CSI to perform a number of functions including (1) selecting the set of N_S best available transmission channels for data transmission, (2) determining the coding and modulation scheme to be used for data transmission on the selected transmission channels, and (3) determining the allocation of power for the selected transmission channels. The characteristics (e.g., channel gains or received SNRs) of the transmission channels available for data transmission may be determined based on various techniques as described and provided to the transmitter system.

[0041] The techniques described herein may be used for data transmission on the downlink from a base station to one or more terminals, and may also be used for data transmission on the uplink from each of one or more terminals to a base station. For the downlink, transmitter system 410 may represent part of a base station and receiver system 450 may represent part of a terminal. For the uplink, transmitter system 410 may represent part of a terminal and receiver system 450 may represent part of a base station.

[0042] The elements of the transmitter and receiver systems may be implemented with one or more digital signal processors (DSP), application specific integrated circuits (ASIC), processors, microprocessors, controllers, microcontrollers, field programmable gate arrays (FPGA), programmable logic devices, other electronic units, or any combination thereof. Some of the functions and processing described herein may also be implemented with software executed on a processor. Certain aspects of the invention may also be implemented with a combination of software and hardware.

[0043] The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.