Beamforming method for a MIMO space division multilplexing system

BACKGROUND OF THE INVENTION

1. Field of the Invention

0001The present invention relates generally to an SDM/MIMO (Space Division Multiplexing/Multiple Input Multiple Output) system, and in particular, to a beamforming method for the SDM/MIMO system.

2. Description of the Related Art

0002SDM is a scheme for transmitting signals from a base station (BS) to mobile terminals on multiple antennas, while spatially identifying them. This scheme forms a beam for each mobile terminal and cancels interference between mobile terminals, such that a plurality of mobile terminals share one channel without interference. Advantageously, the capacity of a system sharing one channel increases.

0003A MIMO system uses multiple antennas at the receiver and the transmitter, and increases system capacity in proportion to the number of the antennas used.

0004Typically, SDM operates under the assumption that each mobile terminal is equipped with a single antenna. In this case, interference between mobile terminals is cancelled by multiplexing a signal for each mobile terminal by a beamforming weight vector. Alternatively, in a MIMO environment, the beamforming weight is determined not as a vector, but as a matrix, along with the increase in number of the antennas of the mobile terminal. The beamforming weight is designed to transmit a signal at a maximum power to a target mobile terminal, and not to other mobile terminals, thereby canceling interference between mobile terminals.

0005The computation of the beamforming weight requires feedback of channel information from each mobile terminal to the BS. In a TDD (Time Division Duplex) mode, the downlink channel is estimated under the assumption that the uplink and downlink channels are identical. Therefore, SDM is applicable to the downlink and the uplink.

0006In a real communication environment, however, accurate channel estimation is hard to implement and some errors are involved in the channel estimate as a result of the effects of noise and the difference in gain and phase between multiple antennas. It is a distinctive shortcoming of SDM that because the beamforming weight is determined from the estimated channel and interference is cancelled between mobile terminals using the beamforming weight, the channel estimation error causes a serious deterioration of system performance. That is, a beam cannot be formed in an accurate direction and it is impossible to cancel interference between mobile terminals entirely.

0007Consequently, a lot of research is being performed on determining a beamforming weight that mitigates the SDM performance degradation in an environment bearing channel estimation error. The research results of beamforming in applying SDM to a system using multiple antennas at a BS and a single antenna at a mobile terminal are well known.

0008However, research is ongoing to achieve an optimal beamforming weight for SDM in the MIMO environment. To compute the beamforming weight in the SDM/MIMO environment, zero-forcing may be exploited to cancel interference between mobile terminals. In this case, the BS uses a channel estimation fed back from a mobile terminal. Because the channel estimate is not accurate and it is difficult to anticipate beam and null formation with a beamforming weight, interference occurs between mobile terminals. If more SDM users share one channel or a great error is involved in the channel estimate, the impact of interference increases and system performance is seriously degraded. Further, transmit power increases relative to the signal-to-interference ratio of a received signal, resulting in an overall decrease of system efficiency.

SUMMARY OF THE INVENTION

0009Therefore, the present invention has been designed to substantially solve at least the above problems and/or disadvantages and to provide at least the advantages described below. Accordingly, an object of the present invention is to provide a beamforming method for mitigating degradation of SDM performance in an environment bearing channel estimation error.

0010Another object of the present invention is to provide a beamforming method for computing a beamforming weight, taking into account a single antenna and multiple antennas at a mobile terminal in a conventional SDM/MIMO environment.

0011A further object of the present invention is to provide a beamforming method for minimizing transmit power and reducing an impact of interference between mobile terminals in proportion to the minimized transmit power.

0012Still another object of the present invention is to provide a beamforming method for improving system performance by minimizing an average of interference power caused by channel estimation error.

0013The above and other objects are achieved by providing a beamforming method for an SDM/MIMO communication system.

0014According to one aspect of the present invention, in a beamforming method in a communication system including a transmitter for transmitting signals to users on a plurality of transmit antennas, the method includes spatially identifying the users and a plurality of receivers for receiving the signals discriminately, and determining a beamforming weight based on channel information received from each of the receivers, taking into account whether the each receiver uses a single antenna or a plurality of antennas. A transmission signal is multiplied by the beamforming weight and transmitted.

BRIEF DESCRIPTION OF THE DRAWINGS

0015The above and other objects, features, and advantages of the present invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings in which: <ul id="ul0001" list-style="none" compact="compact"><li>FIG. 1 illustrates an SDM/MIMO system to which the present invention is applied;</li><li>FIG. 2 is a flowchart illustrating beamforming methods according to the present invention;</li><li>FIGs. 3A and 3B are graphs comparing the inventive beamforming with conventional beamforming in terms of SINR (Signal-to-Interference and Noise Ratio); and</li><li>FIGs. 4A and 4B are graphs comparing the inventive beamforming with the conventional beamforming in terms of BER (Bit Error Rate).</li></ul>

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

0016Preferred embodiments of the present invention will be described in detail herein below with reference to the accompanying drawings. In the following description, well-known functions or constructions are not described in detail since they would obscure the invention in unnecessary detail.

0017FIG. 1 illustrates an SDM/MIMO system to implement a beamforming method according to an embodiment of the present invention. Referring to FIG. 1, a BS 11 transmits signals to a plurality of mobile terminals 13, 15, and 17 through a plurality of transmit (Tx) antennas. Each of the mobile terminals 13, 15, and 17 are equipped with a plurality of receive (Rx) antennas for receiving the signals in the spatial dimension.

0018According to a preferred embodiment of the present invention, a communication system comprising K mobile terminals sharing one channel, N antennas at a BS, and N_r,k antennas at a k_th mobile terminal (i.e. user) is illustrated. H_k is an N_r,kxN_t matrix representing the channel between the BS and the k_th mobile terminal. To cancel signal interference between mobile terminals sharing one subchannel on the SDM downlink, it is necessary to multiply a signal by a beamforming matrix W_k. A transmission signal s produced by summing the product of each signal x_k and W_k can be determined as shown in Equation (1).<maths id="math0001" num=""><img file="EP1598955A2_D0001.tif" /></maths>

0019In order to prevent the signal for the k^th user from going to other users, W_k must take on the characteristic shown in Equation (2).<maths id="math0002" num="(2)"><math display="block"><mrow><msub><mrow><mtext>H</mtext></mrow><mrow><mtext mathvariant="italic">l</mtext></mrow></msub><msub><mrow><mtext>W</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mtext> =0, if </mtext><mtext mathvariant="italic">l≠k</mtext></mrow></math><img file="EP1598955A2_D0002.tif" /></maths> H is a channel matrix.

0020To achieve W_k, the channel matrix for every user is defined as shown in Equation (3).<maths id="math0003" num="(3)"><math display="block"><mrow><msub><mrow><mtext>H = [H</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msub><mrow><mtext>;H</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><msub><mrow><mtext>;···;H</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mtext>]</mtext></mrow></math><img file="EP1598955A2_D0003.tif" /></maths>

0021<i>H</i><maths id="math0004" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext mathvariant="italic">c</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></mfrac></mrow></math><img file="EP1598955A2_D0004.tif" /></maths> is defined as the remaining matrix of H, not including H_k. <i>H</i><maths id="math0005" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext mathvariant="italic">c</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></mfrac></mrow></math><img file="EP1598955A2_D0005.tif" /></maths> is a matrix of size<maths id="math0006" num=""><img file="EP1598955A2_D0006.tif" /></maths>

0022As described above, W_k is designed to prevent transmission of the signal for the k^th user to the other users. Therefore, W_k is a basis matrix for the null space of <i>H</i><maths id="math0007" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext mathvariant="italic">c</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></mfrac></mrow></math><img file="EP1598955A2_D0007.tif" /></maths>. That is, one of several basis matrices representing the null space of <i>H</i><maths id="math0008" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext mathvariant="italic">c</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></mfrac></mrow></math><img file="EP1598955A2_D0008.tif" /></maths> is selected and designated as W_k. W_k is of size <i>N</i>_<i>r,k</i> × <maths id="math0009" num=""><math display="inline"><mrow><mover accent="true"><mrow><mtext mathvariant="italic">N</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1598955A2_D0009.tif" /></maths>_<i>t,k</i> where<maths id="math0010" num=""><img file="EP1598955A2_D0010.tif" /></maths>

0023When the transmission signal for the k^th user be represented by a vector x_k of size <maths id="math0011" num=""><math display="inline"><mrow><mover accent="true"><mrow><mtext mathvariant="italic">N</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1598955A2_D0011.tif" /></maths>_<i>t,k</i> × <i>1</i>, a signal y_k received by the k^th user is defined as shown in Equation (4):<maths id="math0012" num=""><img file="EP1598955A2_D0012.tif" /></maths> where n_k is a vector of size <i>N</i>_<i>r,k</i> × <i>1</i> representing noise that the Rx antennas have experienced. Every element of the vector n_k is assumed to be the normal distribution probability variable of (0, <i>σ</i><maths id="math0013" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext mathvariant="italic">2</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></mfrac></mrow></math><img file="EP1598955A2_D0013.tif" /></maths>). H_kW_k is defined as <maths id="math0014" num=""><math display="inline"><mrow><mover accent="true"><mrow><mtext mathvariant="italic">H</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1598955A2_D0014.tif" /></maths>_<i>k</i> and thus, <i>y</i>_<i>k</i><i>=</i><maths id="math0015" num=""><math display="inline"><mrow><mover accent="true"><mrow><mtext mathvariant="italic">H</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1598955A2_D0015.tif" /></maths>_<i>k</i><i>x</i>_<i>k</i><i>+n</i>_<i>k</i>. As a result, <maths id="math0016" num=""><math display="inline"><mrow><mover accent="true"><mrow><mtext mathvariant="italic">H</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP1598955A2_D0016.tif" /></maths>_<i>k</i> is a real channel for the k^th user, and interference from other users using the same channel is perfectly cancelled. Notably, the perfect cancellation of the interference requires the condition that<maths id="math0017" num=""><img file="EP1598955A2_D0017.tif" /></maths>

0024However, there is no perfect channel information in a real communication environment. Although the channel information is collected through channel estimation, the noise causes an error in the channel estimate, leading to the degradation of system performance. The channel estimate of the k^th user can be given by Equation (5):<maths id="math0018" num="(5)"><math display="block"><mrow><msub><mrow><mover accent="true"><mrow><mtext>H</mtext></mrow><mo>ˆ</mo></mover></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><msub><mrow><mtext> = H</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><msub><mrow><mtext> + ΔH</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub></mrow></math><img file="EP1598955A2_D0018.tif" /></maths> where H_k is a real channel matrix, Ĥ_<i>k</i> is the channel estimate, and Δ<i>H</i>_<i>k</i> is the channel estimation error. Every element of Δ<i>H</i>_<i>k</i> is assumed to be independent and a probability variable with distribution (0, σ<maths id="math0019" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext mathvariant="italic">2</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></mfrac></mrow></math><img file="EP1598955A2_D0019.tif" /></maths>).

0025Having no knowledge of H_k, the transmitter determines a weight using <i>Ĥ</i>_<i>k</i>. Therefore, the weight <i>Ŵ</i>_<i>k</i> is derived from <i>Ĥ</i>_<i>k</i> in the real system. That is, the condition is satisfied that <i>Ĥ</i>_<i>l</i><i>Ŵ</i>_<i>k</i><i>= 0</i>, <i>if l</i>≠<i>k</i>. Using <i>Ŵ</i>_<i>k</i>, the transmission signal is expressed as shown in Equation (6):<maths id="math0020" num=""><img file="EP1598955A2_D0020.tif" /></maths> and a signal received at the k^th user is defined as shown in Equation (7).<maths id="math0021" num=""><img file="EP1598955A2_D0021.tif" /></maths> Because <u><i>H</i></u>_{<u><i>k</i></u>}<u><i>Ŵ</i></u>_{<u><i>l</i></u>}<u><i>≠ 0</i> for <i>k ≠ l</i></u>, an interference signal from the other users<maths id="math0022" num=""><img file="EP1598955A2_D0022.tif" /></maths> is received at the k^th user. The interference affects system performance, and thus it is necessary to reduce the effects of the interference.

0026In the beamforming method according to an embodiment of the present invention, a minimum transmit power weight is used to reduce the effects of channel information error in a system combining MIMO with SDM.

0027An analysis of the effects of channel estimation error reveals that the power of signal interference is proportional to transmit power. That is, strong power for a particular user interferes with signals from other users. Therefore, one method for reducing the signal interference is to transmit a signal to each user at minimum power. In order to reduce the transmit power without affecting the received signal, the transmission signal is defined as shown in Equation (8):<maths id="math0023" num=""><img file="EP1598955A2_D0023.tif" /></maths> where a is a vector that is orthogonal to the channel of every user. The addition of a to the transmission signal has no influence on the received signal in an environment having accurate channel information. Therefore, the use of a minimizes the transmit power without affecting the received signal. Because a must be orthogonal to the channel of every user (channel estimate in a real environment), a is defined as shown in Equation (9):<maths id="math0024" num="(9)"><math display="block"><mrow><mtext>a = Nα</mtext></mrow></math><img file="EP1598955A2_D0024.tif" /></maths> where N is an orthogonal basis for the zero space of <i>Ĥ = [Ĥ</i>_<i>1</i><i>;Ĥ</i>_<i>2</i><i>;...;Ĥ</i>_<i>k</i><i>;]</i> and α is an arbitrary vector to represent a. Therefore, the transmission signal is expressed as shown in Equation (10).<maths id="math0025" num=""><img file="EP1598955A2_D0025.tif" /></maths>

0028To minimize the power of the transmission signal <img file="EP1598955A2_D0026.tif" />, a is computed as shown in Equation (11).<maths id="math0026" num=""><img file="EP1598955A2_D0027.tif" /></maths>

0029Because a can be defined as the least square of <i>ŝ</i> = -<i>N</i>α,<maths id="math0027" num="(12)"><math display="block"><mrow><msup><mrow><mtext>α=-N</mtext></mrow><mrow><mtext>†</mtext></mrow></msup><mover accent="true"><mrow><mtext>s</mtext></mrow><mo>ˆ</mo></mover></mrow></math><img file="EP1598955A2_D0028.tif" /></maths> where ^(.)† is a pseudo-inverse.

0030By substituting Equation (12) into Equation (10), the transmission signal is given as shown in Equation (13).<maths id="math0028" num=""><img file="EP1598955A2_D0029.tif" /></maths> I is an identity matrix with the appropriate size.

0031The transmission signal has minimum transmit power. Its symbol vector x_k is multiplied by the beamforming weight shown in Equation (14).<maths id="math0029" num=""><img file="EP1598955A2_D0030.tif" /></maths>

0032The above weight minimizes the transmit power, thereby reducing the power of the signal interference.

0033In a beamforming method according to another embodiment of the present invention, a minimum interference power weight is used to reduce the effects of channel information error in a system combining MIMO with SDM.

0034The channel estimation model is partially modified to minimize the signal interference power caused by the channel estimation error. It is assumed that the channel estimation error <i>ΔH</i>_<i>k</i> is independent of <i>H</i>_<i>k</i>. However, <i>Ĥ</i>_<i>k</i> is not independent of <i>ΔH</i>_<i>k</i> because <i>Ĥ</i>_<i>k</i><i>= H</i>_<i>k</i><i>+ ΔH</i>_<i>k</i>. Thus, in an environment where the power of the channel estimation error much higher than the channel power, that is, when <i>∥H</i>_<i>k</i><i>∥</i>^<i>2</i><i>>>∥ΔH</i>_<i>k</i><i>∥</i>^<i>2</i>, an approximation can be achieved such that <i>ΔH</i>_<i>k</i> is independent of <i>H</i>_<i>k</i>. Therefore, the assumption that <i>ΔH</i>_<i>k</i> is independent of <i>H</i>_<i>k</i> is held while deriving the minimum interference power weight.

0035To investigate the effects of the transmission signal for the k^th user on other users, the signal of the k^th user received at every user is defined as a vector shown in Equation (15):<maths id="math0030" num="(15)"><math display="block"><mrow><msub><mrow><mtext>y</mtext></mrow><mrow><mtext mathvariant="italic">k,all</mtext></mrow></msub><mtext> = H</mtext><msub><mrow><mover accent="true"><mrow><mtext>W</mtext></mrow><mo>ˆ</mo></mover></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><msub><mrow><mtext>x</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub></mrow></math><img file="EP1598955A2_D0031.tif" /></maths> where y_k,all is a<maths id="math0031" num=""><img file="EP1598955A2_D0032.tif" /></maths> vector, i.e., a value received at every user for the signal of the k^th user. In an environment where perfect channel information is achieved and there is no interference between users, y_k,all is zero for all users except for the k^th user.

0036Assuming that a_k is added to the k^th user signal (i.e. <i>Ŵ</i>_<i>k</i><i>x</i>_<i>k</i><i>+a</i>_<i>k</i>) for transmission, y_k,all is defined as shown in Equation (16):<maths id="math0032" num=""><img file="EP1598955A2_D0033.tif" /></maths> where <i>ĤŴ</i>_<i>k</i><i>x</i>_<i>k</i> is non-zero for only the k^th user with perfect interference cancellation, and <i>Ĥa</i>_<i>k</i><i>- ΔHŴ</i>_<i>k</i><i>x</i>_<i>k</i><i>- ΔHa</i>_<i>k</i> is the interference caused by the k^th user. Thus, a_k that minimizes the average power of this term must be found. An optimal value of a_k is computed as shown in Equation (17).<maths id="math0033" num=""><img file="EP1598955A2_D0034.tif" /></maths>

0037<i>J</i>^<i>2</i><i>=</i> ∥<i>Ĥa</i>_<i>k</i><i>- ΔHŴ</i>_<i>k</i><i>x</i>_<i>k</i><i>- ΔHa</i>_<i>k</i>∥² must be minimized. This is developed as shown in Equation (18):<maths id="math0034" num="(18)"><math display="block"><mrow><msup><mrow><mtext mathvariant="italic">J</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><msubsup><mrow><mtext> = a</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext>H</mtext></mrow></msubsup><mtext>H</mtext><msup><mrow><mover accent="true"><mrow><mtext>H</mtext></mrow><mo>ˆ</mo></mover></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msup><mover accent="true"><mrow><mtext>H</mtext></mrow><mo>ˆ</mo></mover><msub><mrow><mtext>a</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><msubsup><mrow><mtext> + x</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msubsup><msubsup><mrow><mover accent="true"><mrow><mtext>W</mtext></mrow><mo>ˆ</mo></mover></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msubsup><msup><mrow><mtext>ΔH</mtext></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msup><mtext>ΔH</mtext><msub><mrow><mover accent="true"><mrow><mtext>W</mtext></mrow><mo>ˆ</mo></mover></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><msub><mrow><mtext>x</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><msubsup><mrow><mtext> + a</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msubsup><msup><mrow><mtext>ΔH</mtext></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msup><msub><mrow><mtext>ΔHa</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mspace linebreak="newline" /><msubsup><mrow><mtext>+ 2Re{-a</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msubsup><mtext></mtext><msup><mrow><mover accent="true"><mrow><mtext>H</mtext></mrow><mo>ˆ</mo></mover></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msup><mtext>ΔH</mtext><msub><mrow><mover accent="true"><mrow><mtext>W</mtext></mrow><mo>ˆ</mo></mover></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><msub><mrow><mtext>x</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><msubsup><mrow><mtext> - a</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msubsup><msup><mrow><mover accent="true"><mrow><mtext>H</mtext></mrow><mo>ˆ</mo></mover></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msup><msub><mrow><mtext>ΔHa</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><msubsup><mrow><mtext> +x</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msubsup><msubsup><mrow><mover accent="true"><mrow><mtext>W</mtext></mrow><mo>ˆ</mo></mover></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msubsup><msup><mrow><mtext>ΔH</mtext></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msup><msub><mrow><mtext>ΔHa</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mtext>}</mtext></mrow></math><img file="EP1598955A2_D0035.tif" /></maths> where ^(·)H is a Hermitian transpose. Under the assumption that <i>ΔH</i>_<i>k</i> is independent of <i>H</i>_<i>k</i> and <i>E[ΔH</i>^<i>H</i><i> ΔH]=N</i>_<i>r,all</i><i>σ</i>^<i>2</i><i>I</i><maths id="math0035" num=""><img file="EP1598955A2_D0036.tif" /></maths> to achieve the expected value of J², Equation (19) is determined.<maths id="math0036" num=""><img file="EP1598955A2_D0037.tif" /></maths>

0038To achieve a_k that minimizes E[J²], E[J²] is differentiated with respect to a_k and the right-hand side is put to zero. Thus,<maths id="math0037" num="(20)"><math display="block"><mrow><msup><mrow><mover accent="true"><mrow><mtext>H</mtext></mrow><mo>ˆ</mo></mover></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msup><mover accent="true"><mrow><mtext>H</mtext></mrow><mo>ˆ</mo></mover><msub><mrow><mtext>a</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mtext> + </mtext><msub><mrow><mtext mathvariant="italic">N</mtext></mrow><mrow><mtext mathvariant="italic">r,all</mtext></mrow></msub><msup><mrow><mtext>σ</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><msub><mrow><mtext>a</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mtext> + </mtext><msub><mrow><mtext mathvariant="italic">N</mtext></mrow><mrow><mtext mathvariant="italic">r,all</mtext></mrow></msub><msup><mrow><mtext>σ</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><msub><mrow><mover accent="true"><mrow><mtext>W</mtext></mrow><mo>ˆ</mo></mover></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><msub><mrow><mtext>x</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mtext> = 0 ,</mtext></mrow></math><img file="EP1598955A2_D0038.tif" /></maths> which is re-arranged with respect to a_k as follows, thereby achieving an optimal solution as shown in Equation (21).<maths id="math0038" num="(21)"><math display="block"><mrow><msub><mrow><mtext>a</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><mtext>=-(</mtext><mfrac><mrow><mtext>1</mtext></mrow><mrow><msub><mrow><mtext>N</mtext></mrow><mrow><mtext mathvariant="italic">r,all</mtext></mrow></msub><msup><mrow><mtext>σ</mtext></mrow><mrow><mtext>2</mtext></mrow></msup></mrow></mfrac><msup><mrow><mover accent="true"><mrow><mtext>H</mtext></mrow><mo>ˆ</mo></mover></mrow><mrow><mtext mathvariant="italic">H</mtext></mrow></msup><mover accent="true"><mrow><mtext>H</mtext></mrow><mo>ˆ</mo></mover><msup><mrow><mtext>+I)</mtext></mrow><mrow><mtext>-1</mtext></mrow></msup><msub><mrow><mover accent="true"><mrow><mtext>W</mtext></mrow><mo>ˆ</mo></mover></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub><msub><mrow><mtext>x</mtext></mrow><mrow><mtext mathvariant="italic">k</mtext></mrow></msub></mrow></math><img file="EP1598955A2_D0039.tif" /></maths>

0039Based on Equation (21), the transmission signal for the k^th user is expressed as shown in Equation (22).<maths id="math0039" num=""><img file="EP1598955A2_D0040.tif" /></maths>

0040Thus, a minimum interference power weight for the k^th user is determined by Equation (23).<maths id="math0040" num=""><img file="EP1598955A2_D0041.tif" /></maths>

0041The use of the minimum interference power weight reduces the effects of signal interference between users in a channel estimation error-having environment.

0042While the beamforming weights are derived for the downlink in the above-described beamforming methods, the same can be applied to the uplink with some slight modification. The same reception power or SINR can be maintained using low transmit power by modifying Equation (14) and Equation (23), thereby decreasing the norms of the weight matrices.

0043FIG. 2 is a flowchart illustrating the beamforming methods according to the present invention. Referring to FIG. 2, a BS first collects channel information from feedback signals received from a plurality of mobile terminals in step S21 and generates a beamforming weight for each of the mobile terminals based on the number of antennas and channel information of the mobile terminal in step S22. The BS applies the beamforming weight to a transmission signal for the mobile terminal in step S23 and forms a beam for the mobile terminals in step S24.

0044The beamforming weight designed to minimize the transmit power of the signal or minimize the average value of interference signal power caused by a channel estimation error.

0045The beamforming method of the present invention and a conventional zero-forcing weight deciding method were simulated in terms of performance.

0046For example, FIGs. 3A and 3B are graphs comparing the inventive beamforming methods with the conventional beamforming method in terms of performance. Referring to FIG. 3A, when K=3, N_t=10, and N_r,k=3, changes in SINR are shown with respect to the standard deviation of a channel estimation error, σ². Here, SNR (Signal to Noise Ratio)=20dB. SNR is defined as the ratio of average transmit power to received noise power σ<maths id="math0041" num=""><math display="inline"><mrow><mfrac linethickness="0"><mrow><mtext mathvariant="italic">2</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></mfrac></mrow></math><img file="EP1598955A2_D0042.tif" /></maths> per user. The conventional zero-forcing weight deciding method uses an orthogonal matrix as a weight, which was designed simply to be orthogonal to other user channels without any regard to channel estimation error.

0047As illustrated in FIG. 3A, the beamforming methods according to the first and second embodiments of the present invention offer better SINR performance than the conventional beamforming method. More specifically, the beamforming method using a minimum interference power weight according to the second embodiment of the present invention produces the best performance in an environment having a large channel estimation error.

0048FIG. 3B illustrates the simulation result when K=4, N_t=8, and N_r,k=2. Similarly to the simulation result illustrated in FIG. 3A, the inventive beamforming methods have better performances.

0049FIGs. 4A and 4B are graphs comparing the inventive beamforming with the conventional beamforming in terms of BER performance with respect to SNR. In the simulations, σ² is fixed to 0.025, every element of x_k is a QPSK (Quadrature Phase Shift Keying) symbol, and ML (Maximum Likelihood) detection is used at a receiver. In FIG. 4A, K=3, N_t=10, and N_r,k=3, and in FIG. 4B, K=4, N_t=8, and N_r,k=2. As noted from FIGs. 4A and 4B, the beamforming methods according to the first and second embodiment of the present invention have better performance than the conventional beamforming method. More specifically, the beamforming using a minimum interference power weight according to the second embodiment of the present invention produces the best performance.

0050As described above, the beamforming methods according to the present invention minimize channel estimation errors, thereby preventing the degradation of system performance. Also, the same SINR can be maintained with a low transmit power.

0051While the present invention has been shown and described with reference to certain preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present invention as defined by the appended claims.