in a mimo system , transmission power has to be properly distributed over the antennas to maximize the system capacity . for an unknown channel , uniform power distribution over the antennas can be applied . referring to the example function block diagram in fig1 , a svd - type mimo system 100 includes a transmitter tx and a receiver rx , providing a beamforming technique used in closed - loop mimo systems . using svd , a mimo channel can be decomposed into several independent channels for data transmission , and therefore , there are no interferences between different data streams at the receiver . in the mimo system 100 of fig1 , for the mimo channel h with n t transmit antennas and n r receiving antennas , the received signal y can be represented as : where x is the n t × 1 transmitted signal vector , p is a diagonal matrix with loading power α i along the diagonal , and n is the additive noise in the channel . the channel h is a n r × n t matrix where its element h ij is the channel response from j th transmit antenna to i th receiving antenna . by applying svd to h , h can be expressed as : where u and v are unitary matrices ( i . e ., u is a n r × n ss matrix where n ss is the number of data stream , and v h is a n ss × n t matrix ) and d is a diagonal matrix with elements equal to the square - root of eigenvalues of the matrix ( hh h ), where (·) h is the hermitian operation . the example mimo system 100 in fig1 implements methods of quantized power loading at the transmitter tx , and automatic detection of power loading at the receiver , according to the present invention . in the mimo system 100 of fig1 , demux processing 102 splits the information bits into several streams , wherein each stream is provided to a different transmit antenna . a combiner 104 multiplies the data stream output vector x of the demux 102 and power loadings p . then , v processing 106 multiplies the input data vector by the matrix v at the transmitter tx , wherein relation ( 1 ) can be represented as : then u h processing 108 in the receiver rx multiplies the received data vector by the matrix u h , wherein the received signal after processing , x p , can be expressed as : wherein the transmitted data x can be completely separated after this operation because d and p are diagonal matrices . it can be shown in that the capacity c for such a mimo system can be expressed as : c = ∑ i = 1 n t ⁢ log ⁢ ⁢ ( 1 + λ i ⁢ p i 2 n 0 ) ( 5 ) where λ i and p i 2 are the eigenvalue and transmitted power corresponding to the decomposed channels and n 0 is the noise power . from relation ( 5 ), it is observed that the transmitted power plays an important role in determining the system capacity as other parameters , λ i and n 0 , are related to channel condition and can not be controlled . in order to maximize the system capacity , the conventional “ water filling ” algorithm has often been used to calculate the transmitted power . under the assumption that total transmitted power is fixed , wherein : ∑ i = 1 n t ⁢ p i 2 = p total ( 6 ) where p total is a fixed number for total transmitted power , and the optimal power for maximum capacity is expressed by : p i 2 = ( δ - n 0 λ i ) ( 7 ) in general , the capacity in relation ( 5 ) is a continuous capacity . as noted , in practice however , the system capacity , is a quantized one because only a finite number of data transmission rates can be supported in a communication system . further , the total transmit power from the transmitter is fixed to a certain level due to government regulations . therefore , there are some constraints and limitations in implementing the “ water filling ” algorithm for power loading in a mimo beamforming system . furthermore , the power loading information is necessary for a receiver to detect the transmitted signals correctly . the mechanism to eliminate the parameter mismatch between the transmitter and receiver is an important factor for the system performance . fig2 shows an example functional block diagram of a mimo beamforming system 200 which implements methods of quantized power loading ( e . g ., fig3 ) in the transmitter , and automatic detection / estimation of power loading ( e . g ., fig4 ) in the receiver , according to another embodiment of the present invention . the mimo system 200 in fig2 comprises a transmitter ( tx ) 201 including a demux function 202 , a power loading calculation and quantization function 204 ( e . g ., implementing steps of fig3 ), a combiner 206 , and a v processing function 208 . the demux 202 splits the information bits into n ss streams . based on the channel information , the quantization function 204 calculates and quantizes the power loading values for each stream ( e . g ., implementing steps of fig3 ). the combiner 206 further multiplies the incoming data by the quantized power loadings to generate the input to v processing function 208 that multiples that input by the matrix v to generate the output . the mimo system 200 further comprises a receiver ( rx ) 203 including a u h processing function 210 , an automatic detection and dequantization processing function 212 ( e . g ., implementing steps of fig4 ), and a combiner 214 . the received signal is first multiplied by the u h matrix in the processing function 210 to generate the output x p . based on x p , the dequantization processing function detects and de - quantizes the power loading values , p , that are used at the transmitter , and outputs the inverse values of the estimated power loading , p − 1 the combiner 214 multiplies x p with p − 1 . according to an embodiment of the present invention , the transmission rate is selected based on channel measurements . because the number of the supported data rates is a finite number , according to the present invention a set of quantized values q i are used to represent un - quantized power loading value α i with a power sum constraint as in relation ( 8 ) below : n , ∑ i = 1 n t ⁢ α i 2 = n t ( 8 ) wherein the power for each data stream , p data , is assumed to be identical . a primary reason to use quantized values for power loadings is that the receiver 203 requires knowledge of the power loading values ( weights ) α i used by the transmitter 201 in order to detect the transmitted signals correctly . this can be done by either a first approach which involves sending power loading weights α i to the receiver 203 through the signaling channels , or by a second approach which involves the receiver automatically detecting and calculating power loading based on received reference signals , such as pilot signals , according to the present invention . in the first approach above , using quantized values q i can reduce the memory size for fixed length representation , i . e ., reduce the overhead size in the signaling field . in the second approach , using quantized values q i significantly decreases power loading detection errors at the receiver 203 . this is because generally received reference signals are corrupted by random noise , which introduce detection errors for continuous power loading values , no matter what the noise power is . using quantized values q i according to the present invention , detection error is smaller and occurs essentially when noise with sufficiently large power is present . in one example , for a rank ordered set of power loading values α i , where α 1 ≧ α 2 ≧ . . . ≧ α nt , we have : n t & gt ; α 1 2 & gt ; 0 ; and ⁢ ⁢ n t - ∑ j = 1 i - 1 ⁢ α j 2 & gt ; α i 2 & gt ; 0 , i & gt ; 1 ( 10 ) wherein the range for α i 2 increases as the value of n t increases . therefore , if uniform quantization with fixed step size is used , the number of quantized levels increases as n t increases . in general , the higher the number of quantized levels , the better the performance , i . e ., it depends on the quantization step size δ . on the other hand , the principal terms ( channels ) with largest eigenvalues in relation ( 5 ) contribute most portions of the total capacity . thus , the quantized level for the most energetic power loading q i should be as large as possible to approach the un - quantized value α i , while satisfying the power sum constraint in relation ( 8 ). in order to satisfy the condition in relation ( 8 ), for a fixed step size δ , the quantized value q i corresponding to the power loading α i 2 , can be determined by the following example quantization procedure : ( i ) calculate and rank order α i based on relations ( 5 ) and ( 9 ). ( ii ) determine quantized value q i corresponding to power loading α i 2 . r i represents residual power for the sum of the selected power q j , j = 1 , . . . , i , wherein : if ⁢ ⁢ r i = ( n t - ∑ j = 1 i ⁢ q j ) ≥ ( n t - i ) × δ ( 11 ) where k is the smallest integer to satisfy relation ( 11 ). because q i is greater or equal to δ , the residual power has to be equal or greater than ( n t − i )× δ , the value of q i is reduced until relation ( 11 ) holds . fig3 shows a flowchart of the steps of an example process implementing the above quantization procedure . the quantization process involves : calculating p i according to relation ( 7 ) and rank - ordering the p i ( step 300 ); determining q i corresponding to power loading α i 2 , with step size δ ( step 302 ); initiating the index i as i = 1 : n t ( step 304 ); determining if the relation ( n t - ∑ j = 1 i ⁢ q i ) ≥ ( n t - i ) × δ is true ( step 306 ), and if so , in step 308 setting q i = q i ( if the relation ( n t - ∑ j = 1 i ⁢ q i ) ≥ ( n t - i ) × δ is true , the residual power is large enough for assigning the remaining power loadings ; otherwise , the current assigned value has to be reduced as shown in step 310 below ), otherwise , setting q i = q i − δ * k ( step 310 ); incrementing i by one ( step 312 ); determining if i & gt ; n t ( step 214 ), and if so ending the process , otherwise proceeding to previous step 306 . in another embodiment , instead of calculating power loadings based on relation ( 7 ), alternative methods of calculating power loadings , such as the example reverse power loading method described in commonly assigned patent application , titled : “ power loading method and apparatus for throughput enhancement in mimo systems ”, attorney docket sam2b . pau . 17 ( incorporated herein by reference ), can be used . a numerical example quantization according to the present invention is now described . consider a set of quantized power loading values q i with n t = 4 and δ = 0 . 2 , where q 1 = 2 . 2 , q 2 = 1 . 6 , q 3 = 0 . 4 , and q 4 = 0 . 2 . in order to satisfy the condition in relation ( 8 ), q i is adjusted as follows : ( 1 ) with i = 1 , the value r 1 = 1 . 8 ≧ 0 . 6 in relation ( 11 ), then q 1 = 2 . 2 . ( 2 ) with i = 2 , the value r 2 = 0 . 2 & lt ; 0 . 4 , then q 2 = 1 . 6 − 0 . 2 = 1 . 4 , and k = 1 . ( 3 ) with i = 3 , the value r 3 = 0 & lt ; 0 . 2 , then q 3 = 0 . 4 − 0 . 2 = 0 . 2 , and k = 1 . ( 4 ) with i = 4 , the value r 4 = 0 . 2 ≧ 0 . 2 in relation ( 11 ), then q 4 = 0 . 2 . the final result for q i =[ 2 . 2 , 1 . 4 , 0 . 2 , 0 . 2 ], which satisfies the condition in relation ( 8 ). in accordance with another aspect of the present invention , in order to process the received signal correctly , the receiver 203 is provided with a mechanism to detect the power loading used at the transmitter 201 . in one embodiment , by detecting the power loading of received reference signals with known power , such as pilot signals , the power loading can be effectively computed by the receiver 203 . recalling relation ( 4 ), and after separation operation in processing function 210 in the receiver 203 , letting r i represent the power for received pilot signals for the i th data stream , then r i can be expressed as : where s 2 is the transmitted pilot power . it should be noted that the power sum constraint in relation ( 8 ) still holds . therefore , estimation ( calculation ) of α i at the receiver 203 can be performed by computing the ratio or the difference of various r i as : r i r j = α i 2 ⁢ λ i ⁢ s 2 + n 0 α j 2 ⁢ λ j ⁢ s 2 + n 0 ≈ α i 2 ⁢ λ i α j 2 ⁢ λ j ( 13 ⁢ a ) difference : r i − r j =( α i 2 λ i − α j 2 λ j ) s 2 ( 13b ) wherein relative high signal - to - noise ratio is assumed in relation ( 13a ). because the power of the transmitted pilot signal s 2 and the channel eigenvalues λ i are known at the receiver 203 , α i can be calculated in the receiver 203 using relations ( 8 ) and ( 13a ) or ( 13b ). further , because the quantized values q i are used for all power loadings , the power ratio / difference in relations ( 13a ) and ( 13b ) should be fixed values from a finite set of numbers once a quantization table is defined . in such cases , the detection errors caused by noise / interference will be significantly decreased because the detection errors occur only when the noise with sufficient large power is present . the following is a example power loading computation / detection procedure in the receiver 203 , wherein a unit power pilot is assumed for simplicity : c i = r i ∑ j = i + 1 n t ⁢ r j ( 14 ⁢ a ) d i = r i - ∑ j = i + 1 n t ⁢ r j ( 14 ⁢ b ) ( c ) find the nearest pair of quantization numbers corresponding to c i or d i ( d ) for i = i + 1 , repeat steps ( a ) and ( b ) until i & gt ; n t . fig4 shows a flowchart of the steps of an example implementation of the above power loading computation / detection procedure . the detection process involves : calculating and rank - ordering pilot signal power r i ( step 400 ); initiating index i as i = 1 : n t ( step 402 ); computing c i according to relation ( 14a ) or computing d i according to relation ( 14b ) ( step 404 ); finding q i corresponding to c i or d i ( step 406 ); incrementing i by one ( step 408 ); determining if i & gt ; n t ( step 410 ), and if so ending the process , otherwise proceeding to previous step 404 . accordingly , utilizing quantization in the transmitter 201 to provide transmit power loading values , allows automatic detection of power loading values in the receiver 203 . as a result , the transmitter 201 need not provide the receiver 203 with the power loading values , thereby increasing throughput of the system 200 . the receiver 203 can detect the power loading values automatically based on the quantization values . in one example , relations ( 13a ) and / or ( 13b ), implemented as the process in fig4 , are used by the receiver 203 for power loading estimation and detection . at the transmitter 201 , quantization is performed sequentially for the channels ( i . e ., quantization is performed for a first channel , and then a second channel , etc .). preferably , quantization beings with the channel having the largest eigenvalue , as this is most efficient . the present invention provides a practical way to meet the power sum constraint in implementing the optimal ‘ water filling ’ algorithm or any other uneven power loading algorithms for a communication system . by using the quantized values for the optimal power loading weights , the memory size for fixed length representation is reduced , i . e ., the overhead size in the signaling field is reduced in notifying the receiver . further , when automatic detection is performed , using quantized values can significantly decrease the detection errors of the power loading weights at the receiver . the present invention has been described in considerable detail with reference to certain preferred versions thereof ; however , other versions are possible . for example , instead of uniform step size quantization , an un - uniform quantization method can be used . in another example , instead of using automatic detection , the receiver may know the power loading weights through the signaling fields from the transmitter . further , the pilot signal with known power is only one of the choices used for power loading estimation . any reference signals with known power , such as pilot , training sequences , beacon , . . . , etc ., can be used for estimation . therefore , the spirit and scope of the appended claims should not be limited to the description of the preferred versions contained herein .