HK1078192B - Device and method for multiple-input multiple-output (mimo) radio communication - Google Patents

Description

Apparatus and method for MIMO wireless communication

Technical Field

The invention relates to a system and a method for multiple-input multiple-output wireless communication.

Background

The present invention relates to systems and methods for maximizing the capacity and/or range of a wireless communication link between two wireless communication devices.

Multiple-input multiple-output (MIMO) wireless communication techniques are well known for improving the received SNR of signals transmitted from one device to another. Research in MIMO wireless algorithms has led to the transmission of multiple signal streams simultaneously from multiple antennas of one device to another, thus significantly increasing the data rate of a wireless communication channel between two devices. One conventional method of transmitting multiple signal streams simultaneously via multiple antennas utilizes a power limitation and a water-filling solution (water-filling solution) on all the power transmitted via multiple joint antennas. The so-called water-filling solution requires a plurality of full-power amplifiers on the transmitting device, since for some channels it is possible that all or almost all of the transmit power is transmitted by one power amplifier. There is also room for MIMO systems to improve the design of devices for MIMO wireless communication systems, especially when it is desired to fabricate the wireless transceiver devices on an integrated circuit.

Disclosure of Invention

Briefly, the present invention provides a system, method and apparatus for synchronous wireless communication of multiple signals (signal streams) between a first device having N sets of antennas and a second device having M antennas. Unlike prior art methods, the method provided in the present invention adds a power limit on each transmit antenna path of the transmitting device.

According to an aspect of the present invention, there is provided a method for wireless communication between a first device having N antennas and a second device having M antennas, the method comprising: processing a vector s representing L signals with a transmit matrix A calculated to maximize channel capacity subject to a power constraint between the first device and the second device, wherein the power transmitted by each of the N antennas is less than or equal to a maximum power, and wherein the transmit matrix A synchronizes the L signals [ s ] transmitted along eigenvectors weighting of the channel between the N antennas and the M antennas of the second device₁...s_L](ii) a When N is less than or equal to M, the emitting matrix A is VD, where V is H^HH, H being the channel response from said first device to said second device, and a matrix D ═ I · sqrt (P)_max/N) and I is an identity matrix, so that the power transmitted by each of the N antennas is equal to each other and equal to P_maxN, wherein P_maxIs the total transmit power combined from all N antennas.

According to another aspect of the present invention provideA wireless communication device, comprising: a.N antennas; n wireless transmitters, each transmitter connected to a corresponding one of the plurality of antennas; c. a baseband signal processor coupled to the N wireless transmitters for processing vectors s representing L signals with a transmit matrix A, wherein the transmit matrix A is calculated to maximize channel capacity subject to a power constraint between the device and a remote device, wherein power transmitted by each of the N antennas is less than or equal to a maximum power, and wherein the transmit matrix A weights the L signals [ s ] transmitted synchronously along eigenvectors of the channel between the N antennas and the M antennas of the remote device₁...s_L](ii) a When N is less than or equal to M, the emitting matrix A is VD, where V is H^HH, H being the channel response from said device to said remote device, and a matrix D ═ I · sqrt (P)_max/N) and I is an identity matrix, so that the power transmitted by each of the N antennas is equal to each other and equal to P_maxN, wherein P_maxIs the total transmit power combined from all N antennas.

According to yet another aspect of the present invention, there is provided a wireless communication system, comprising: a. a first device; i.N antennas; n wireless transmitters, each transmitter connected to a corresponding one of the plurality of antennas; a baseband signal processor coupled to the N wireless transmitters, processing vectors s representing L signals with a transmit matrix A, wherein the transmit matrix A is calculated to maximize channel capacity subject to a power constraint between the first device and a second device, wherein power transmitted by each of the N antennas is less than or equal to a maximum power, and the transmit matrix A weights L signals [ s ] transmitted synchronously along eigenvectors of channels between the N antennas and the M antennas of the second device₁...s_L](ii) a When N is less than or equal to M, the emitting matrix A is VD, where V is H^HH, H being the channel response from said first device to said second device, and a matrix D ═ I · sqrt (Pmax/N), andi is an identity matrix, so the power transmitted by each of the N antennas is the same as each other and is equal to Pmax/N, where Pmax is the total transmit power combined from all N antennas; b. a second device, comprising: i.M antennas; m wireless transmitters, each transmitter connected to a corresponding one of a plurality of antennas; a baseband signal processor connected to the N wireless transmitters for processing the output signals from the plurality of wireless receivers by the reception weights and combining the resultant signals to recover the L signals [ s ]₁...s_L]。

On the first device, L sets of signals [ s ] to be transmitted are represented₁…s_L]Is processed through a transmit matrix a to maximize the capacity of the channel between the first device and the second device, wherein the channel is subject to a power limitation, i.e., the power transmitted through each of the N sets of channels is less than or equal to a maximum power. The power limit for each antenna may be the same for all antennas or for a particular antenna, or may be different. For example, the power limit for each antenna may be the same as the sum of the powers transmitted by the N groups of antennas divided by N. Said transmission matrix A distributes said L groups of signals [ s ] among N groups of antennas₁…s_L]To transmit synchronously to the second device. In the second device, the signals received by the M groups of antennas are processed with the reception weights, and the resulting signals are integrated to recover the L groups of signals. This applies to N > M and N ≦ M.

If the communication devices in a system are designed to be at about the power limit of each antenna, the performance of the communication system will be as good as a near-optimal water-level solution, and provide more significant performance benefits. The wireless transmitter may be implemented with a power amplifier that requires low power output capacity. The area of the silicon wafer required can also be reduced. Thus, the DC current drained via the transmitter will be relatively low and the on-chip interference caused via the power amplifier will also become relatively low.

The foregoing technical features and objects and other advantages of the present invention will become more apparent upon consideration of the following detailed description and the accompanying drawings.

Drawings

Fig. 1 shows a system diagram of two multi-antenna wireless communication devices, wherein multiple signal streams are simultaneously transmitted from a first device to a second device.

Fig. 2 shows mapping and multiplexing of signals to multiple antenna paths for simultaneous transmission.

Fig. 3 is a block diagram of a wireless communication device capable of implementing the MIMO wireless communication techniques shown in fig. 1.

Fig. 4 shows a block diagram of a preferred embodiment of the transmitter portion of a modem (modem) forming part of the device of fig. 3.

Fig. 5 shows a block diagram of a preferred embodiment of the receiver portion of the modem.

Fig. 6 shows a coordinate plot illustrating the relative performance of MIMO wireless techniques in accordance with the present invention.

Detailed Description

Referring to fig. 1 and 2, a system 10 is shown in which a first wireless communication device 100 having N sets of antennas 110(1) through 110(N) communicates with a second wireless communication device 200 having M antennas 210(1) through 210(M) via a wireless communication link. In the following detailed description, only the situation of transmission from the first wireless communication device to the second wireless communication device will be described, and the second wireless communication device to the first wireless communication deviceThe device then only needs to apply the same analysis results. The multiple-input multiple-output (MIMO) channel responses from the N antennas of the first communication device to the M antennas of the second communication device are illustrated by a channel matrix H. The channel matrix is H in the opposite direction^T。

The apparatus 100 will synchronously transmit L groups of signals S via the antennas 110(1) to 110(N)₁，S₂，...，S_L. A vector S will be represented by L sets of signals S transmitted at baseband₁...S_L]Is defined such that S ═ S₁...S_L]^T. The number of signals that can be transmitted simultaneously (L) is related to the channel H between the devices 100 and 200, in particular L ≦ Rank of H^HH is less than or equal to min (N, M). For example, if N is 4 and M is 2, then L ≦ Rank of H^HH≤2。

The device 100 has knowledge of the channel state (e.g., using training sequences, feedback, etc.), i.e., the device 100 knows H. Techniques for obtaining and updating the channel knowledge at the transmitting device (between the transmitting device and the receiving device) are well known in the art and are not described in detail herein. For example, training and feedback techniques have been described in detail in U.S. patent No. 6,144,711 to Raleigh et al.

Two matrices are introduced next: v is H^HH and A is H^HH eigenvalue matrix. The apparatus 100 transmits the inner product As, where the matrix a is a spatial multiplicative transmit matrix and a is VD. The matrix D ═ diag (D)₁，...，d_L) Wherein | d_p|²Is at P^thThe transmission power in the mode, or in other words, the power of the pth of said L groups of signals. Device 200 receives HAs + n and after the maximum ratio, for each mode combination, device 200 calculates c-a^HH^HHAs+A^HH^Hn＝D^HD As+D^HV^HH^Hn。

As shown in fig. 2, in the first deviceIn this case, a large number of bits from a stream { b } are mapped to a vector s by a mapping technique. The mapping technique may optionally include coded modulation to improve link margin. The stream of bits b may be a file or collection of bits representing any form of data, such as speech, video, audio, computational data, etc., partitioned or separated into frames (typically associated with signals) of discrete blocks to be spatially multiplexed or synchronously transmitted. An example of this is the multitasking IEEE802.1lx frame (per S)_iPossibly a different time slot) from the first device 100 to the second device 200, where, for example, the first device 100 is an IEEE802.11 Access Point (AP) and the second device is a client (STA). The product of the emission matrix a and the matrix s is a vector x. The matrix multiplication step effectively weights each element of the vector s across each of the N antennas, thereby distributing the plurality of signals among the plurality of antennas for simultaneous transmission. Element x of vector x derived from matrix multiplication block₁To x_NAnd subsequently to the corresponding antenna of said first communication device. For example, element x₁The sum of the weighted elements of the vector x for all antennas 1, element x₂The sum of the weighted elements of the vector x for all antennas 2, and so on.

The transmitted matrix A includes the transmission weight W_T，ijWhere i is 1 to L and j is 1 to N. Each antenna weight may be frequency dependent to account for a frequency dependent channel H. For example, for a multicarrier modulation system, such as an Orthogonal Frequency Division Multiplexing (OFDM) system, there is typically one matrix a for each subcarrier frequency k. In other words, each transmit weight W_T，ijAs a function of the subcarrier frequency k. For a time-domain (single carrier) modulation system, each transmit weight W_T，ijPossibly a filter of a strip delay line.

With respect to the weight d in the prior art_pMethod of selecting to maximize capacity

Subject to a full power limit transmitted by a plurality of transmitting antennas combined with the transmitted matrix a, that is to say

P_TOT＝Tr(AA^H)·E|s_p|²＝Tr(VDD^HV^H)·E|s_p|²

＝Tr(VDD^HV^H)＜P_max(assuming E|s_p|²＝1)

The best solution to this problem is to use the water filling level (waterfilling) to select the weight d_p. (that is, the fill level is used to put more power on the eigen-channel and higher SNR λ_P。)

The water-filled solution requires N power amplifiers at the transmitting device that can withstand full power, since, for some channels, it is possible for the best method to require all or nearly all power to be transmitted from one antenna path.

For repetition, the prior art method limits the total power transmitted from all of the combined antenna paths, just Σ p_i＝P_TOT＜P_max(for i ═ 1 to N antennas), where P_maxIs a total power limit, and P_iThen is the power from the transmitted antenna path i.

A better approach is to use power limiting for each individual transmit antenna path. One such limitation is that the power transmitted from each antenna is less than the power P transmitted from all N antenna combinations_maxDivided by N, i.e. for each i Pi ≦ P_maxand/N. Using such a method, i.e. a method related to "antenna power limitation", each power amplifier can be designed to output (not exceed) P_maxAverage power of/N, where P_maxIs the maximum power transmitted from all N antenna combinations. An important benefit of this approach is that the power amplifier can be designed to have a low output power capability, thus requiring less silicon chip area. The use of smaller and lower output power amplifiers has the benefits of lower on-power chip amplifier interference and lower DC leakage currents.

When using a P for each antenna_maxPower limitation of/N, the problem will become:

maximum capacity C is limited to (AA)^H)_ii＜P_max/N，i＝1，...，N。

For d_pThis is a very difficult problem to solve because it is related to finding the root in a non-linear function (one of each of the N constraints mentioned earlier) using N Lagrange multiplications. However, this is a separate simple non-optimal solution for both cases.

Condition 1: n is a radical of≤M：

In this case, the transmitting device (with N antennas) will represent the L signals [ s ] to be transmitted₁...s_L]^TMultiplying the transmit matrix A (i.e., calculating As), where the transmit matrix A is set to D and I.sqrt (P)_maxN) (where I is the identity matrix) are calculated equally to implement equal power in each mode. Thus, H^HH is Hermitian and (with a probability of 1) is full-rank (full-rank full-rank, i.e., V is said to be orthogonal)^H)_ii＝(VDD^HV^H)_ii＝(VV^H)_ii P_max/N＝P_maxN, i.e. representing equal power P_maxN is transmitted via each antenna of a corresponding power amplifier in the device 100, and the total transmit power is associated with P_maxAre equal.

Condition 2: n is more than M:

in this condition, H^HH is not a full-rank. Let v be₁，...，v_LRepresenting H with non-zero eigenvalues^HL eigenvectors of H. Let V equal [ V₁...v_L]And D is sqrt (D. P)_maxN) · I, where the power in each mode is equal, and d is 1 to L for p ═ 1_pD. The power on antenna path I is given by the formula (d.P)_max/N)·(VV^H)_iiTo decide. Thus, from each of the I antenna pathsThe power of the shots may be different. The transmitting device (with N antennas) will represent the L signals s to be transmitted₁...s_L]^TMultiply the transmit matrix A (i.e., calculate As), where the transmit matrix A is set to D and sqrt (d.P)_maxI, and wherein the power is the same in each mode, and d_pD for p 1 to L.

The method comprises the following steps: setting d to 1/z, wherein z isThe maximum power from any antenna path is P_maxand/N. All power from all antenna paths may prove to be at least P_maxIs not more than P_max。

The method 2 comprises the following steps: set d to 1. In this case, all the power transmitted by the plurality of antennas is P_maxM and the power transmitted by the antenna i (i 1 to N) is then P_max/N·(VV^H)_ii。

Assuming that the power amplifiers on the devices at both ends of the link have the same peak output power, the total power transmitted from the N antenna devices will be equal to the total power transmitted from the M antenna devices for case 1 and case 2/method 2. Thus, the connection between the two devices is symmetrical in these cases. Case 2/method 1 is only slightly more complex (since it requires a normalization step), but has a larger transmit power compared to method 2.

The previously described approach is sufficient to perform at the Shannon limit of 1dB for each symmetrical system (with the same number of antennas on both ends of the link), but facilitates the use of a smaller but more efficient power amplifier in the radio transceiver, and therefore achieves lower on-chip interference between the two radio paths (caused by the power amplifier) compared to the water-filled approach.

For each of the transmit antennas, for example,the antenna power limits need not be the same and may be specialized for individual antennas or different from one another. In addition, even if different antenna power limits are used for each antenna, each particular antenna power limit may be less than or equal to P_max。

The device 200 with M antennas described will suffer the same type of power limitation on each of the M antennas when transmitting to 100. The situation described above applies to the comparison of M with respect to N, and an appropriate solution is used to transmit a signal to the device 100.

Fig. 3 shows a block diagram of a wireless communication device suitable for use with devices 100 and 200. The apparatus 100 includes a modem 120, digital-to-analog converters (DACs)130, analog-to-digital converters (ADCs) 140, a MIMO wireless transceiver 150 connected to the antennas 110(1) through 110(N), and a control processor 160. The modem 120 is associated with a baseband signal processor and is configured to perform modulation of the transmitted signal (vector s) at baseband and demodulation of the received signal at baseband. By doing so, the modem 120 will represent the L signals [ s ] to be transmitted₁...s_L]^TMultiplied by the transmit matrix a. The DACs 130 are complex DACs for converting digital baseband modulated signals representing As into corresponding analog signals, and the DACs 130 are coupled to the transmit path of the MIMO wireless transceiver 150. The ADCs 140 convert signals received from the receive paths associated with the MIMO radio transceiver 150 into digital signals to provide baseband demodulation by the modem 120. During baseband demodulation, the modem 120 applies appropriate receive weights to the received signals to recover the L signals s₁...s_L]^T. The MIMO transceiver 150 includes a plurality of wireless transceivers, each including an associated transmitter 152(i) and receiver 154(i) and connected to a corresponding antenna via a corresponding switch 156 (i). Each transmitter includes a power amplifier (not shown)In (1). The MIMO wireless transceiver 150 may be implemented as a single integrated circuit or as two or more separate integrated circuits. An embodiment of a single integrated MIMO wireless transceiver is disclosed in co-published U.S. patent application No. 10/065,388(2002, 10/11), which is also incorporated by reference herein.

There are many ways to implement the modem 120. Fig. 4 and 5 are block diagrams of the transmitter portion 120A and the receiver portion 120B, respectively, of the modem 120 for a multi-carrier, e.g., Orthogonal Frequency Division Multiplexing (OFDM) application. In general, matrix multiplication of the type described above is performed on each OFDM subcarrier individually to optimize the performance of the internal frequency-selective channels (frequency-selective channels). Referring to fig. 4, the transmitter portion 120A of the modem includes a frequency inverter block 310, a convolutional encoder 315, an interpolator block 320, a spatial multiplexer block 325 that performs matrix multiplication (i.e., a (k)) with a transmit matrix a that differs by OFDM subcarriers k, a subcarrier modulator 330, an Inverse Fast Fourier Transform (IFFTs), and a low pass filter block 340. The output of the low pass filter block 340 is connected to the DACs 130 (fig. 3). A preamble generator 350 is also coupled to the DACs 130. As shown in fig. 4, assuming the modem is in an N-antenna device, there are L blocks 315, 320, and 325 used to process the signals associated with each transmit antenna path for each baseband transmit signal stream and N blocks 335, 340, and 130.

The receiver portion 120B shown in fig. 5 includes a block 415 of resampling, a low pass filter block 420, Numerical Control Oscillators (NCOs), FFTs block 430, equalizer block 435, in which the receive weights are applied to the received signal, a de-interpolator block 440, and a depuncture decoder 445 block. A preamble processing and automatic gain control block (AGC)450 and a channel estimation block 455 are also provided for channel estimation calculations and other functions. The preamble and AGC block 450 reverts to a preamble on the received signal and the channel estimator 445 generates knowledge of the channel H, which is provided to the equalizer 435 to calculate and apply receive weights to the output of the FFT block 430. Assuming the modem is located in an N-antenna device, there are N instances of blocks 415, 420, and 425 for each received signal stream and L instances of blocks 435, 440, and 445 for recovering the L signals.

As suggested by the above description of fig. 4 and 5, a first device communicates channel response information to a second device upon passing through each antenna by transmitting a known OFDM training preamble, e.g., a packet preamble. For a frequency-domain implementation, the second device performs a Spatial Frequency Decomposition (SFD) that knows the channel information, and uses the SFD data to process the received signal from the device and transmit the signal back to the other device. This assumes reciprocity over the link and therefore MIMO phase correction at each device has to be performed. Information regarding MIMO phase correction has been disclosed in commonly assigned and filed U.S. patent application No. 10/457,293 (6/9/2003), which is incorporated by reference herein. Information about the cluster order as a function of the subcarrier index and the eigen-channel may also be included in the preamble. Each subcarrier has an associated cluster order for use on each eigenchannel. In the transmitter portion 120A, a multi-dimensional Vector Trellis Encoder (VTE) may be used to map the input bits from the preamble onto the OFDM constellation symbols. Embodiments of multi-dimensional VTE's are well known in the relevant prior art. Other techniques for obtaining channel state information are also known in the art and are described in detail above.

A modem may be configured to apply the power limiting principles described above to a time domain system implementation in which the filters of the stripline delay line are used.

FIG. 6 illustrates that the power limitation described herein is more efficient than the optimized fill level approach.

In summary, the present invention provides a system and method for MIMO wireless communication between a first device having N antennas and a second device having M antennas. In said first means, L signals [ s ] representing the transmitted signal₁...s_L]Is processed by a transmit matrix a to optimize the capacity between the first device and the second device of a channel subject to a power limitation such that the power transmitted through each of the N antennas is less than a maximum power value. In this way, the transmission matrix A distributes L signals [ s ] in N antennas₁...s_L]To transmit synchronously to said second device. Similarly, a wireless communication device is provided comprising N antennas, N wireless transmitters, each coupled to a corresponding one of the plurality of antennas, and a baseband signal processor coupled to the N antennas of the wireless transmitter for processing L signals [ s ] representing the transmitted signals with a transmit matrix A₁...s_L]To maximize the capacity of a channel between the first device and the second device subject to a power limitation such that the power transmitted through each of the N antennas is less than a maximum power value. In this way, the transmission matrix A distributes the L signals [ s ]₁...s_L]To transmit synchronously to the second device via N antennas. The transmit matrix a calculation is subject to different power constraints than one or more antennas or the same power constraints as each of the N antennas. For example, in the latter case, the transmit matrix a may calculate a power limit subject to the same power limit as each of the N antennas, corresponding to the sum of the total maximum powers transmitted by all of the N antennas divided by the value of N.

The foregoing description is only exemplary of the invention.

Claims (15)

1. A method of transmitting signals over a channel between a first device having N antennas and a second device having M antennas, the method comprising:

processing a vector s representing L signals with a transmit matrix A, wherein the transmit matrix A is calculated to maximize channel capacity subject to a power constraint between the first device and the second device, wherein power transmitted by each of the N antennas is less than or equal to a maximum power, and wherein the transmit matrix A weights L signals [ s [ ]₁...s_L]And distributing the L signals s1 … sL among the N antennas for synchronous transmission]To a second device; and

when N is less than or equal to M, the emitting matrix A is VD, wherein V is H^HH, H being the channel response from said first device to said second device, and a matrix D ═ I · sqrt (P)_max/N) and I is an identity matrix, so that the power transmitted by each of the N antennas is equal to each other and equal to P_maxN, wherein P_maxIs the total transmit power combined from all N antennas.

2. The method of claim 1, wherein when N > M, at least two of the N antennas transmit different power levels from each other.

3. The method of claim 1, wherein the transmit matrix a is equal to VD, where V is H^HH, H being the channel response from said first device to said second device, D ═ diag (D)₁，…，d_L) And for P ═ 1 to L, | dp | shunts²Is transmitting power.

4. A method according to claim 3, wherein when N > M, D ═ sqrt (D · P)_maxI, where the power transmitted via antenna I is (d.p) for I ═ 1 to N_max/N)·(VV^H)_iiAnd d ═ d_pFor p 1 to L.

5. A method as claimed in claim 4, characterized in that d is 1/z andthe maximum power from any of the N antennas is therefore equal to Pmax/N, and the total power transmitted by the combined N antenna combination is between Pmax/M and Pmax.

6. The method of claim 4, wherein d is 1, such that via antennas i, i is 1 to N, the transmitted power is (P) N_max/N)·(VV^H)_iiAnd the total power transmitted by the combined N antennas is P_max/M。

7. The method of claim 1 further comprising receiving at the second device M antenna signals transmitted by the first device, and processing the signals received at each of the M antennas with receive weights and combining the resulting signals to recover the L signals.

8. The method of claim 1 wherein each of the L signals is baseband modulated using a multiple carrier modulation process, and wherein the processing comprises multiplying the vector s by the transmit matrix a (k) on each of a plurality of subcarriers k.

9. A wireless communication device for communicating signals over a channel, the wireless communication device comprising:

n antennas;

n wireless transmitters, each transmitter connected to a corresponding one of a plurality of antennas;

a baseband signal processor coupled to the N wireless transmitters to process a vector s representing L signals with a transmit matrix A, wherein the transmit matrix A is calculated to maximize channel capacity subject to a power constraint between the wireless communication device and a remote device, wherein power transmitted by each of the N antennas is less than or equal to a maximum power, and wherein the transmit matrix A weights L signals [ s [ s ] ]₁...s_L]And distributing the L signals s1 … sL among the N antennas for synchronous transmission]To the remote device; when N is less than or equal to M, the transmitting matrix A is VD, where M is the number of antennas of the remote device and V isH^HH, H being a channel response from the wireless communication device to the remote device, and a matrix D ═ I · sqrt (P)_max/N) and I is an identity matrix, so that the power transmitted by each of the N antennas is equal to each other and equal to P_maxN, wherein P_maxIs the total transmit power combined from all N antennas.

10. The wireless communication apparatus as claimed in claim 9, wherein when N > M, at least two of the N antennas transmit different power from each other.

11. The wireless communication device of claim 9 wherein the transmission matrix a is equal to VD, wherein V is H^HH, H being a channel response from the wireless communication device to the remote device, D ═ diag (D)₁，…，d_L) And for P ═ 1 to L, | dp | shunts²Is transmitting power.

12. The wireless communication apparatus of claim 11, wherein the baseband signal processor multiplies the calculated transmit matrix a by the vector s when N > M, wherein D-sqrt (D-P)_maxI, where the power transmitted via antenna I is (d.p) for I ═ 1 to N_max/N)·(VV^H)_iiAnd d ═ d_pFor p 1 to L.

13. The wireless communication device of claim 12, wherein d-1/z, andthe maximum power from any of the N antennas is therefore equal to Pmax/N, and the total power transmitted by the combination of N antennas is between P_maxM and P_maxAnd (3) removing the solvent.

14. The wireless communication device of claim 12, wherein d-1, such that via antennas i, i-1 through N, the transmitted power is (P ═ N)_max/N)·(VV^H)_iiAnd the total power transmitted by the combined N antennas is P_max/M。

15. The wireless communication device as claimed in claim 9, wherein each of the L signals is baseband modulated using a multiple carrier modulation process, wherein the baseband signal processor multiplies the vector s by the transmit matrix a (k) on each of a plurality of subcarriers k.