Apparatus and methods for providing efficient space-time structures for preambles, pilots and data for multi-input, multi-output communications systems

Abstract

Apparatus and methods for providing efficient space-time structures for preambles, pilots and data for multi-input, multi-output (MIMO) communications systems are provided. One such embodiment includes providing a computer program that includes logic configured to provide an initial structure. The computer program further includes logic configured to verify that the rows of the initial structure are linearly independent and logic configured to apply an orthonormalization procedure to the initial structure to obtain a space-time structure. Methods are also provided for providing efficient space-time structures for preambles, pilots and data for MIMO communications systems.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

With respect to EQ. 1, k represents the sub-carrier or sub-channel of received demodulated signals and T represents a dimension variable that is typically equivalent to Q, although it may have other values. As discussed above, Q and L represent, respectively, the number of modulators 16 and respective transmit antennas 18 and the number of demodulators 22 and respective receive antennas 20 with respect to a typical MIMO communications system 6.

FIG. 4 is a graphic illustration of a version of the receive sample matrix R′ shown in FIG. 3 that is applicable to the MIMO communications system of FIG. 1, when employing Orthogonal Frequency Division Multiplexing (OFDM). As shown, the x axis represents space, the y axis represents time, and the z axis represents frequency. Each receive sample matrix R_k that is depicted in the space-time dimensions is similar to the receive sample matrix R discussed above with respect to FIG. 3. However, each element of the receive sample matrix R′ illustrated in FIG. 4 also has N frequency components that are each represented by an index, “k”. As k varies from 0 to N−1 for the elements of each receive sample matrix R_k in FIG. 4, the frequency component of the received symbol varies accordingly. Thus, the three-dimensional receive sample matrix R′ can be viewed as including N receive sample matrices R_k of dimensions Q×L or Q*L vectors R_1,j of length N. For example, with respect to the symbol received by the 1^st antenna and demodulated by the 1^st demodulator, there is a vector of elements R_1,0, R_1,1, . . . , R_1,N−1, as depicted in FIG. 4.

FIG. 5 illustrates an exemplary frame 50 that may be implemented in a MIMO communications system that has Q transmit antennas, such as the communications system depicted in FIGS. 1 and 3. As depicted in FIG. 5, the frame 50 typically includes Q signal structures 52, which correspond respectively to the Q antennas. Each signal structure 52 typically includes a preamble 54 and a data section 56. As discussed above for FIG. 2, the preamble 54 is typically inserted into the data section 56 by the pilot/training symbol inserter 32. The preamble 54 typically includes one or more training blocks 58 of length N_I and cyclic prefixes 57 of length G, as depicted in FIG. 5. The combination of a cyclic prefix 57 and a training block 58 forms a training symbol 53 that has a length of G+N_I samples in the time domain. Thus, as depicted, the preamble 54 typically includes Q training symbols 53 that have an overall length of Q*(G+N_I) samples in the time domain. A cyclic prefix 57 may also be referred to as a guard interval, since the cyclic prefix 57 typically functions to guard the signal structures 52 from inter-symbol interference (ISI) during transmission as a frame 50 across the channel 19. The time length of the cyclic prefix 57 is typically greater than the maximum length of the channel impulse response h_ij, which was discussed above for FIG. 3.

As also depicted in FIG. 5, the data section 56 typically includes one or more data blocks 59 of length N and cyclic prefixes 57 of length G. The combination of a cyclic prefix 57 and a data block 59 forms a data symbol 55 that has a length of G+N samples in the time domain. Therefore, the data section 56 of the signal structure 52 typically includes Q or more data symbols 55 that have an overall length of P*Q*(G+N) samples in the time domain, as depicted in FIG. 5, where P is some positive integer. Although not depicted in FIG. 5, for simplicity, pilot symbols may also be intermittently inserted into the data symbols 55 by the pilot/training symbol inserter 32, as discussed above.

The length N_I of a training block 58 may be shorter than the length N of a data block 59 in a signal structure 52. Typically, the length N_I of a training block 58 in the preamble 54 is established as a fraction of the length N of a data block 59 in the data section 56 to provide the relationship of N_I being equivalent to N/I, where I is some positive integer. For example, N_I may be equivalent to N/4 (i.e., I=4). If the length N_I of a training block 58 is not established, the length N_I may be assumed to be equivalent to N (i.e., I=1). Typically, the length of a training symbol 53 (i.e., G+N_I) is equivalent to the length of a data symbol 55 (i.e., G+N). However, it is feasible for the training symbol 53 to be shorter than the data symbol 55 in the context of the signal structure 52.

A primary purpose of the preamble 54 is to enable the receiver 10 (FIG. 1) to identify the arrival of the signal structure 52. Thus, the preamble 54 may facilitate time synchronization, frequency synchronization, channel parameter estimation, and noise variance estimation. Efficient space-time structures for the preamble 54 (“space-time preamble structures”), in accordance with the present invention, provide time synchronization, frequency synchronization, channel parameter estimation, and noise variance estimation through synchronization signals that have low peak-to-average power ratios (PAPR) (e.g., at or approaching unity).

A space-time preamble structure, which may also be referred to as a space-time training structure, may be represented by a signal transmission matrix S_k. In accordance with an embodiment of the present invention, the signal transmission matrix S_k of an efficient space-time preamble structure should be a unitary transmission matrix in the frequency domain and have a low PAPR in the time domain. In this regard, efficient space-time preamble structures provide enhanced performance in MIMO communications systems.

A unitary transmission matrix contains rows and columns that are orthogonal to each other, and the energy of the signals represented by each row or column is unity. In mathematical terms, a unitary transmission matrix has the properties represented by the following equations:

$\begin{array}{cc}\underset{j=1}{\sum ^Q}{S}_{i,j}{S}_{i^{\prime },j}^{*}=\{\begin{array}{cc}1& i=i^{\prime }\\ 0& i\ne i^{\prime }\end{array}& \mathrm{EQ}.2A\\ \underset{i=1}{\sum ^Q}{S}_{i,j}{S}_{i,j^{\prime }}^{*}=\{\begin{array}{cc}1& j=j^{\prime }\\ 0& j\ne j^{\prime }\end{array}& \mathrm{EQ}.2B\end{array}$
where S_i,j represents the constituent symbols of the unitary transmission matrix.

Providing a space-time preamble structure that is a unitary signal transmission matrix S_k reduces or eliminates noise enhancement during channel estimation of the received signals. Moreover, providing a space-time preamble structure that possesses a low PAPR reduces or eliminates signal non-linearities and spurious, out-of-band signal transmissions. As will be discussed below, data structures formed by space-time processing (i.e., space-time data structures) to be a unitary transmission matrix also provide enhanced performance in MIMO communications systems.

The following descriptions present several examples of data structures that, in accordance with the present invention, can be applied and/or modified to provide space-time preamble structures that are unitary transmission matrices. As a first example, a diagonal data structure can be applied and/or modified to provide a space-time preamble structure in accordance with the present invention. In this regard, the resulting diagonal space-time preamble structure is a unitary transmission matrix. The following diagonal structure S_D1 is an example of this unitary transmission matrix that can be applied as a space-time preamble in a MIMO communications system with Q antennas:

$\begin{array}{cc}{S}_D=\left[\begin{array}{cccc}{S}_1& 0& \cdots & 0\\ 0& S_2& \cdots & ⋮\\ ⋮& 0& \ddots & 0\\ 0& \cdots & 0& S_Q\end{array}\right]& \mathrm{EQ}.3\end{array}$

The foregoing diagonal space-time preamble structure S_D1 can be simplified so that the same training symbol (e.g., S₁) can be transmitted from each antenna, instead of Q different training symbols (i.e., S₁, S₂, etc.), as shown by the following simplified diagonal structure S_DS that can be applied, in accordance with the present invention, as a space-time preamble structure in a MIMO communications system with Q antennas:

$\begin{array}{cc}{S}_{\mathrm{DS}}=\left[\begin{array}{cccc}{S}_1& 0& \cdots & 0\\ 0& S_1& \cdots & ⋮\\ ⋮& 0& \ddots & 0\\ 0& \cdots & 0& S_1\end{array}\right]& \mathrm{EQ}.4\end{array}$

When the foregoing diagonal structures S_D, S_DS are applied as space-time preamble structures in a MIMO communications system, the training symbols are transmitted sequentially in time from each corresponding transmit antenna, and the parameters of the received symbols are estimated by the receivers connected to each receive antenna. Due to their unitary characteristic, the diagonal structures S_D, S_DS, provide simplified signal acquisition (i.e., synchronization) and parameter estimation when applied as a space-time preamble structure in a MIMO communications system. These diagonal structures S_D, S_DS, are preferably applied as space-time preamble structures, in MIMO communications systems that use two transmit antennas. As the number (Q) of transmit antennas in the MIMO system is increased, the power output from each transmit antenna typically has to be reduced by a factor of Q due to the nature of MIMO systems. As a result, the efficiency of the diagonal space-time preamble structures S_D, S_DS may decrease in MIMO systems with more than two transmit antennas, since the diagonal structures S_D, S_DS only include symbols on the main diagonal (i.e., spanning from the top-left to the bottom).

A data structure that was introduced by S. Alamouti is another example of a data structure that can be applied and/or modified, in accordance with the present invention, to provide a space-time preamble structure S_A. This data structure is a unitary transmission matrix, and it can be applied as a space-time preamble structure S_A, in MIMO communications systems that employ two transmit antennas. The space-time preamble structure S_A has the following form:

$\begin{array}{cc}{S}_A=\left[\begin{array}{cc}{S}_1& S_2\\ -S_2^{*}& S_1^{*}\end{array}\right]& \mathrm{EQ}.5\end{array}$

In the above space-time preamble structure S_A, the “*” symbol indicates a complex conjugate operation. The foregoing space-time preamble structure S_A can also be simplified, in accordance with the present invention, so that the same training symbol is transmitted from each of the two antennas of the MIMO system, as shown by the following simplified space-time preamble structure S_AS:

$\begin{array}{cc}{S}_{\mathrm{AS}}=\left[\begin{array}{cc}{S}_1& S_1\\ -S_1^{*}& S_1^{*}\end{array}\right]& \mathrm{EQ}.6\end{array}$

Several orthogonal structures that were introduced by V. Tarokh, et al. are examples of data structures that can be applied and/or modified, in accordance with the present invention, to provide space-time preamble structures that are unitary transmission matrices. These data structures can be applied as space-time preamble structures, in accordance with the present invention, in MIMO communications systems that employ four or eight transmit antennas. For a four-antenna MIMO system, the following space-time preamble structure S_T4 can be applied, in accordance with present invention, when the constituent symbols have real number values:

$\begin{array}{cc}{S}_{T4}=\left[\begin{array}{cccc}{S}_1& S_2& S_3& S_4\\ -S_2& S_1& -S_4& S_3\\ -S_3& S_4& S_1& -S_2\\ -S_4& -S_3& S_2& S_1\end{array}\right]& \mathrm{EQ}.7\end{array}$
The foregoing space-time preamble structure S_T4 can be simplified, in accordance with the present invention, so that the same training symbol is transmitted from each of the four antennas of the MIMO system, as shown by the following simplified space-time preamble structure S_T4S. The symbols of this structure S_T4S may have complex values (e.g., W+jX):

$\begin{array}{cc}{S}_{T4S}=\left[\begin{array}{cccc}{S}_1& S_1& S_1& S_1\\ -S_1& S_1& -S_1& S_1\\ -S_1& S_1& S_1& -S_1\\ -S_1& -S_1& S_1& S_1\end{array}\right]& \mathrm{EQ}.8\end{array}$

The foregoing simplified structures S_AS, S_T4S (i.e., EQ. 6 and EQ. 8) typically form unitary transmission matrices when applied as space-time preamble structures, without further modification. Furthermore, the PAPR of the simplified space-time preamble structures S_AS, S_T4S are typically unity when the symbols consist of chirp-type sequences, such as:

$\begin{array}{cc}{s}_n=\exp \left(\frac{j\pi n^2}{N}\right),n=0,1,\dots ,N-1\hspace{1em}).& \mathrm{EQ}.9\end{array}$
Therefore, these simplified structures S_AS, S_T4S are typically efficient (i.e., they provide time and frequency synchronization, estimation of noise variance and channel parameters, and low PAPR) when applied, in accordance with the present invention, as space-time preamble structures.

The foregoing structures S_A, S_T4 (i.e., EQ. 5 and EQ. 7) are also typically efficient when applied as space-time preamble structures, in accordance with the present invention. The structure S_T4 is typically not efficient when applied as space-time data structures in a MIMO communications system. However, both structures S_A, S_T4 can be modified and then applied as efficient space-time data structures, in accordance with the present invention. Since the structures S_A, S_T4 will include symbols with complex values when they are applied as space-time data structures, the resultant data structures will typically not be unitary transmission matrices. Therefore, the structures S_A, S_T4 can be modified, in accordance with the present invention, to form unitary transmission matrices and, thus, provide efficient space-time data structures. Methods, in accordance with the present invention, to transform these structures S_A, S_T4 and other structures into efficient space-time data structures will be described below.

The following space-time preamble structure S_T8 is based on another data structure by Tarokh, et al., and the structure S_T8 can be applied in eight-antenna MIMO communications systems, in accordance with present invention, when the constituent symbols have real number values:

$\begin{array}{cc}{S}_{T8}=\left[\begin{array}{cccccccc}{S}_1& S_2& S_3& S_4& S_5& S_6& S_7& S_8\\ -S_2& S_1& -S_4& S_3& S_6& -S_5& -S_8& S_7\\ -S_3& -S_4& S_1& -S_2& S_7& S_8& -S_5& -S_6\\ -S_4& S_3& S_2& S_1& S_8& -S_7& S_6& -S_5\\ -S_5& -S_6& -S_7& -S_8& S_1& S_2& S_3& S_4\\ -S_6& S_5& -S_8& S_7& -S_2& S_1& -S_4& S_3\\ -S_7& S_8& S_5& -S_6& -S_3& S_4& S_1& -S_2\\ -S_8& -S_7& S_6& S_5& -S_4& -S_3& S_2& S_1\end{array}\right]& \mathrm{EQ}.10\end{array}$

The foregoing space-time preamble structure S_T8 can be simplified, in accordance with the present invention, so that the same training symbol is transmitted from each of the eight antennas of the MIMO system, as shown by the following simplified space-time preamble structure S_T8S

$\begin{array}{cc}{S}_{T8S}=\left[\begin{array}{cccccccc}{S}_1& S_1& S_1& S_1& S_1& S_1& S_1& S_1\\ -S_1& S_1& S_1& -S_1& S_1& -S_1& -S_1& S_1\\ -S_1& -S_1& S_1& S_1& S_1& S_1& -S_1& -S_1\\ -S_1& S_1& -S_1& S_1& S_1& -S_1& S_1& -S_1\\ -S_1& -S_1& -S_1& -S_1& S_1& S_1& S_1& S_1\\ -S_1& S_1& -S_1& S_1& -S_1& S_1& -S_1& S_1\\ -S_1& S_1& S_1& -S_1& -S_1& S_1& S_1& -S_1\\ -S_1& -S_1& S_1& S_1& -S_1& -S_1& S_1& S_1\end{array}\right]& \mathrm{EQ}.11\end{array}$

The foregoing structures S_T8, S_T8S (i.e., EQ. 10 and EQ. 11) are typically efficient when applied as space-time preamble structures, in accordance with the present invention. However, these structures S_T8, S_T8S are typically not efficient when applied as space-time data structures in a MIMO communications system. The structure S_T8 preferably can be modified and then applied as efficient space-time data structures, in accordance with he present invention. Since the structure S_T8 will include symbols with complex values when it is applied as a space-time data structure, the resultant data structure will typically not be a unitary transmission matrix. Therefore, the structure S_T8 can be modified, in accordance with the present invention, to form a unitary transmission matrix and, thus, provide an efficient space-time data structure. Methods, in accordance with the present invention, to transform this structure S_T8 and other structures into efficient space-time data structures will be described below.

Orthogonal structures, such as those introduced by Tarokh, et al., typically only have applications to MIMO communications systems that employ two, four, or eight transmit antennas. As described above, some of the orthogonal structures can be applied, in accordance with the present invention, in two-antenna MIMO systems as space-time data structures, with complex symbols, that are unitary transmission matrices. However, the application of existing orthogonal structures using complex symbols (e.g., for space-time data structures) in MIMO systems having more than two transmit antennas typically results in a loss of the system diversity gain and/or system bandwidth. For example, the following orthogonal structure S_T3 was introduced by Tarokh, et al. for use as a data structure with complex symbols in a three-antenna MIMO system:

$\begin{array}{cc}{S}_{T3}=\left[\begin{array}{ccc}{S}_1& S_2& \frac{S_3}{\sqrt{2}}\\ -S_2^{*}& S_1^{*}& \frac{S_3}{\sqrt{2}}\\ \frac{S_3^{*}}{\sqrt{2}}& \frac{S_3^{*}}{\sqrt{2}}& \frac{-S_1-S_1^{*}+S_2-S_2^{*}}{2}\\ \frac{S_3^{*}}{\sqrt{2}}& \frac{S_3^{*}}{\sqrt{2}}& \frac{S_2+S_2^{*}+S_1-S_1^{*}}{2}\end{array}\right]& \mathrm{EQ}.12\end{array}$

When the foregoing structure S_T3 is applied in a three-antenna MIMO system, it does not provide the full diversity performance of the system, which is the capability to transmit three symbols over three symbol periods. Instead, the structure S_T3 only provides for the transmission of three symbols over four symbol periods, which is apparent since the structure has a four rows instead of three. This lack of full diversity may result in a loss of as much as 25% of system throughput. However, methods, in accordance with the present invention, will be discussed below to transform such inefficient structures into efficient space-time structures (for preambles or data) that provide full diversity performance in MIMO communications systems.

The foregoing space-time preamble structures, in accordance with the present invention, can be applied in a Q-antenna MIMO communications system, such as the system 6 depicted in FIG. 1, using any applicable technique. For example, the space-time preamble structure S_T4 may be stored in a pilot/training symbol inserter 32 of the transmitter 8 of a four-antenna MIMO communications system 6 and combined with one or more data symbols for transmission over a channel 19, as discussed above.

In general the transmission matrix for Q transmit antennas over Q symbol intervals can be represented by the following matrix S_Q²:

$\begin{array}{cc}{S}_{Q^2}=\left[\begin{array}{cccc}{S}_1& S_2& \cdots & S_Q\\ S_{Q+1}& S_{Q+2}& \cdots & S_{2Q}\\ ⋮& & & ⋮\\ S_{Q\left(Q-1\right)+1}& \cdots & \cdots & S_{Q^2}\end{array}\right]& \mathrm{EQ}.13\end{array}$
This general transmission matrix S_Q² can be composed using Q² different symbols (or sequences in the case of OFDM modulation). However, in general, only Q sequences are used to form a structure. As discussed above, the transmission performance of Q symbols over Q symbol periods indicates full diversity performance of the MIMO system and also indicates the utilization of the full bandwidth of the system. Thus, such performance indicates the optimal use of the system resources.

In order to utilize the structure of the foregoing general transmission matrix S_Q² to construct efficient space-time sequence structures for preambles, pilots and data to be applied in MIMO communications systems, the matrix S_Q² is pre-processed and/or pre-conditioned in accordance with the present invention.

FIG. 6 is a flow chart illustrating a method 120 for providing efficient space-time structures for preambles, pilots and data that may be implemented in a MIMO communications system, such as the system 6 depicted in FIG. 1. The method 120 begins with a step 122 in which one or more initial structures S_in are provided for conversion into efficient space-time structures for preambles or data. The structure S_in will typically have a form that is applicable to a Q×L MIMO communications system, where Q represents the number of transmit antennas and L represents the number of receive antennas, as discussed above. Thus, if the initial structure S_in is to be applied to a MIMO system that has 4 transmit antennas (i.e., Q=4), the structure will typically have 4 columns and 4 rows, similar to the general transmission matrix S_Q² described above. Typically, the initial structure S_in is formed of symbols from a known symbol alphabet. As discussed above, a symbol alphabet typically includes a finite set of values. In general, the initial structure S_in may be any structure that has a possible application to a MIMO communications system with Q transmit antennas. One method, among others, to determine an initial structure S_in will be discussed below with respect to FIG. 7.

Following step 122, the method 120 proceeds to step 124 in which the rows of the initial structure S_in are verified to be linearly independent. The check for linear independence of the rows of the initial structure S_in may be performed by various methods and techniques, which may be known in the art. For example, the rows of the initial structure S_in can be tested for linear independence by determining the rank of the initial structure S_in. If the rank of the initial structure S_in is determined to be Q, the rows of the initial structure S_in are linearly independent. If the rows of the initial structure S_in are determined to be linearly independent, the method 120 proceeds to the next step 126. However, if the rows of the initial structure S_in are determined not to be linearly independent, the method 120 returns to step 122, in which one or more different initial structures S_in are provided and the method 120 proceeds again to step 124.

In the step 126, an orthonormalization (i.e., orthogonalization and normalization) procedure is applied to the initial structure S_in. The orthonormalization procedure may be any procedure that transforms the initial structure S_in to a space-time structure S_out that has the properties of a unitary signal transmission matrix. As discussed above, a unitary transmission matrix has the following mathematical properties:

$\begin{array}{cc}\sum _{j=1}^Q{S}_{i,j}{S}_{i^{\prime },j}^{*}=\{\begin{array}{cc}1& i=i^{\prime }\\ 0& i\ne i^{\prime }\end{array}& \mathrm{EQ}.2A\\ \sum _{i=1}^Q{S}_{i,j}{S}_{i,j^{\prime }}^{*}=\{\begin{array}{cc}1& j=j^{\prime }\\ 0& j\ne j^{\prime }\end{array}& \mathrm{EQ}.2B\end{array}$
where S_i,j represents the constituent symbols of the unitary transmission matrix. One example of an orthonormalization procedure that may be applied to the initial structure S_in to obtain a space-time structure S_out that is a unitary signal transmission matrix is known as a row-wise Gram-Schmidt procedure. An example application of a row-wise Gram-Schmidt procedure will be presented below.

The resultant space-time structure S_out that is obtained by the step 126 may be applied as an efficient space-time preamble structure or an efficient space-time data structure, depending on the characteristics of the constituent symbols of the structure. For example, as discussed above, an efficient space-time preamble structure includes symbols that provide time and frequency synchronization and estimation of noise variance and channel parameters. In contrast, an efficient space-time data structure typically includes symbols that have complex values, as also discussed above. Further, if OFDM modulation is employed in the communications system, the constituent symbols will be symbol sequences, as also discussed above.

The resultant space-time structure S_out may be applied accordingly as a space-time preamble or data structure in a Q-antenna MIMO communications system, such as the system 6 depicted in FIG. 1, using any applicable technique, which may be known in the art. For example, a resultant space-time preamble structure S_out may be stored in a pilot/training symbol inserter 32 of MIMO communications system transmitter 8 and combined with one or more data symbols for transmission over a channel 19, as discussed above.

FIG. 7 is a flow chart illustrating an exemplary method 140, among others, to determine an initial structure S_in for use in the step 122 described above for FIG. 6. The exemplary method 140 begins with a step 142 in which a symbol alphabet is chosen to provide the symbols for the initial structure S_in. Preferably, the symbols (or symbol sequences in the case of OFDM modulation) are derived from a complex alphabet on the unit circle, that is, all of the alphabet points have the same energy. The following are exemplary alphabets in this regard:

• • Binary Phase Shift Keying (BPSK) alphabet: +1, −1
  • Quadrature Phase Shift Keying (QPSK) alphabet: 1+j, −1+j, −1−j, 1−j
  • 8-Phase Shift Keying (8-PSK) alphabet: exp(j*2πi/8), i=0, 1, 2, . . . , 7
  • 16-Phase Shift Keying (16-PSK) alphabet: exp(j*2πi/16), i=0, 1, 2, . . . , 15
  • 32-Phase Shift Keying (32-PSK) alphabet: exp(j*2πi/32), i=0, 1, 2, . . . , 31
  • In general, M-Phase Shift Keying (M-PSK) alphabet: exp(j*2πi/M), i=0, 1, 2, . . . , M−1; M=8, 16, 32, . . .

The symbols or symbols sequences may also be derived from polyphase sequences, such as Chirp sequences; Milewski sequences; Frank-Zadoff sequences; Chu sequences; Suehiro polyphase sequences; and Ng et al. sequences, among others known in the art.

Following the step 142, the method 140 concludes with a step 144 in which the initial configuration of the initial structure S_in is chosen. The determination of the initial configuration may add certain specific characteristics to the structure. For example, the initial configuration typically reduces the number of possible symbol combinations from Q² to Q. The initial configuration may be chosen from any structure configuration. The following are several examples of a possible initial configuration of the initial structure S_in:

• • Circular configuration, S_C:

$\begin{array}{cc}{S}_C=\left[\begin{array}{cccc}{S}_1& S_2& \cdots & S_Q\\ S_Q& S_1& \cdots & S_{Q-1}\\ ⋮& & & ⋮\\ S_2& \cdots & \cdots & S_1\end{array}\right]& \mathrm{EQ}.14\end{array}$

• • Symmetric configuration, S_S:

$\begin{array}{cc}{S}_S=\left[\begin{array}{cccc}{S}_1& S_2& \cdots & S_Q\\ S_2& S_1& \cdots & S_{Q-1}\\ ⋮& & & ⋮\\ S_Q& \cdots & \cdots & S_1\end{array}\right]& \mathrm{EQ}.15\end{array}$

Based on the determination of the symbol alphabet and the initial structure configuration in the step 142 and the step 144, respectively, an initial structure S_in can be determined. This initial structure S_in can be used in the method 120, depicted in FIG. 6, to obtain an efficient space-time structure, as discussed above.

FIG. 8 is a flow chart illustrating an alternative method 160 for providing efficient space-time structures for preambles, pilots and data that may be implemented in a MIMO communications system, such as the system 6 depicted in FIG. 1. The method 160 begins with a step 162 in which one or more initial structures S_in are provided for conversion into efficient space-time structures for preambles or data. The step 162 is at least substantially similar to the step 122 discussed above with respect to FIG. 6. Following the step 162, the method 160 proceeds to a step 164 in which the rows of the initial structure S_in are verified to be linearly independent. This step 164 is at least substantially similar to the step 124 discussed above with respect to FIG. 6.

If the rows of the initial structure S_in are determined to be linearly independent, the method 160 proceeds from the step 164 to a step 166 in which an orthonormalization procedure is applied to the initial structure S_in to transform the initial structure S_in to a space-time structure S_out that has the properties of a unitary signal transmission matrix. This step 166 is at least substantially similar to the step 126 discussed above with respect to FIG. 6. However, if the rows of the initial structure S_in are determined not to be linearly independent, the method 160 returns to step 162.

Following the step 166, the method 160 proceeds to a step 168 in which the alphabet points of the constituent symbols of the resultant space-time structure S_out are checked to be within a tolerable distance of the alphabet points of the constituent symbols of the initial structure S_in. The amplitude of the alphabet points may be modified during the orthonormalization procedure in the step 166. The tolerable distance is typically dependent on the operating capability of components of the MIMO communications system 6, such as digital-to-analog (D/A) converters. The constituent symbols of the space-time structure S_out may be checked to be within a tolerable distance of the original alphabet points by various methods and techniques, which are known in the art. For example, the constituent symbols of the space-time structure S_out may be checked to be within a tolerable distance by application of a Euclidean distance metric represented, for example, by the following equation:
d_t,l=∥S_t−S_l∥²  EQ. 16

If the constituent symbols of the space-time structure S_out are found to be within a tolerable distance from the original alphabet points of the initial structure S_in, the space-time structure S_out is stored in a memory or other device for application in a MIMO communications system. However, if the constituent symbols of the space-time structure S_out are not determined to be within a tolerable distance from the original alphabet points, the method 160 returns to step 162, in which one or more different initial structures S_in are provided and the method 160 proceeds again as described above.

In the case of a MIMO communications system that employs OFDM modulation, the steps 162 through 168 may be repeated until a sufficient number of space-time structures S_out that are unitary signal transmission matrices are obtained and stored, as discussed above.

If the symbols are within a tolerable distance, in step 170, the stored space-time structure S_out used to construct space-time sequence structures S_out,k, where k represents a sub-carrier or sub-channel index of the OFDM setup. The space-time sequence structures S_out,k may be constructed by an encoder, as described above with respect to FIGS. 2 and 5, or other methods, which may be known in the art, may be utilized to construct the space-time sequence structures S_out,k.

In the final step 172 of the method 160, the peak-to-average power ratio (PAPR) of the space-time sequence structures S_out,k are tested to determine if the PAPR of the structures is low enough to provide efficient signal transmission and reception in a MIMO OFDM communications system. The PAPR of the training sequences may be tested by various methods and techniques, which may be known in the art. For example, the PAPR of the space-time sequence structures S_out,k may be tested by converting the structures to the time domain (e.g., by inverse Fourier transform or “IFT”) and calculating the PAPR of the resultant signal samples. If the PAPR of the space-time sequence structures S_out,k is found to be acceptable (e.g., at or approaching unity), the structures have been determined to be efficient, in accordance with the present invention, and may be used for preambles or data in a MIMO communications system 6 employing OFDM modulation. However, if the PAPR of the space-time sequence structures S_out,k are found to be unacceptably high, the method 160 returns to step 162, in which one or more different initial structures S_in are provided and the method 160 proceeds again as described above.

In the case of some orthogonal polyphase sequences, complex coefficients b_i that are used to modulate the sequences may be useful to form efficient space-time sequence structures S_out,k. In this regard, modulation of the orthogonal polyphase sequences by the complex coefficients b_i may make the rows of the corresponding space-time structures S_out linearly independent. Furthermore, the modulation by the complex coefficients b_i may also reduce the PAPR of the resulting space-time sequence structures S_out,k that are formed from the space-time structures S_out.

In the step 126 of the method 120 and the step 166 of the method 160, described above with respect to FIGS. 6 and 8, respectively, an orthonormalization procedure is applied to the initial structure S_in to transform the initial structure S_in to a space-time structure S_out that has the properties of a unitary signal transmission matrix. As discussed above, one example of such an orthonormalization procedure is a row-wise Gram-Schmidt procedure. In general, when a matrix S_k is subjected to the Gram-Schmidt procedure, the resulting matrix S′_k will be unitary, so long as the rank of S_k is Q or the rows of S_k are linearly independent. In a row-wise application of the Gram-Schmidt procedure to a matrix S_k, the first row of the matrix S_k is unchanged and used as a reference to make the remaining rows orthonormal (i.e., orthogonal and normal). The following matrices illustrate the application of a row-wise Gram-Schmidt procedure to a 4×4 matrix S_k to obtain the orthogonalized unitary matrix S′_k:

$\begin{array}{cc}{S}_k=\left[\begin{array}{cccc}\mathrm{.5}{e}^{-\mathrm{.03}j}& \mathrm{.5}{e}^{\mathrm{.00}j}& \mathrm{.5}{e}^{\mathrm{.00}j}& \mathrm{.5}{e}^{\mathrm{.07}j}\\ \mathrm{.5}{e}^{-\mathrm{.89}j}& \mathrm{.5}{e}^{-\mathrm{.49}j}& \mathrm{.5}{e}^{\mathrm{.17}j}& \mathrm{.5}{e}^{-\mathrm{.32}j}\\ \mathrm{.5}{e}^{-\mathrm{.69}j}& \mathrm{.5}{e}^{-\mathrm{.80}j}& \mathrm{.5}{e}^{\mathrm{.20}j}& \mathrm{.5}{e}^{-\mathrm{.28}j}\\ \mathrm{.5}{e}^{-1.3j}& \mathrm{.5}{e}^{-\mathrm{.72}j}& \mathrm{.5}{e}^{-\mathrm{.70}j}& \mathrm{.5}{e}^{-\mathrm{.74}j}\end{array}\right]& \mathrm{EQ}.17\\ S_k^{\prime }=\left[\begin{array}{cccc}\mathrm{.5}{e}^{-\mathrm{.03}j}& \mathrm{.5}{e}^{\mathrm{.00}j}& \mathrm{.5}{e}^{\mathrm{.00}j}& \mathrm{.5}{e}^{\mathrm{.07}j}\\ \mathrm{.62}{e}^{-2.0j}& \mathrm{.16}{e}^{-1.4j}& \mathrm{.76}{e}^{1.3j}& \mathrm{.1}{e}^{-\mathrm{.2}j}\\ \mathrm{.47}{e}^{-\mathrm{.75}j}& \mathrm{.83}{e}^{-2.2j}& \mathrm{.24}{e}^{1.3j}& \mathrm{.14}{e}^{-1.0j}\\ \mathrm{.37}{e}^{-2.6j}& \mathrm{.17}{e}^{-2.4j}& \mathrm{.34}{e}^{-\mathrm{.70}j}& \mathrm{.85}{e}^{-\mathrm{.88}j}\end{array}\right]& \mathrm{EQ}.18\end{array}$

It is noted that embodiments of the present invention, such as those described above, may be implemented in hardware, software, firmware, or a combination thereof. For example, in some embodiments, the present invention may be implemented as a computer program or application in software or firmware that is stored in a memory and that is executed by a suitable instruction execution system. In other embodiments the present invention may be implemented, for example, with one or a combination of the following technologies, which may be known in the art: one or more discrete logic circuit(s) having logic gates for implementing logic functions upon data signals, an application specific integrated circuit (ASIC) having appropriate combinational logic gates, a programmable gate array(s) (PGA), a field programmable gate array (FPGA), etc.

It is further noted that any process descriptions or blocks in flow charts described above may represent modules, segments, and/or portions of a computer program or application code that includes one or more executable instructions for implementing specific logical functions or steps in the process. Alternate implementations are included within the scope of the present invention in which functions may be executed out of order from that shown in the figures and/or discussed above, including substantially concurrently or in reverse order, depending at least in part on the functionality involved, as will be understood by those skilled in the art.

With regard to any block diagrams described above, although the flow of data or other elements may be depicted as unidirectional or bi-directional, such depictions are merely exemplary and not limiting. Variations of the flows depicted in the block diagrams are included within the scope of the present invention. Furthermore, the functionality of some of the blocks may be implemented by a single combined block within the scope of the present invention.

Moreover, embodiments of the present invention, such as those described above, may comprise an ordered listing of executable instructions for implementing logical functions which can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. In the context of this disclosure, a “computer-readable medium” may be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. The computer readable medium may be, for example but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, device, or propagation medium. More specific examples (i.e., a non-exhaustive list) of the computer-readable medium include the following: an electrical connection (electronic) having one or more wires, a portable computer diskette (magnetic), a random access memory (RAM) (electronic), a read-only memory (ROM) (electronic), an erasable programmable read-only memory (EPROM or Flash memory) (electronic), an optical fiber (optical), and a portable compact disc read-only memory (CDROM) (optical). It is noted that the computer-readable medium may even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via for instance optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.

Finally, it should be emphasized that the above-described embodiments of the present invention are merely possible examples of implementations set forth for a clear understanding of the principles of the invention. Many variations and modifications may be made to the above-described embodiment(s) of the invention without departing substantially from the spirit and principles of the invention. All such modifications and variations are intended to be included herein within the scope of this disclosure and the invention, and protected by the following claims.

Claims

1. A computer program embodied in a computer readable medium for providing efficient space-time structures for preambles, pilots and data for multi-input, multi-output communications systems, the computer program comprising:

logic configured to provide an initial structure;

logic configured to verify that rows of said initial structure are linearly independent;

logic configured to apply an orthonormalization procedure to said initial structure to obtain a space-time structure for a preamble or pilot in a time or frequency domain; and

logic configured to insert the space-time structure as a preamble or pilot in the time or frequency domain with one or more data symbols for transmission in the multi-input, multi-output communications system.

2. The computer program of claim 1, wherein said logic configured to provide an initial structure comprises:

logic configured to choose a symbol alphabet to provide symbols for said initial structure; and

logic configured to choose an initial configuration of said initial structure.

3. The computer program of claim 1, further comprising:

logic configured to confirm that symbols of said space-time structure are within a predetermined distance of symbols of said initial structure;

logic configured to construct a space-time sequence structure from a plurality of said space-time structures; and

logic configured to verify that a peak-to-average power ratio of said space-time structure is less than a predetermined value.

4. The computer program of claim 3, wherein said logic configured to confirm chat the symbols of said space-time structure are within a predetermined distance of the symbols of said initial structure comprises logic configured to apply a Euclidean distance metric to determine the distance between the symbols of said space-time structure and the symbols of said initial structure.

5. The computer program of claim 1, wherein said logic configured to verify that the rows of said initial structure are linearly independent comprises logic configured to determine rank of said initial structure.

6. The computer program of claim 1, wherein said logic configured to apply an orthonormalization procedure to said initial structure to obtain a space-time structure comprises logic configured to apply a row-wise Gram-Schmidt procedure to said initial structure to obtain a space-time structure.

7. A non-transitory computer readable medium having instructions stored thereon, the instructions comprising:

instructions to produce a plurality of pilot symbols derived from at least one sequence, wherein the at least one sequence is a Frank-Zadoff or Chu sequence;

instructions to produce a plurality of data symbols;

instructions to provide a space time structure for transmission, wherein the space time structure includes a time dimension including a plurality of symbol time intervals and a space dimension including a plurality of antenna outputs; and

instructions to insert the plurality of pilot symbols and the plurality of data symbols into the space time structure for transmission in a multi-input, multi-output communications system, wherein the plurality of pilot symbols are inserted in the time and frequency domain for each antenna of the plurality of antenna outputs.

8. The computer readable medium of claim 7, wherein the multi-input, multi-output communications system is an orthogonal frequency division multiple access or single carrier frequency domain equalization communication system.

9. A method comprising:

producing a plurality of pilot symbols derived from at least one sequence, wherein the at least one sequence is a Frank-Zadoff or Chu sequence;

producing a plurality of data symbols;

providing a space time structure for transmission, wherein the space time structure includes a time dimension including a plurality of symbol time intervals and a space dimension including a plurality of antenna outputs; and

inserting the plurality of pilot symbols and the plurality of data symbols into the space time structure for transmission in a multi-input, multi-output communications system, wherein the plurality of pilot symbols are inserted in the time and frequency domain for each antenna of the plurality of antenna outputs.

10. The method of claim 9, wherein the multi-input, multi-output communications system is an orthogonal frequency division multiple access or single carrier frequency domain equalization communication system.

11. A multi-input, multi-output communications system comprising:

an encoder configured to:

produce a plurality of pilot symbols derived from at least one sequence, wherein the at least one sequence is a Frank-Zadoff or Chu sequence;

receive a plurality of data symbols;

provide a space time structure for transmission, wherein the space time structure includes a time dimension including a plurality of symbol time intervals and a space dimension including a plurality of antenna outputs; and

insert the plurality of pilot symbols and the plurality of data symbols into the space time structure, wherein the plurality of pilot symbols are inserted in the time and frequency domain for each antenna of the plurality of antennas; and

a plurality of modulators configured to receive an output of the encoder; and

a plurality of antennas configured to receive outputs of the plurality of modulators.

12. The system of claim 11, wherein the system is an orthogonal frequency division multiple access or single carrier frequency domain equalization communication system.

13. A multi-input, multi-output communications system comprising:

a plurality of antennas;

a plurality of demodulators configured to receive outputs from the plurality of antennas; and

a decoder configured to receive the output of the plurality of demodulators and further configured to:

recover data from a received space time structure, wherein the space time structure includes a time dimension including a plurality of symbol time intervals and a space dimension associated with the plurality of antennas; wherein a plurality of pilot symbols and a plurality of data symbols are inserted into the space time structure; wherein the pilot symbols are inserted in the time and frequency domain for each antenna of the plurality of antennas; wherein the pilot symbols are derived from at least one sequence; and wherein the at least one sequence is a Frank-Zadoff or Chu sequence.

14. The system of claim 13, wherein the system is an orthogonal frequency division multiple access or single carrier frequency domain equalization communication system.