Space-Time Coded Massive Multiple-Input Multiple-Output (MIMO) Wireless Systems and Methods of Making Using the Same

Abstract

Space-time coded massive (STCM) and space-frequency coded (SFC) massive multiple-input multiple-output (MIMO) wireless communication systems and methods of making and using the same are disclosed. The STCM-MIMO system utilizes two massive MIMO antenna arrays that transmit data over two or more channel vectors to a user with at least one receive antenna. This configuration permits the system to use the asymptotic orthogonal qualities of massive MIMO pre-coding to eliminate the interference from other users' channel vectors and signals. The system also maintains the diversity of space-time codes to recover lost data through treating each transmitting massive MIMO array similarly to a 21 Alamouti space-time code. The STCM-MIMO wireless system can significantly outperform those using space-time coding techniques only. The SFC massive MIMO wireless system may be similar to the STCM-MIMO wireless system, except for the encoder block. In the exemplary SFC massive MIMO architecture, instead of spreading the code across the time slots, the code is spread across the subcarriers.

Claims

1. A wireless communication system, comprising: an encoder configured to space-time or space-frequency encode data; N.sub.t transmitters, each having M/N.sub.t transmit antennas and being configured to transmit the space-time or space-frequency encoded data from the corresponding M/N.sub.t transmit antennas, where N.sub.t is an integer of at least 2, and M is an integer of at least 4; a receiver having N.sub.r receive antennas configured to receive the space-time or space-frequency encoded data, where N.sub.r is an integer of at least 1; and a decoder configured to decode the space-time or space-frequency encoded data from the receiver.

2. The wireless communication system of claim 1, wherein N.sub.t is an integer of at least 3, and M is an integer of at least 12.

3. The wireless communication system of claim 2, wherein N.sub.t is an integer of at least 4, and M is an integer of at least 100.

4. The wireless communication system of claim 1, wherein N.sub.r is an integer of at least 2.

5. The wireless communication system of claim 4, wherein the encoder encodes the data at a rate of 1 symbol or less per transmission time period.

6. The wireless communication system of claim 5, wherein the rate at which the encoder encodes the data is (N.sub.t1)/N.sub.t symbols or less per transmission time period.

7. The wireless communication system of claim 6, wherein N.sub.t is an integer of at least 3.

8. The wireless communication system of claim 7, wherein the encoder encodes the data as an N.sub.tN.sub.t matrix.

9. The wireless communication system of claim 8, wherein each of the M/N.sub.t transmit antennas transmits a corresponding and/or unique row of the data in or from the matrix.

10. The wireless communication system of claim 9, wherein the data comprises a sequence of symbols.

11. The wireless communication system of claim 10, wherein each of the symbols has at least 4 states.

12. The wireless communication system of claim 11, wherein each of the symbols has at least 16 states.

13. The wireless communication system of claim 1, wherein the encoder encodes the data at a rate of 1 symbol or less per transmission time period.

14. The wireless communication system of claim 1, wherein the data comprises a sequence of symbols.

15. A method of wirelessly communicating data, comprising: space-time or space-frequency encoding data; transmitting the space-time or space-frequency encoded data from N.sub.t transmitters, each having M/N.sub.t transmit antennas, where N.sub.t is an integer of at least 2, and M is an integer of at least 4; receiving the space-time or space-frequency encoded data at a receiver having N.sub.r receive antennas, where N.sub.r is an integer of at least 1; and decoding the space-time encoded data.

16. The method of claim 15, wherein N.sub.t is an integer of at least 3, M is an integer of at least 12, and N.sub.r is an integer of at least 2.

17. The method of claim 15, wherein the encoder encodes the data at a rate of 1 symbol or less per transmission time period.

18. The method of claim 15, wherein the data comprises a sequence of symbols, and each of the symbols has at least 4 states.

19. A method of making a wireless communication system, comprising: operably connecting N.sub.t transmitters to an encoder configured to space-time or space-frequency encode data, each of the N.sub.t transmitters having M/N.sub.t transmit antennas and being configured to transmit the space-time or space-frequency encoded data from the corresponding M/N.sub.t transmit antennas, where N.sub.t is an integer of at least 2, and M is an integer of at least 4; operably connecting a decoder configured to decode the space-time or space-frequency encoded data to a receiver having N.sub.r receive antennas configured to receive the space-time encoded data, where N.sub.r is an integer of at least 1; and configuring the N.sub.t transmitters and the receiver so that the N.sub.t transmitters wirelessly communicate the space-time or space-frequency encoded data to the receiver.

20. The method of claim 19, wherein N.sub.t is an integer of at least 3, M is an integer of at least 12, and N.sub.r is an integer of at least 2.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0034] FIG. 1 is a table showing an Alamouti space-time code in which two symbols are transmitted from two antennas at different times.

[0035] FIG. 2 is a wireless communication system using a 21 Alamouti model.

[0036] FIG. 3 is an exemplary massive multiple-input multiple-output (MIMO) wireless communication system.

[0037] FIG. 4 is an exemplary space-time coded massive MIMO wireless communication system with two transmitter arrays and one receiver in accordance with one or more embodiments of the present invention.

[0038] FIG. 5 is a generalized space-time coded wireless communication system with four transmitters and two receivers.

[0039] FIG. 6 is an exemplary space-time coded massive MIMO wireless communication system with two massive transmitter arrays and one receiver in accordance with one or more embodiments of the present invention.

[0040] FIG. 7 an exemplary space-time coded massive MIMO wireless communication system with four massive transmitter arrays and two receivers in accordance with one or more embodiments of the present invention.

[0041] FIG. 8 is a graph showing bit error rates (BERs) for space-time coded massive MIMO vs. Alamouti 21 systems, simulated for signals over a range of signal-to-noise ratios (SNRs).

[0042] FIG. 9 is a graph showing BERs for a space-time coded massive MIMO system with 100 transmit antennas per array at varying user densities, simulated for signals over a range of SNRs.

[0043] FIG. 10 is a graph showing BERs for a space-time coded massive MIMO system with 600 transmit antennas per array at varying user densities, simulated for signals over a range of SNRs.

[0044] FIG. 11 is a graph showing BERs for various space-time coded massive MIMO systems and a massive MIMO system each with 500 total transmitter antennas, simulated for signals over a range of SNRs.

[0045] FIG. 12 is a graph showing BER versus number of transmitter antennas for exemplary space-time coded massive MIMO systems and a massive MIMO system over a static SNR of 2 dB.

[0046] FIG. 13 is a diagram of an exemplary wideband space-time coded massive MIMO transmitter (e.g., base station) in accordance with one or more embodiments of the present invention.

[0047] FIG. 14 is a diagram of an exemplary wideband space-time coded massive MIMO receiver in accordance with one or more embodiments of the present invention.

DETAILED DESCRIPTION

[0048] Reference will now be made in detail to various embodiments of the invention, examples of which are illustrated in the accompanying drawings. While the invention will be described in conjunction with the following embodiments, it will be understood that the descriptions are not intended to limit the invention to these embodiments. On the contrary, the invention is intended to cover alternatives, modifications and equivalents that may be included within the spirit and scope of the invention as defined by the appended claims. Furthermore, in the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be readily apparent to one skilled in the art that the present invention may be practiced without these specific details. In other instances, well-known methods, procedures, components, and circuits have not been described in detail so as not to unnecessarily obscure aspects of the present invention.

[0049] The technical proposal(s) of embodiments of the present invention will be fully and clearly described in conjunction with the drawings in the following embodiments. It will be understood that the descriptions are not intended to limit the invention to these embodiments. Based on the described embodiments of the present invention, other embodiments can be obtained by one skilled in the art without creative contribution and are in the scope of legal protection given to the present invention.

[0050] Furthermore, all characteristics, measures or processes disclosed in this document, except characteristics and/or processes that are mutually exclusive, can be combined in any manner and in any combination possible. Any characteristic disclosed in the present specification, claims, Abstract and Figures can be replaced by other equivalent characteristics or characteristics with similar objectives, purposes and/or functions, unless specified otherwise.

[0051] Interference cancellation and communication channel reliability can be attained through space-time coding and by employing massive MIMO technology. Space-time coding permits the system to take advantage of symbol diversity, which allows the receiver to recover data by evaluating redundant transmitted symbols. For the problem of space-time coding schemes and efficient function with the interference from a large user density, massive MIMO techniques excel.

[0052] The current invention combines the advantages of space-time codes and massive MIMO systems and may be referred to as space-time coded massive (STCM) MIMO. The current invention benefits from the diversity feature of space-time codes and the interference cancellation capability of massive MIMO systems. The diversity of space-time codes is preserved by treating multiple arrays of massive MIMO transmit antenna elements, similarly to how a space-time code would treat individual transmit antennas. This arrangement allows an antenna array to transmit data over a channel vector to the receiver, while each additional antenna array does the same over other channel vectors.

[0053] When the number of transmit antennas are much larger than the number of receive antennas, the law of large numbers permits massive MIMO systems to treat the channels as being orthogonal, allowing for an approximate elimination the other signals' and channels' interference to the desired signal. This concept is combined in the present STCM-MIMO system as two separate massive MIMO systems working in tandem at a base station in order to eliminate the interference of the signals and channels not directed at the desired users. A wireless system employing the present STCM-MIMO technology may significantly outperform ones with only space-time coding techniques.

[0054] Space-Time Coded Massive MIMO

[0055] The present invention utilizes the diversity of space-time codes and the pre-coding of massive MIMO. This goal is accomplished with a base station with two arrays of M transmit antennas transmitting to users with one receive antenna. A model of this STCM-MIMO system is shown in FIG. 4.

[0056] The orthogonal channel vectors (e.g., channel vector 420a-b) eliminate most of the interference from other peripheral signals. With the massive MIMO portion of the system implemented, the Alamouti space-time matrix can be utilized (FIG. 1). The symbols, in the corresponding time block, are transmitted from the two massive MIMO arrays 412a-b in the space dimension of the matrix. The Alamouti space-time matrix permits the system to transmit multiple copies of the original signals in one or more subsequent time slots, allowing for signal diversity and clarity. Equation (6) may be applied to ideally exploit both the space-time coding and massive MIMO systems in the combined scheme:

[00004]$\begin{array}{cc}{\tilde{r}}_0=\tilde{r}\left(t\right)=w_0^H.Math.h_0.Math.s_0+w_1^H.Math.h_1.Math.s_1+\underset{j0}{\overset{K-1}{.Math.}}.Math.\left(w_{2.Math.j}^H.Math.h_0.Math.s_{2.Math.j}+w_{\left(2.Math.j+1\right)}^H.Math.h_1.Math.s_{\left(2.Math.j+1\right)}\right)+{\tilde{n}}_0.Math..Math.{\tilde{r}}_1=\tilde{r}\left(t+T\right)=.Math.-w_0^H.Math.h_0.Math.s_1^{}+w_1^H.Math.h_1.Math.s_0^{}+\underset{j0}{\overset{K-1}{.Math.}}.Math.\left(-w_{2.Math.j}^H.Math.h_0.Math.s_{\left(2.Math.j+1\right)}^{}+w_{\left(2.Math.j+1\right)}^H.Math.h_1.Math.s_{2.Math.j}^{}\right)+{\tilde{n}}_1& \left(6\right)\end{array}$

[0057] When the signals are received, they are now able to follow the linear combination of the Alamouti Code and take advantage of its diversity. The combined signals can be expressed as Equation (7):

{tilde over (s)}.sub.0=h.sub.0.sup.2{tilde over (r)}.sub.0+h.sub.1.sup.2{tilde over (r)}.sub.1*

{tilde over (s)}.sub.1=h.sub.1.sup.2{tilde over (r)}.sub.0+h.sub.0.sup.2{tilde over (r)}.sub.1*(7)

where {tilde over (s)}.sub.0 and {tilde over (s)}.sub.1 are then sent to the likelihood detector to estimate s.sub.0 and s.sub.1. In order to evaluate this system fairly, the power of the transmit signals in both STCM-MIMO and Alamouti scheme are normalized to one. This allows for the STCM-MIMO system to be evaluated at the same overall power that the Alamouti system radiates with two antennas.

[0058] Through this process, the signal undergoes the pre-coding techniques of a massive MIMO system, eliminating most of the interference from other users and other channels, and also undergoes the Alamouti space-time diversity scheme, allowing signals that were distorted by AWGN to be reevaluated and recovered from the redundancy of the space-time aspect of the system.

[0059] Generalized Space-Time Codes

[0060] A wireless communication system may be generalized to be configured with N.sub.t transmit antennas and N.sub.r receive antennas. Alamouti's space-time encoding may be expanded from a 22 encoder (e.g., FIG. 1) to a N.sub.tt space-time encoder that corresponds to the number of transmit antennas and the number of time slots used in the space-time code configuration. The generalized received signal takes into account the N.sub.t transmit antennas and N.sub.r receive antennas, and can be expressed in the following Equation (8):

[00005]$\begin{array}{cc}{r}_{t,p}=\underset{j=0}{\overset{N_t-1}{.Math.}}.Math.h_{p,j}.Math.x_{t,j}+n_{t,p}& \left(8\right)\end{array}$

where r.sub.t,p is the received signal at time t and receive antenna p, N.sub.t is the total number of transmit antennas, h.sub.p,j is the channel between receive antenna p and transmit antenna j, and n.sub.t,p is the AWGN. The signal x.sub.t,j is the specific symbol at time t from transmit antenna j corresponding to the X space-time coded matrix in Equation (9):

[00006]$\begin{array}{cc}X=\left(\begin{array}{cccc}{s}_0& s_1& \frac{s_2}{\sqrt{2}}& \frac{s_2}{\sqrt{2}}\\ -s_1^{}& s_0^{}& \frac{s_2}{\sqrt{2}}& -\frac{s_2}{\sqrt{2}}\\ \frac{s_2^{}}{\sqrt{2}}& \frac{s_2^{}}{\sqrt{2}}& \frac{\left(-s_0-s_0^{}+s_1-s_1^{}\right)}{2}& \frac{\left(-s_1-s_1^{}+s_0-s_0^{}\right)}{2}\\ \frac{s_2^{}}{\sqrt{2}}& -\frac{s_2^{}}{\sqrt{2}}& \frac{\left(s_1+s_1^{}+s_0-s_0^{}\right)}{2}& -\frac{\left(s_0+s_0^{}+s_1-s_1^{}\right)}{2}\end{array}\right)& \left(9\right)\end{array}$

[0061] The specific symbols x.sub.t,j, where j=1, 2, . . . , N.sub.t are transmitted simultaneously at time t from transmit antennas 1 through N.sub.t.

[0062] In the system 500 with four transmit antennas and two receive antennas shown in FIG. 5, the symbols are encoded from the space-time code matrix X at the transmitter 510. The matrix X shows three symbols being transmitted over four transmit antennas. This is to allow a higher data rate than the transmission of four symbols, due to the smaller amount of time blocks necessary to achieve orthogonality. This code has a rate of 3/4, derived from three symbols being transmitted through four time blocks.

[0063] Once the received signal is detected, a corresponding and/or appropriate 3/4 rate decoder in the receiver 530 estimates the transmitted signal. The appropriate decoding formulas, corresponding to the space-time code matrix X, can be expressed as Equation (10) below, where {tilde over (s)}.sub.0, {tilde over (s)}.sub.1, and {tilde over (s)}.sub.2 are the estimated signals of s.sub.0, s.sub.1, and s.sub.2 respectively. This code can be used to develop a STCM-MIMO structure with high-dimension MIMO configurations and space-time codes.

[00007]$\begin{array}{cc}{\tilde{s}}_0=\underset{j=0}{\overset{N_r-1}{.Math.}}.Math..Math.r_{0,j}.Math.h_{0,j}^{*}+\left(r_{1,j}\right)*h_{1,j}+\frac{\left(r_{3,j}-r_{2,j}\right).Math.\left(h_{2,j}^{*}-h_{3,j}^{*}\right)}{2}-\frac{\left(r_{2,j}+r_{3,j}\right)*\left(h_{2,j}+h_{3,j}\right)}{2}& \left(10.Math.a\right)\\ {\tilde{s}}_1=\underset{j=0}{\overset{N_r-1}{.Math.}}.Math..Math.r_{0,j}.Math.h_{1,j}^{*}-\left(r_{1,j}\right)*h_{0,j}+\frac{\left(r_{3,j}+r_{2,j}\right).Math.\left(h_{2,j}^{*}-h_{3,j}^{*}\right)}{2}+\frac{\left(-r_{2,j}+r_{3,j}\right)*\left(h_{2,j}+h_{3,j}\right)}{2}& \left(10.Math.b\right)\\ {\tilde{s}}_2=\underset{j=0}{\overset{N_r-1}{.Math.}}.Math..Math.\frac{\left(r_{0,j}+r_{1,j}\right).Math.\left(h_{2,j}^{*}\right)}{\sqrt{2}}+\frac{\left(r_{0,j}-r_{1,j}\right).Math.\left(h_{3,j}^{*}\right)}{\sqrt{2}}+\frac{\left(r_{2,j}\right)*\left(h_{0,j}+h_{1,j}\right)}{\sqrt{2}}+\frac{\left(r_{3,j}\right)*\left(h_{0,j}-h_{1,j}\right)}{\sqrt{2}}& \left(10.Math.c\right)\end{array}$

[0064] Generalized Space-Time Coded Massive MIMO

[0065] Even a relatively simple 2N1 STCM-MIMO system exploits the interference cancellation provided from the massive MIMO pre-coding. Each transmit antenna array, N.sub.t, has N transmit antennas, where N=M/N.sub.t antennas. FIG. 6 depicts a system 600 of a 2N1 STCM-MIMO system, where two symbols are transmitted from two transmitters 612a-b, each having a corresponding antenna array 615a-b. This system 600 utilizes a full-rate symbol encoding scheme with two transmit antenna arrays 615a-b and two time slots for transmission. The pre-coded symbols are transmitted across channel vectors 620a-b and the received signal at the receiver 630 can be expressed as Equation (11):

[00008]$\begin{array}{cc}{\tilde{r}}_0=\tilde{r}\left(t\right)=w_0^H.Math.h_0.Math.s_0+w_1^H.Math.h_1.Math.s_1+\underset{j0}{\overset{K-1}{.Math.}}.Math.\left(w_{2.Math.j}^H.Math.h_0.Math.s_{2.Math.j}+w_{\left(2.Math.j+1\right)}^H.Math.h_1.Math.s_{\left(2.Math.j+1\right)}\right)+{\tilde{n}}_0& \left(11.Math.a\right)\\ {\tilde{r}}_1=\tilde{r}\left(t+T\right)=-w_0^H.Math.h_0.Math.s_1^{*}+w_1^H.Math.h_1.Math.s_0^{*}+\underset{j0}{\overset{K-1}{.Math.}}.Math.\left(-w_{2.Math.j}^H.Math.h_0.Math.s_{\left(2.Math.j+1\right)}^{*}+w_{\left(2.Math.j+1\right)}^H.Math.h_1.Math.s_{2.Math.j}^{*}\right)+{\tilde{n}}_1& \left(11.Math.b\right)\end{array}$

where {tilde over (r)}.sub.0 is the received signal at time slot t, {tilde over (r)}.sub.1 is the received signal at time slot t+T, w.sub.j is the massive MIMO pre-coding parameter equal to (N.sub.t/M)h.sub.j, and K is the number of users with one receive antenna each.

[0066] A generalized STCM-MIMO system can be constructed where N.sub.t is dependent on the space-time encoder being used, and N.sub.r is dependent on the desired diversity for the system. In the case of the 3/4 rate encoder from space-time code X, there are four columns in the encoder (e.g., 710 [FIG. 7]) matrix, which correspond to N.sub.t=4 arrays of N=M/N.sub.t transmit antennas each, for a total of M transmit antennas for the system. The coded symbol from each column in matrix X are transmitted from the corresponding array of N=M/4 transmit antennas (e.g., 715a-d in FIG. 7) to the receiver (e.g., 730).

[0067] In a 4N1 configuration, the system includes one receive antenna. The system takes into account the diversity gain from four channel vectors being used from the four transmit antenna arrays to the one receive antenna. If greater diversity is required, more receive antennas can be utilized to create more channels from transmitter to receiver. In the case of a 4N2 system 700 as shown in FIG. 7, two receive antennas 725a-b are used, and the diversity of the system is evaluated over eight channel vectors 721a-722d from transmitter 710 to receiver 730.

[0068] Through combining Equation (8) and Equation (11), Equation (12) can be derived, which is generalized to use any encoding scheme desired for essentially any STCM-MIMO system:

[00009]$\begin{array}{cc}{r}_{t,p}^k=\underset{i=0}{\overset{n_t-1}{.Math.}}.Math.{\left(w_{p,i}^k\right)}^H.Math.h_{p,i}^k.Math.x_{t,i}^k+\underset{np}{\overset{N_r-1}{.Math.}}.Math.\underset{j=0}{\overset{N_t-1}{.Math.}}.Math.{\left(w_{n,j}^k\right)}^H.Math.h_{p,j}^k.Math.x_{t,j}^k+\underset{qp}{\overset{K-1}{.Math.}}.Math.\underset{v=0}{\overset{N_r-1}{.Math.}}.Math.\underset{l=0}{\overset{N_t-1}{.Math.}}.Math.{\left(w_{v,l}^q\right)}^H.Math.h_{p,l}^k.Math.x_{t,l}^q+{\tilde{n}}_{t,p}^k& \left(12\right)\end{array}$

where r.sup.k.sub.t,p is the received signal at time t at receive antenna p for user k, (w.sup.k.sub.p,i).sup.H is the pre-code vector parameter corresponding to the channel from transmit antenna i to receive antenna p, at user k, N.sub.t is the total number of transmit antenna arrays in the system, N.sub.r is the total number of receive antennas, K is the total number of users, and x.sup.k.sub.t,i is the specific symbol at time t from transmit antenna i for user k, which corresponds to the coded symbols of spacetime code X, and f.sup.k.sub.t,p is the AWGN.

[0069] The first term of Equation (12) is the desired part of the received signal in which the transmitted symbols are preserved. The second term of Equation (12) is the auto-interference of the system, stemming from each additional pre-coded vector parameter utilized to correspond to each additional receive antenna at the user. The third term of Equation (12) is the interference from the addition of other users. When M (the number of transmit antennas) is large, the second and third terms of this equation are essentially cancelled due to the interference cancelling properties of the massive MIMO portion of the system's configuration, leaving only the first term to be evaluated at the space-time decoder.

[0070] This configuration allows the STCM-MIMO system to utilize any combination of transmit antennas and receive antennas. The estimated signals can be found through the techniques where the space-time coded symbols used can be simply linearly decoded. For example, a 4N4 space-time encoder, such as X, can be used within this STCM-MIMO system. Using this 3/4 rate space-time encoder, the STCM-MIMO received signals can subsequently be decoded as seen in the 3/4 rate combiner shown in Equation (13):

[00010]$\begin{array}{cc}{\tilde{s}}_0=\underset{j=0}{\overset{N_r-1}{.Math.}}.Math..Math.r_{0,j}^k.Math.{.Math.h_{0,j}^k.Math.}^2+{\left(r_{1,j}^k\right)}^{*}.Math.{.Math.h_{1,j}^k.Math.}^2+\frac{\left(r_{3,j}^k-r_{2,j}^k\right).Math.\left({.Math.h_{2,j}^k.Math.}^2-{.Math.h_{3,j}^k.Math.}^2\right)}{2}-\frac{{\left(r_{2,j}^k+r_{3,j}^k\right)}^{*}.Math.\left({.Math.h_{2,j}^k.Math.}^2+{.Math.h_{3,j}^k.Math.}^2\right)}{2}& \left(13.Math.a\right)\\ {\tilde{s}}_1=\underset{j=0}{\overset{N_r-1}{.Math.}}.Math..Math.r_{0,j}^k.Math.{.Math.h_{1,j}^k.Math.}^2-{\left(r_{1,j}^k\right)}^{*}.Math.{.Math.h_{0,j}^k.Math.}^2+\frac{\left(r_{3,j}^k+r_{2,j}^k\right).Math.\left({.Math.h_{2,j}^k.Math.}^2-{.Math.h_{3,j}^k.Math.}^2\right)}{2}+\frac{{\left(-r_{2,j}^k+r_{3,j}^k\right)}^{*}.Math.\left({.Math.h_{2,j}^k.Math.}^2+{.Math.h_{3,j}^k.Math.}^2\right)}{2}& \left(13.Math.b\right)\\ {\tilde{s}}_2=\underset{j=0}{\overset{N_r-1}{.Math.}}.Math..Math.\frac{\left(r_{0,j}^k-r_{1,j}^k\right).Math.\left({.Math.h_{2,j}^k.Math.}^2\right)}{\sqrt{2}}+\frac{\left(r_{0,j}^k-r_{1,j}^k\right).Math.{.Math.h_{3,j}^k.Math.}^2}{\sqrt{2}}+\frac{{\left(r_{2,j}^k\right)}^{*}.Math.\left({.Math.h_{0,j}^k.Math.}^2+{.Math.h_{1,j}^k.Math.}^2\right)}{\sqrt{2}}+\frac{{\left(r_{3,j}^k\right)}^{*}.Math.\left({.Math.h_{0,j}^k.Math.}^2-{.Math.h_{1,j}^k.Math.}^2\right)}{\sqrt{2}}& \left(13.Math.c\right)\end{array}$

where {tilde over (s)}.sub.0, {tilde over (s)}.sub.1, and {tilde over (s)}.sub.2 are the estimated symbols of s.sub.0, s.sub.1, and s.sub.2, respectively. Here the system is taking advantage of the space-time code's diversity, while already having benefited from the interference cancellation due to the massive MIMO linear pre-coding.

[0071] FIG. 7 shows a 4N2 STCM-MIMO system 700, where each antenna array 715a-d includes N=M/4 (three) transmit antennas of the total of M (12) transmit antennas. Three symbols, s.sub.0, s.sub.1, and s.sub.2 are encoded and then transmitted from the four transmit antenna arrays 715a-d across eight channel arrays 721a-d and 722a-d, using the 3/4 rate space-time encoding from X. Generally, the transmitted symbol from the corresponding transmit antenna array is pre-coded with a sum of N.sub.r pre-code vector parameters, due to unique qualities of each channel from that transmit antenna array to each of the receive antennas 725a-b. In the case of FIG. 7, two pre-code vector parameters are used at each array to correspond to the two wireless channels created from each transmit antenna array 715a-d to the two receive antennas 725a-b. Without the sum of the corresponding pre-code vector parameters, the transmit symbol may be lost at one or more of the receive antennas (e.g., at antenna 725b) due to the interference cancellation property of the system, in which case no additional diversity would be achieved from the additional receive antenna.

[0072] Computer Experiment Results

[0073] The graph 800 in FIG. 8 demonstrates the bit error rate (BER) efficiency of a STCM-MIMO system exemplifying the system 400 of FIG. 4 in comparison to a system using the Alamouti space-time code only. The STCM-MIMO system (line 810) utilizes two massive MIMO transmit antenna arrays of 100 antennas each (M=200) and a user with one receive antenna, while the system using Alamouti space-time code only (line 820) uses the 21 transmit antenna-receive antenna configuration. Otherwise, the two systems are identical. The simulations of the STCM-MIMO and Alamouti systems also take into account the interference of two other users by introducing the interfering users' signals and channels to the individual simulations. This is done to demonstrate the interference-canceling abilities of the massive MIMO portion of the present system, and to maintain equal conditions for both simulations.

[0074] Both the STCM-MIMO and Alamouti code systems are similar in the signal combining and signal estimation processes at the receiver, and both have their signal power normalized. In the simulations, Rayleigh fading wireless channels and AWGN are assumed and considered. The STCM-MIMO system simulation performed with significantly improved efficiency over the Alamouti 21 system simulation. The STCM-MIMO system simulation reaches a BER of 10.sup.3 at a signal to noise ratio (SNR) of 4 dB, which is 4 dB better than the Alamouti system simulation, which reached a BER of 10.sup.3 at an SNR of 8 dB. As the SNR becomes higher, the STCM-MIMO system simulation produces a BER of 10.sup.4 at an SNR of 5 dB, whereas the Alamouti system simulation reaches a BER of 10.sup.4 at an SNR of 11 dB, a 6 dB difference.

[0075] The graph 900 in FIG. 9 demonstrates the effect that increased user density has on the STCM-MIMO system. In the simulation, 100 transmitting antennas per array are utilized to evaluate 5 users (line 910), 10 users (line 920), and 20 users (line 930). As the ratio of transmit antennas to number of users gets smaller, the interference becomes more noticeable and can affect the clarity of the signal to the desired user.

[0076] The simulation results in FIG. 9 demonstrate that at 100 transmit antennas and 5 users (line 910), the BER approaches 10.sup.5 at an SNR of 8 dB, but appears to level out where it converges with the value of the interference of the five users. At 10 users (line 920), the BER converges to 10.sup.3 at an SNR of 8 dB, and at 20 users (line 930), the BER converges at 10.sup.2 at an approximate SNR of 6 dB. This BER convergence can be reduced to much smaller values for increased reliability performance by introducing more transmit antennas.

[0077] The graph 1000 in FIG. 10 demonstrates the STCM-MIMO system performance with 5 users (line 1010), 10 (line 1020), and 20 users (1025), but with 600 transmit antennas per antenna array. The BER convergence is significantly smaller, and the reliability is not nearly as affected as it is in the simulation in FIG. 9. The simulation produced a BER of nearly 10.sup.5 at an SNR of 5 dB with 5 users (line 1010), which performed only 0.5 dB better than when the interference of 10 users (line 1020) is simulated. When 20 users (line 1025) are simulated, the BER of 10.sup.5 was reached at an SNR of 7 dB, approximately 2 dB worse than five users. FIG. 10 shows that by adding additional transmit antennas, the signal remains very reliable for a growing user density.

[0078] The results as described with respect to FIGS. 8-10 show that the current invention performs more efficiently than either the Alamouti coding scheme or a massive MIMO system alone. Space-time codes provide transmit diversity, which allow the signal an opportunity to retain or recover the data if a symbol is lost during transmission. Massive MIMO systems enable a spectrum-efficient multi-user wireless communication system. By combining space-time coding techniques with a massive MIMO system, space-time coded massive MIMO systems offer the benefits of both technologies.

[0079] The graph 1100 in FIG. 11 demonstrates STCM-MIMO systems with 4N1 (line 1125), 4N2 (line 1120), and 4N4 (line 1115) antenna configurations while utilizing the 3/4 rate space-time encoding, in comparison to a space-time coded-only system and to a massive MIMO system (line 1130) of M (i.e., 4) transmit antennas and one receive antenna. Both the STCM-MIMO and the massive MIMO system simulations have a base station that includes M=500 total transmit antennas, each normalized in power to be equal to the four transmit antennas of the space-time coded configurations. Each simulation also considers the interference created by having three users in each scheme.

[0080] The 4N1 STCM-MIMO configuration (line 1125) reached a BER of 10.sup.5 at an SNR of 4 dB, performing 2.5 dB better than the massive MIMO system simulation (line 1130), which has a BER of 10.sup.5 at an SNR of 6.5 dB. While the 4N2 STCM-MIMO configuration (line 1120) reached a BER of 10.sup.5 at an SNR of 3 dB, performing 1 dB better than the 4N1 STCM-MIMO system simulation (line 1125), and 3.5 dB better than the massive MIMO system simulation (line 1130). Ultimately, the 4N4 STCM-MIMO system simulation (line 1115) reached a BER of 10.sup.5 at an SNR of 1.5 dB, which performed 1.5 dB better than the 4N2 STCM-MIMO system simulation (line 1120), 2.5 dB better than the 4N1 STCM-MIMO system simulation (line 1125), and 5 dB better than the massive MIMO simulation (line 1130).

[0081] The graph 1200 in FIG. 12 demonstrates the systems' BER as M transmit antennas increases for a 4N4 (line 1215), a 4N2 (line 1220) STCM-MIMO system, and a traditional massive MIMO system (line 1225). The static SNR in this simulation was set to 2 dB to observe the BER trends of the three different configurations. Similar to FIG. 11, the simulations of FIG. 12 also have normalized overall system power, and three users are considered for each system to introduce interference so the interference cancelling properties of the massive MIMO portion of the systems can be utilized.

[0082] The massive MIMO simulation (line 1225) did not vary significantly with additional antennas at an SNR of 2 dB, due to the system's lack of diversity gain, so it stayed consistent at a BER of about 10.sup.1. The 4N2 STCM-MIMO configuration (line 1220) shows great improvement in BER from 10.sup.1 to 10.sup.4 as the total number of transmit antennas for the system increased to 400. The 4N4 STCM-MIMO configuration (line 1215) demonstrates a more rapid improvement of the system as the number of transmit antennas increases. The simulation shows that the 4N4 STCM-MIMO system (line 1215) improves its BER from 10.sup.0.5 to 10.sup.5.5 as the total number of transmit antennas for the system increased to 400 antennas. It shows improvement over both other configurations when the total number of transmit antennas for the system is as small as 50.

[0083] From these simulations, it is clear that when M>>(N.sub.tN.sub.r), the systems are able to take advantage of both the diversity provided by the space time codes and the interference cancellation of the massive MIMO technique. When N.sub.t=4 and M=500, the total number of transmit antennas for each transmit antenna array in the system is N=125, which remains sufficient to maintain the diversity and interference cancellation for all STCM-MIMO systems in the computer simulation. As N.sub.r receive antennas increases, so does the number of pre-coding vector parameters that are needed at the transmitter. The number of pre-coding vector parameters is equal to N.sub.r. The system then creates auto-interference while transmitting across its multiple channels due to a need to assess the redundant pre-coding parameter coefficients to ensure that diversity is preserved throughout the system. The system also experiences interference from the signals over N.sub.tN.sub.r number of channels from each other user. FIGS. 11 and 12 demonstrate that when M>>(N.sub.tN.sub.r), then the STCM-MIMO system cancels additional interference and still retains the diversity provided by the space-time coding.

[0084] The generalized STCM-MIMO system performs more efficiently than a corresponding massive MIMO system alone. Generalized STCM-MIMO systems take advantage of generalized space-time coding techniques to obtain diversity of the system, while maintaining the interference cancelling properties provided by massive MIMO antenna arrays. For STCM-MIMO systems with large N.sub.t and large N.sub.r, where M is much larger than N.sub.tN.sub.r the system maintains both diversity gain and interference cancellation capability.

[0085] Wideband Space-Time Block Coded Massive MIMO

[0086] A general block diagram of an exemplary transmitter 1300 for a wideband space-time coded massive MIMO system is shown in FIG. 13, where the base station (BS) with an antenna array 1310 of size M is configured to transmit data to K users over multipath wireless channels. The system can include one to N.sub.r receiver antennas (see FIG. 14 and the discussion thereof below). All users are served over the same time, code and frequency resources.

[0087] An Exemplary Wideband STBC Massive MIMO Transmitter

[0088] The number of digital decoders and the subarrays in the transmitter 1300 depends on the space dimension of the space-time block that the system uses. For simplicity, a 22 Alamouti space-time block code is used in the exemplary system. Hence, the number of digital precoders 1320a-b and subarrays 1312, 1314 in the BS 1300 is two, and each subarray 1312, 1314 has M/2 antennas (where M is, e.g., an integer of at least 4, 8, 16, or any other integer greater than 4). The first antenna subarray 1312 comprises antenna elements 1313a-n. The second antenna subarray comprises antenna elements 1315a-n.

[0089] As shown in FIG. 13, the two data vectors to be transmitted to a user k, denoted by X.sup.k.sub.1 and X.sup.k.sub.2, are sent to the space-time encoder UE.sub.k 1330k. Similarly, the two data vectors to be transmitted to a first user, denoted by X.sup.1.sub.1 and X.sup.1.sub.2, are sent to the space-time encoder UE.sub.1 1330a. Each of the data vectors (e.g., X.sup.k.sub.1 and X.sup.k.sub.2) contains N symbols (where N is an integer of at least 2) that are generated by a digital modulation technique, such as QAM or PSK, or their higher constellation sizes. These data vectors can be given as:

X.sub.1.sup.k=[X.sub.1.sup.k(1),X.sub.1.sup.k(2), . . . ,X.sub.1.sup.k(N)]

X.sub.2.sup.k=[X.sub.2.sup.k(1),X.sub.2.sup.k(2), . . . ,X.sub.2.sup.k(N)]

where N is the size of the N-point inverse fast Fourier transform (IFFT) and fast Fourier transform (FFT) functions, or the number of the subcarriers that the system uses in the frequency domain. The output of the space-time coder for each user k is:

[00011]$\left[\begin{array}{cc}-X_2^k& X_1^k\\ -X_1^k& {X.Math.}_2^k\end{array}\right]$

where the number of columns indicate the number of time slots of the code that the system uses, which is 2 in the present example. A similar output is generated for the first user and any users between the first and k.sup.th users. The first and second rows of the matrix code for each user k{1, 2, . . . , K} is, respectively, supplied to the first and second massive MIMO digital precoders 1320a-b. The precoders 1320a-b use the following coefficient vector for user k to encode its data:

W.sup.k=[W.sup.k(1),W.sup.k(2), . . . ,W.sup.k(N)].sup.T

where W.sup.k(n)C.sup.M1. When the input of a precoder is {X.sup.1.sub.t, X.sup.2.sub.t, . . . X.sup.K.sub.t}, its output U.sub.t=[U.sub.t,1, U.sub.t,2, . . . , U.sub.t,M].sup.TC.sup.MN becomes:

[00012]$U_t=\{\left(\underset{\underset{\mathrm{subcarrier}.Math..Math.1}{}}{\left[\begin{array}{c}{w}_1^1\left(1\right)\\ \mathrm{.Math.}\\ w_M^1\left(1\right)\end{array}\right].Math.X_t^1\left(1\right)+\mathrm{.Math.}.Math.+\left[\begin{array}{c}{w}_1^K\left(1\right)\\ \mathrm{.Math.}\\ w_M^K\left(1\right)\end{array}\right].Math.X_t^K\left(1\right)}\right),\mathrm{.Math.}.Math.,.Math.(\underset{\underset{\mathrm{subcarrier}.Math..Math.N}{}}{\left[\begin{array}{c}{w}_1^1\left(N\right)\\ \mathrm{.Math.}\\ w_M^1\left(N\right)\end{array}\right].Math.X_t^1\left(N\right)+\mathrm{.Math.}+.Math.\left(\left[\begin{array}{c}{w}_1^K\left(N\right)\\ \mathrm{.Math.}\\ w_M^K\left(N\right)\end{array}\right].Math.X_t^K\left(N\right)\right)\}}$

[0090] Therefore, the m.sup.th output line of the precoder generate vector U.sub.t,M=[U.sub.t,m(1), U.sub.t,m(2), . . . , U.sub.t,m(N)] where its n.sup.th entry U.sub.t,m(n) is determined or computed as follows:

U.sub.t,m(n)=w.sub.m.sup.1(1)X.sub.t.sup.1(n)+w.sub.m.sup.2(n)X.sub.t.sup.2(n)+ . . . +w.sub.m.sup.K(n)X.sub.t.sup.K(n)

[0091] Each output line of the precoders 1320a-b is connected to an IFFT processing block 1340a-n, 1345a-n. Each of the IFFT processing blocks 1340a-n, 1345a-n converts the signal from the frequency domain to the time domain. When the input vector U.sub.t,m is fed to the m.sup.th IFFT 1345n, it produces the time domain signal S.sub.t,m=F.sup.1(U.sub.t,m)C.sup.1N, where

S.sub.t,m=[S.sub.t,m(1),S.sub.t,m(2), . . . ,S.sub.t,m(N)]

[0092] As shown in FIG. 13, the transmitter 1300 then adds a cyclic prefix or other data/information block isolator at 1350a-n, 1355a-n to the output of each (e.g., m.sup.th) data/information block from the IFFT processor 1340a-n, 1345a-n, and sends it over wireless channels using the corresponding (e.g., m.sup.th) antenna element 1313a-n, 1315a-n. For example, a cyclic prefix may isolate different blocks of data or information (e.g., OFDM data) from each other when the wireless channel contains multiple paths. It may be an exact copy of the last part of an OFDM symbol (e.g., in the block) and may function as a guard interval to protect the OFDM signals (e.g., in the block) from inter-symbol interference.

[0093] The transmitter 1300, including the space-time encoders 1330a-k, the digital precoders 1320a-b, the IFFT blocks 1340a-n, 1345a-n, and the cyclic prefix adder blocks 1350a-n, 1355a-n, can be implemented in a digital signal processor, a field-programmable gate array (FPGA) or an application-specific integrated circuit (ASIC), such as a SNAPDRAGON system-on-chip (SOC) ASIC/processor (available from Qualcomm Inc., San Diego, Calif.), or a SPARTAN-3 FPGA (available from Xilinx Inc., San Jose, Calif.).

[0094] An Exemplary Wideband STBC Massive MIMO Receiver

[0095] A block diagram of an exemplary wideband space-time coded massive MIMO receiver 1400 is shown in FIG. 14. For simplicity, we assume that each user has one of the receive antennas 1410a-k. Consider the following baseband channel impulse response (CIR) vector between a transmit antenna (e.g., 1315n) and user k:

[00013]$h_{k,m}\left(t\right)=\underset{l=1}{\overset{L}{.Math.}}.Math.h_{k,m}\left(l\right).Math.\left(t-{}_l\right)$

where L is the CIR length, .sub.l denotes the l.sup.th tap delay of the channel, and (x) is the Dirac delta function (i.e., (x)=1 when x=0, and (x)=0 otherwise). Dropping the time index t, the CIR between the transmit antenna (e.g., 1315n) and the user k in a vector form can be represented as:

h.sub.k,m=[h.sub.k,m(1),h.sub.k,m(2), . . . ,h.sub.k,m(L)]

where h.sub.k,m(l) denotes the complex gain of the l.sup.th tap.

[0096] The received signal vector of user k (i.e., EU.sub.k) for the p.sup.th transmitted orthogonal frequency-division multiplexing (OFDM) symbol can be expressed as:

y.sub.p.sup.k=h.sub.k,1*S.sub.p,1+h.sub.k,2*S.sub.p,2+ . . . +h.sub.k,M*S.sub.p,M

where * is the convolution operator. As is known in the art, OFDM signals may include a number of closely-spaced, modulated carriers. In vector form:

y.sub.p.sup.k=[y.sub.p.sup.k(1),y.sub.p.sup.k(2), . . . ,y.sub.p.sup.k(N+L1)].sup.T

Each of the n.sup.th elements of the received signal vector y.sup.k.sub.p at time i can be computed using:

[00014]$y_p^k\left[i\right]=\underset{m=.Math.1}{\overset{M}{.Math.}}.Math.\underset{=1}{\overset{L}{.Math.}}.Math.h_{k,m}\left(\right).Math.S_{p,m}\left(i-\right)+n_k\left(i\right).Math..Math.\mathrm{and}.Math..Math.i=1,\mathrm{.Math.}.Math.,N$

where n.sub.k(i) is the additive white noise. After removing the cyclic prefix at 1420a-k, the received signal y.sup.k.sub.p can be written in matrix form as:

[00015]$y_p^k=\left[\begin{array}{c}{y}_p^k\left(1\right)\\ \mathrm{.Math.}\\ y_p^k\left(N\right)\end{array}\right]=\left[\mathrm{cir}\left(h_k,1\right)\right][.Math.\begin{array}{c}{S}_{p,1}\left(1\right)\\ \mathrm{.Math.}\\ s_{p,1}\left(N\right)\end{array}]+\left[\mathrm{cir}\left(h_{k,2}\right)\right][.Math.\begin{array}{c}{S}_{p,2}\left(1\right)\\ \mathrm{.Math.}\\ s_{p,2}\left(N\right)\end{array}]+\left[\mathrm{cir}\left(h_{k,M}\right)\right][.Math.\begin{array}{c}{S}_{p,M}\left(1\right)\\ \mathrm{.Math.}\\ s_{p,M}\left(N\right)\end{array}]+n_p^k$

where cir(h.sub.k,m) is a function that creates a circulant matrix of size NN from the channel vector h.sub.k,m and n.sup.k.sub.pC.sup.N1 represents the complex additive white noise vector. As shown in FIG. 14, each user k then takes the FFT of each y.sup.k.sub.p vector for p=1, 2 in the FFT processing blocks 1430a-k to convert the signal from the time domain to the frequency domain and obtain:

Y.sub.p.sup.k=(y.sub.p.sup.k)=H.sub.1.sup.kU.sub.p,1+H.sub.2.sup.kU.sub.p,2+ . . . +H.sub.M.sup.kU.sub.p,M+N.sub.p.sup.k(14)

where N.sup.k.sub.p=F(n.sup.k.sub.p) and H.sup.k.sub.m is a diagonal matrix with diagonal entries of [H.sup.k.sub.m(1), H.sup.k.sub.m(2), H.sup.k.sub.m(N)] that is obtained from the following relation:

H.sub.m.sup.k=(cir(h.sub.k,m))

[0097] By expanding equation (14), we obtain:

[00016]$Y_p^k=\left[\begin{array}{c}{Y}_p^k\left(1\right)\\ \mathrm{.Math.}\\ Y_p^k\left(N\right)\end{array}\right]=\left[H_1^k\right]\left[\begin{array}{c}{U}_{p,1}\left(1\right)\\ \mathrm{.Math.}\\ U_{p,1}\left(N\right)\end{array}\right]+\mathrm{.Math.}+\left[H_M^k\right]\left[\begin{array}{c}{U}_{p,M}\left(1\right)\\ \mathrm{.Math.}\\ U_{p,M}\left(N\right)\end{array}\right]+N_p^k$

[0098] Using the asymptotical orthogonality property of the channels in the frequency domain when M.fwdarw., we arrive at H.sup.k.sub.m(n)*H.sup.k.sub.r(n)=H.sup.k.sub.m(n) when m=r, and zero otherwise. When the precoder coefficient is:

[00017]$w_m^k\left(n\right)=\frac{{\left(H_m^k\left(n\right)\right)}^{*}}{M.Math..Math.H_m^k\left(n\right).Math.}$

and use the asymptotical orthogonality property of the channel vector from Equation (14), when p=t, we obtain:

[00018]$Y_t^k=\left[\begin{array}{c}{Y}_t^k\left(1\right)\\ Y_t^k\left(2\right)\\ \mathrm{.Math.}\\ Y_t^k\left(N\right)\end{array}\right]=\left[\begin{array}{c}{X}_1^k\left(1\right)\\ X_1^k\left(2\right)\\ \mathrm{.Math.}\\ X_1^k\left(N\right)\end{array}\right]+\left[\begin{array}{c}{X}_2^k\left(1\right)\\ X_2^k\left(2\right)\\ \mathrm{.Math.}\\ X_2^k\left(N\right)\end{array}\right]+\left[\begin{array}{c}{N}_t^k\left(1\right)\\ N_t^k\left(2\right)\\ \mathrm{.Math.}\\ N_t^k\left(N\right)\end{array}\right]$

and when p=t+T, we obtain:

[00019]$Y_{t+T}^k=\left[\begin{array}{c}{Y}_{t+T}^k\left(1\right)\\ Y_{t+T}^k\left(2\right)\\ \mathrm{.Math.}\\ y_{t+T}^k\left(N\right)\end{array}\right]=\left[\begin{array}{c}-X_1^{k^{*}}\left(1\right)\\ -X_1^{k^{*}}\left(2\right)\\ \mathrm{.Math.}\\ -X_1^{k^{*}}\left(N\right)\end{array}\right]+\left[\begin{array}{c}{X}_2^{k^{*}}\left(1\right)\\ X_2^{k^{*}}\left(2\right)\\ \mathrm{.Math.}\\ X_2^{k^{*}}\left(N\right)\end{array}\right]+\left[\begin{array}{c}{N}_{t+T}^k\left(1\right)\\ N_{t+T}^k\left(2\right)\\ \mathrm{.Math.}\\ N_{t+T}^k\left(N\right)\end{array}\right]$

The STBC decoder shown in FIG. 14 uses the above two equations to estimate {X.sup.k.sub.1(n), X.sup.k.sub.2(n)} for k{1, 2, . . . , K} and n{1, 2, . . . , N} as follows:

[00020]$.Math.\{\begin{array}{c}{\tilde{X}}_1^k\left(n\right)=Y_t^k\left(n\right)-Y_{t+T}^{k^{*}}\left(n\right)\\ {\tilde{X}}_2^k\left(n\right)=Y_t^k\left(n\right)+Y_{t+T}^{k^{*}}\left(n\right)\end{array}$

[0099] The receiver 1400 (i.e., the cyclic prefix removal blocks 1420a-k, the FFT blocks 1430a-k, and space-time decoders 1440a-k), can also be implemented in a digital signal processor, an FPGA or an ASIC similarly to, but separate from, the transmitter 1300. The present massive MIMO systems can be used to process and communicate data/information in present- and future-generation wireless communication systems. These function blocks in the figures may be implemented in hardware, firmware and/or software. The present systems may be included with other communication function blocks in larger wireless communication systems and/or protocols (e.g., for 4G, 5G, 6G and LTE/LTE-A cellular systems and/or cellular towers).

[0100] An Exemplary Wideband Space-Frequency Coded Massive MIMO System and Method

[0101] The architecture of an exemplary wideband space-frequency coded (SFC) massive MIMO system is similar to that of the wideband STBC massive MIMO system described above with regard to FIGS. 13-14, except for the space-time processing (i.e., the space-time encoders 1330a-1330k). In the exemplary SFC massive MIMO architecture, instead of spreading the code across the time slots, the code is spread across the OFDM subcarriers (subchannels).

[0102] For simplicity, consider the SFC with a 22 Alamouti block and two transmit antenna subarrays (e.g., as shown in FIG. 13). For each user k, the SFC encoder takes in one OFDM symbol X.sup.k.sub.p=[X.sup.k.sub.p(1), X.sup.k.sub.p(2), . . . , X.sup.k.sub.p(N)] and starts the coding process by picking up the first two consecutive symbols X.sup.k.sub.p(1) and X.sup.k.sub.p(2) and creating the first Alamouti block code as:

[00021]$\left[\begin{array}{cc}-X_p^{k^{*}}\left(2\right)& X_p^k\left(1\right)\\ -X_p^{k^{*}}\left(1\right)& X_p^k\left(2\right)\end{array}\right]$

[0103] Repeating this process for the rest of the symbols of X.sup.k.sub.p, assuming that N is even, the SFC encoder produces two OFDM symbols of size N for each user k. Those symbols can be represented by:

X.sub.p,1.sup.k=[X.sub.p.sup.k(1),X.sub.p.sup.k*(2),X.sub.p.sup.k(3),X.sub.p.sup.k*(4), . . . ,X.sub.p.sup.k(N1),X.sub.p.sup.k*(N)]

X.sub.p,2.sup.k=[X.sub.p.sup.k*(1),X.sub.p.sup.k(2),X.sub.p.sup.k*(3),X.sub.p.sup.k(4), . . . ,X.sub.p.sup.k*(N1),X.sub.p.sup.k*(N)]

[0104] The system then sends the first OFDM symbol for all users (i.e., X.sup.k.sub.p,1, k{1, 2, . . . , K} to the first digital precoder 1320a and the second OFDM symbol X.sup.k.sub.p,2 to the second digital precoder 1320b. The remainder of the system and process is similar to that of the wideband STBC massive MIMO system and method described above. The main advantage of this method is that the user equipment can detect the data immediately after receiving each OFDM symbol. In the Universal Mobile Telecommunications System, user equipment refers to any device used directly by an end-user to communicate. In GSM systems, user equipment corresponds to a mobile station. In wideband STBC massive MIMO systems, the user equipment typically receives multiple OFDM symbols (depending on the time dimension of the block code) before detecting the data. The SFC massive MIMO system and method can be restructured to transmit MT SFC codes.

CONCLUSION/SUMMARY

[0105] The foregoing descriptions of specific embodiments of the present invention have been presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed, and obviously many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and its practical application, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the Claims appended hereto and their equivalents.