TRANSMIT DIVERSITY FROM ORTHOGONAL DESIGN FOR FBMC/OQAM

Abstract

How to apply an Alamouti like space-time coding (or transmit diversity) to a Filter Bank Multicarrier (FBMC) transmission using Offset QAM (OQAM). In FBMC, due to the orthogonality in the real domain only, an intrinsic interference results thereof for the imaginary component. Simply adapting the Alamouti scheme to FBMC OQAM is not obvious since the intrinsic interference terms are not equivalent at each antenna since it depends on the surrounding symbols. The application proposes to choose contiguous precoding symbols such that a virtual PAM Alamouti scheme is achieved. Code rates of 1/2 or 2/3 are achieved depending on the number of precoding symbols needed per antenna.

Claims

1. A method for transmitting a multicarrier signal using a transmit diversity technique with a plurality of transmit antennas (Tx1, Tx2), wherein said signal is of the offset quadrature amplitude modulation, OQAM, type comprising symbols in the time-frequency space, wherein the symbols include a data containing symbol (a) and a precoding symbol (x), and wherein the precoding symbol (x) is selected such that intrinsic interference (I) at the data containing symbol (a), when received by a receiver, is forced to a value which ensures an applied orthogonal space-time or space-frequency code.

2. The method for transmitting of claim 1, wherein said symbols are formed by modulating a real-valued symbol and the intrinsic interference corresponds to the imaginary part of the demodulated signal at said receiver, or said symbols are formed by modulating an imaginary valued symbol and the intrinsic interference corresponds to the real-valued part of the demodulated signal at said receiver.

3. The method for transmitting of claim 1, wherein the selecting of the precoding symbol is performed by forcing the intrinsic interference, when received by the receiver, to be zero.

4. The method for transmitting according to claim 1, wherein one precoding symbol is used for each transmitted symbol to cancel out the composite intrinsic interference through transmission of the same PAM symbol by the two antennas, when received by a receiver, to be zero.

5. The method for transmitting of claim 1, wherein there are transmitted real-valued PAM symbols a.sub.1 and a.sub.2 are transmitted using the two resources (m.sub.0,n.sub.0) and (m.sub.0+1,n.sub.0) from the transmit antenna Tx1, wherein from transmit antenna Tx2, these PAM symbols a.sub.1 and a.sub.2 are transmitted with and respectively without taking its minus by using the same two resources but now the used resources for a.sub.1 and a.sub.2 are exchanged so that the receive signals for the subcarriers m.sub.0 and m.sub.0+1 read as $\begin{array}{cc}.Math.y_{m_0,n_0}=H^{\left(1\right)}\left(a_1+j.Math..Math.\stackrel{\stackrel{.fwdarw..Math.0}{}}{I_{m_0,n_0}^{\left(1\right)}}\right)-H^{\left(2\right)}\left(a_2-j.Math..Math.\stackrel{\stackrel{.fwdarw..Math.0}{}}{I_{m_0,n_0}^{\left(2\right)}}\right)+{}_{m_0,n_0}.Math..Math.y_{m_0+1,n_0}=H^{\left(1\right)}\left(a_2+j.Math..Math.\stackrel{\stackrel{.fwdarw..Math.0}{}}{I_{m_{0+1},n_0}^{\left(1\right)}}\right)+H^{\left(2\right)}\left(a_1+j.Math..Math.\stackrel{\stackrel{.fwdarw..Math.0}{}}{I_{m_0+1,n_0}^{\left(2\right)}}\right)+{}_{m_0+1,n_0}& \left(13\right)\end{array}$ wherein y.sub.m.sub.0.sub.,n.sub.0 is the received signal at the resource at (m.sub.0,n.sub.0) in the time-frequency domain, .sub.m.sub.0.sub.,n.sub.0 is AWGN and I.sub.m.sub.0.sub.,n.sub.0.sup.(1) and I.sub.m.sub.0.sub.,n.sub.0.sup.(2) being the intrinsic interference from the first and the second antenna at resource (m.sub.0,n.sub.0) respectively, and wherein precoding symbols x.sub.1,x.sub.2,x.sub.3,x.sub.4 are chosen to cancel (zero) the intrinsic interference individually for each antenna by the symbols x.sub.1,x.sub.2 being chosen to cancel the intrinsic interferences I.sub.m.sub.0.sub.,n.sub.0.sup.(1) I.sub.m.sub.0.sub.+1,n.sub.0.sup.(1) of the first antenna and by x.sub.3,x.sub.4 being chosen to cancel the intrinsic interferences I.sub.m.sub.0.sub.,n.sub.0.sup.(2) I.sub.m.sub.0.sub.+1,n.sub.0.sup.(2) of the second antenna.

6. The method for transmitting according to claim 1, wherein the selecting of the precoding symbol is performed by forcing the intrinsic interference, when received by a receiver, to be a smaller than a predefined non-zero value.

7. The method for transmitting of claim 1, wherein there are transmitted real-valued PAM symbols a.sub.1 and a.sub.2 are transmitted using the two resources (m.sub.0,n.sub.0) and (m.sub.0+1,n.sub.0) from the transmit antenna Tx1, wherein from transmit antenna Tx2, these PAM symbols a.sub.1 and a.sub.2 are transmitted with and respectively without taking its minus by using the same two resources but now the used resources for a.sub.1 and a.sub.2 are exchanged so that the receive signals for the subcarriers m.sub.0 and m.sub.0+1 read as $\begin{array}{c}\begin{array}{c}{y}_{m_0,n_0}=.Math.H^{\left(1\right)}.Math.\stackrel{\stackrel{\stackrel{}{=}.Math..Math.s_1}{}}{\left(a_1+j.Math..Math.I_{m_0,n_0}^{\left(1\right)}\right)}-H^{\left(2\right)}.Math.\stackrel{\stackrel{.Math.s_2^{*}}{}}{\left(a_2-j.Math..Math.I_{m_0,n_0}^{\left(2\right)}\right)}+{}_{m_0,n_0}\\ =.Math.H^{\left(1\right)}.Math.s_1-H^{\left(2\right)}\left(s_2^{*}.Math.\underset{\underset{.fwdarw..Math.0}{}}{+j.Math..Math.I_1}\right)+{}_{m_0,n_0}\end{array}\\ \begin{array}{c}{y}_{m_0+1,n_0}=.Math.H^{\left(1\right)}.Math.\stackrel{\stackrel{\stackrel{}{=}.Math..Math.s_2}{}}{\left(a_2+j.Math..Math.I_{m_0+1,n_0}^{\left(1\right)}\right)}+H^{\left(2\right)}.Math.\stackrel{\stackrel{.Math.s_1^{*}}{}}{\left(a_1+j.Math..Math.I_{m_0+1,n_0}^{\left(2\right)}\right)}+{}_{m_0+1,n_0}\\ =.Math.H^{\left(1\right)}.Math.s_2+H^{\left(2\right)}\left(s_1^{*}.Math.\underset{\underset{.fwdarw..Math.0}{}}{+j.Math..Math.I_2}\right)+{}_{m_0+1,n_0}\end{array}\end{array}$ wherein y.sub.m.sub.0.sub.,n.sub.0 is the received signal at the resource at (m.sub.0,n.sub.0) in the time-frequency domain, .sub.m.sub.0.sub.,n.sub.0 is AWGN and I.sub.m.sub.0.sub.,n.sub.0.sup.(1) and I.sub.m.sub.0.sub.,n.sub.0.sup.(2) being the intrinsic interference from the first and the second antenna at resource (m.sub.0,n.sub.0) respectively, wherein precoding symbols in the second embodiment are chosen to cancel out the composite intrinsic interference, which relates to the combination of two intrinsic interferences and is defined as
I.sub.1I.sub.m.sub.0.sub.+1,n.sub.0.sup.(1)I.sub.m.sub.0.sub.,n.sub.0.sup.(2)
I.sub.2I.sub.m.sub.0.sub.,n.sub.0.sup.(1)+I.sub.m.sub.0.sub.+1,n.sub.0.sup.(2) wherein the precoding symbols are selected so that the composite interference I.sub.1 and I.sub.2 is cancelled to thereby obtain an orthogonal design by forcing interference I.sub.1 and I.sub.2 to zero by the precoding symbols.

8. The method for transmitting of claim 7, wherein the real-valued desired signals are recovered from the complex estimates as
.sub.1=Re{.sub.1} and
.sub.2=Re{.sub.2}.

9. The method for transmitting of claim 6, wherein when considering the ambiguity functions that reflect the interference from neighbouring transmission resources, the receive signals for the subcarriers m.sub.0 and m.sub.0+1 read as
y.sub.m.sub.0.sub.,n.sub.0=H.sup.(1)(s.sub.1.sup.R+j(w.sub.1x.sub.1+I.sub.m.sub.0.sub.,n.sub.0.sup.(1)))H.sup.(2)(s.sub.2.sup.Rj(w.sub.1x.sub.2+I.sub.m.sub.0.sub.,n.sub.0.sup.(2)))+.sub.m.sub.0.sub.,n.sub.0
_{y.sub.m.sub.0.sub.+1,n.sub.0=H.sup.(1)(s.sub.2.sup.R+j(w.sub.3x.sub.1+I.sub.m.sub.0.sub.+1,n.sub.0.sup.(1)))+H.sup.(2)(s.sub.1.sup.R+j(w.sub.3x.sub.2+I.sub.m.sub.0.sub.+1,n.sub.0.sup.(2))).sub.m.sub.0.sub.+1,n.sub.0 and wherein the precoding signals constraints are determined based on the constraints that for the composite interference I.sub.1=I.sub.2=0, which can be written as $\left[\begin{array}{cc}{w}_1& -w_1\\ w_3& w_3\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]=\left[\begin{array}{c}{I}_{m_0,n_0}^{\left(1\right)}-I_{m_0,n_0}^{\left(2\right)}\\ I_{m_0+1,n_0}^{\left(1\right)}+I_{m_0+1,n_0}^{\left(2\right)}\end{array}\right]$ and the desired precoding symbols x.sub.1 and x.sub.2 are determined by solving this equation system.}

10. The method for transmitting of claim 1, wherein said offset quadrature amplitude modulation is applied with the filterbank multicarrier FBMC.

11. The method for transmitting according to claim 1 wherein data is contained on the real part of the demodulated signal.

12. The method for transmitting of claim 1, wherein two real-valued pulse amplitude modulation PAM symbols a1, a2 are to be transmitted, wherein data containing symbols a1, a2 are transmitted using resources (m.sub.0,n.sub.0) and (m.sub.0+u,n.sub.0+v) in the time-frequency domain by the first antenna; wherein data containing symbols a2, a1, are transmitted using resources (m.sub.0,n.sub.0) and (m.sub.0+u,n.sub.0+v) in the time-frequency domain by the second antenna; and wherein u, v are non-zero.

13. The method for transmitting of claim 1, wherein two real-valued pulse amplitude modulation PAM symbols a1, a2 are to be transmitted, wherein data containing symbols a1, a2 are transmitted using resources (m.sub.0,n.sub.0) and (m.sub.0+u,n.sub.0) in the time-frequency domain by the first antenna; wherein data containing symbols a2, a1, are transmitted using resources (m.sub.0,n.sub.0) and (m.sub.0+u,n.sub.0) in the time-frequency domain by the second antenna; and wherein u is non-zero.

14. The method for transmitting of claim 1, wherein two real-valued pulse amplitude modulation PAM symbols a1, a2 are to be transmitted, wherein data containing symbols a1, a2 are transmitted using resources (m.sub.0,n.sub.0) and (m.sub.0,n.sub.0+u) in the time-frequency domain by the first antenna; wherein data containing symbols a2, a1, are transmitted using resources (m.sub.0,n.sub.0) and (m.sub.0,n.sub.0+u) in the time-frequency domain by the second antenna; and wherein u is non-zero.

15. The method for transmitting according to claim 5, wherein two precoding symbols are used for the PAM symbols transmitted by the first antenna and two precoding symbols are used for the PAM symbols transmitted by the second antenna, wherein each of the precoding symbols are selected such as to force the intrinsic interference at each resource used to transmit the PAM symbols, when received by a receiver, to be zero.

16. A receiving method for demodulating a signal transmitted by the transmission method according to claim 1, wherein the received signal is processed by a linear diversity combining for the space-time or space-frequency code and by taking the real part of the output.

17. An apparatus for transmitting a multicarrier signal using a transmit diversity technique with a plurality of transmit antennas (Tx1, Tx2), wherein the apparatus is adapted to carry out the method for transmitting according to claim 1.

Description

DESCRIPTION OF THE DRAWINGS

[0069] FIG. 1 shows the architecture of an FBMC/OQAM transmission scheme with transmit diversity using two transmit antennas.

[0070] FIG. 2 show an Alamouti scheme for transmit diversity as for example used in LTE.

[0071] FIG. 3 shows a single input, single output channel model where a PAM signal is transmitted through a single transmit antenna based on FBMC/OQAM.

[0072] FIG. 4 shows a transmission scheme with two transmit antennas based on FBMC/OQAM where orthogonally is lost through intrinsic interference.

[0073] FIG. 5 shows an orthogonal transmission scheme with transmit diversity through two transmit antennas based on FBMC/OQAM where intrinsic interference is cancelled using one precoding symbol per PAM signal.

[0074] FIG. 6 shows the principle of transmitting one PAM symbol using two resources.

[0075] FIG. 7 shows an orthogonal transmission scheme with transmit diversity through two transmit antennas based on FBMC/OQAM where the composite intrinsic interference is cancelled using one precoding symbol for each pair of PAM signals.

DETAILED DESCRIPTION

[0076] At first, some terms used in the description will be defined in the following list of abbreviations. [0077] AWGN Additive White Gaussian Noise [0078] FBMC Filter Bank Multicarrier [0079] LTE Long Term Evolution (mobile phone standard) [0080] OFDM Orthogonal Frequency Division Multiplexing [0081] OQAM Offset Quadrature Amplitude Modulation [0082] PAM Pulse Amplitude Modulation [0083] QAM Quadrature Amplitude Modulation [0084] SISO Single-In-Single-Out

[0085] The invention is concerned with filter bank multicarrier (FBMC) offset quadrature amplitude modulation (OQAM) transmission with the so called transmit diversity technique using two transmit antennas as illustrated in FIG. 4.

[0086] One objective is to design a transmit diversity scheme from orthogonal design for FBMC/OQAM similar to the above described Alamouti scheme, which Is for example, applied to LTE OFDM system.

[0087] A first embodiment is illustrated in FIG. 5. In this approach orthogonality is achieved in a FBMC/OCAM transmission scheme. In this figure, four precoding symbols are introduced, i.e., two precoding symbols for each transmit antenna.

[0088] In the first embodiment, these precoding symbols are chosen such as to cancel the intrinsic Interferences as follows:

[00010]$\begin{array}{cc}.Math.y_{m_0,n_0}=H^{\left(1\right)}\left(a_1+j.Math..Math.\stackrel{\stackrel{.fwdarw..Math.0}{}}{I_{m_0,n_0}^{\left(1\right)}}\right)-H^{\left(2\right)}\left(a_2-j.Math..Math.\stackrel{\stackrel{.fwdarw..Math.0}{}}{I_{m_0,n_0}^{\left(2\right)}}\right)+{}_{m_0,n_0}.Math..Math.y_{m_0+1,n_0}=H^{\left(1\right)}\left(a_2+j.Math..Math.\stackrel{\stackrel{.fwdarw..Math.0}{}}{I_{m_{0+1},n_0}^{\left(1\right)}}\right)+H^{\left(2\right)}\left(a_1+j.Math..Math.\stackrel{\stackrel{.fwdarw..Math.0}{}}{I_{m_0+1,n_0}^{\left(2\right)}}\right)+{}_{m_0+1,n_0}& \left(13\right)\end{array}$

[0089] Here, y.sub.m.sub.0.sub.,n.sub.0 is the received signal at the resource at (m.sub.0,n.sub.0) In the time-frequency domain, .sub.m.sub.0.sub.,n.sub.0 is AWGN and I.sub.m.sub.0.sub.,n.sub.0.sup.(1) and I.sub.m.sub.0.sub.,n.sub.0.sup.(2) being the intrinsic interference from the first and the second antenna at resource (m.sub.0,n.sub.0) respectively. The precoding symbols x.sub.1,x.sub.2,x.sub.3,x.sub.4 are chosen to cancel (zero) the intrinsic interference individually for each antenna. Specifically, the symbols x.sub.1,x.sub.2 are chosen to cancel the intrinsic interferences I.sub.m.sub.0.sub.,n.sub.0.sup.(1) I.sub.m.sub.0.sub.+1,n.sub.0.sup.(1) of the first antenna and x.sub.3,x.sub.4 are chosen to cancel the intrinsic interferences I.sub.m.sub.0.sub.,n.sub.0.sup.(2) I.sub.m.sub.0.sub.+1,n.sub.0.sup.(2) of the second antenna.

[0090] The first embodiment leads to an orthogonal design and achieves a code rate of 1/2, i.e. the transmission of one data symbol requires two time units since one precoding symbol is transmitted per data symbol.

[0091] FIG. 6 shows only two transmission resources and only a single antenna is considered for simplicity. In the approaches discussed so far, one of the resources is used for sending the precoding signal that is intended to protect useful data sent using another resource to somewhat combat with pure imaginary intrinsic interference observed at the receiver. This means that one real-valued PAM symbol is transmitted using two resources. Hence FIG. 6 illustrates this principle of using a precoding symbol x to protect a real-valued data symbol a to be transmitted, wherein the precoding symbol serves to cancel out intrinsic interference and the value received at the resource used for transmission of the precoding symbol is not otherwise used (useless) at the receiver side.

[0092] A second embodiment is illustrated in FIG. 7. Compared to the first embodiment described above, the second embodiment improves the coding rate is from 1/2 to 2/3. In the second embodiment, only one precoding symbol is used for each transmit antenna.

[0093] The precoding symbols in the second embodiment are chosen to cancel out the so called composite intrinsic interference, which can be defined as

I.sub.1I.sub.m.sub.0.sub.+1,n.sub.0.sup.(1)I.sub.m.sub.0.sub.,n.sub.0.sup.(2)(14)

I.sub.2I.sub.m.sub.0.sub.,n.sub.0.sup.(1)+I.sub.m.sub.0.sub.+1,n.sub.0.sup.(2)(15)

[0094] See also the previous attempt to implement the Alamouti scheme, specifically equations (10) and (11). The term composite thereby relates to the combination of two intrinsic interferences, wherein each of the two intrinsic interferences is obtained at the receiver at one transmission resource and being caused by neighboring resources of said one transmission resource transmitted by one of two antennas, and wherein each of said two intrinsic interference being caused by the transmission of neighboring resources by one of two antennas.

[0095] To illustrate this, the same development of the received signal as in FIG. 4 is used as follows:

[00011]$\begin{array}{cc}\begin{array}{c}\begin{array}{c}{y}_{m_0,n_0}=.Math.H^{\left(1\right)}.Math.\stackrel{\stackrel{\stackrel{}{=}.Math..Math.s_1}{}}{\left(a_1+j.Math..Math.I_{m_0,n_0}^{\left(1\right)}\right)}-H^{\left(2\right)}.Math.\stackrel{\stackrel{.Math.s_2^{*}}{}}{\left(a_2-j.Math..Math.I_{m_0,n_0}^{\left(2\right)}\right)}+{}_{m_0,n_0}\\ =.Math.H^{\left(1\right)}.Math.s_1-H^{\left(2\right)}\left(s_2^{*}.Math.\underset{\underset{.fwdarw..Math.0}{}}{+j.Math..Math.I_1}\right)+{}_{m_0,n_0}\end{array}\\ \begin{array}{c}{y}_{m_0+1,n_0}=.Math.H^{\left(1\right)}.Math.\stackrel{\stackrel{\stackrel{}{=}.Math..Math.s_2}{}}{\left(a_2+j.Math..Math.I_{m_0+1,n_0}^{\left(1\right)}\right)}+H^{\left(2\right)}.Math.\stackrel{\stackrel{.Math.s_1^{*}}{}}{\left(a_1+j.Math..Math.I_{m_0+1,n_0}^{\left(2\right)}\right)}+{}_{m_0+1,n_0}\\ =.Math.H^{\left(1\right)}.Math.s_2+H^{\left(2\right)}\left(s_1^{*}.Math.\underset{\underset{.fwdarw..Math.0}{}}{+j.Math..Math.I_2}\right)+{}_{m_0+1,n_0}\end{array}\end{array}& \left(16\right)\end{array}$

[0096] If the precoding symbols are selected so that the composite interference I.sub.1 and I.sub.2 is cancelled, one obtains an orthogonal design and can apply the simple linear processing as the Alamouti scheme for OFDM to obtain

[00012]$\begin{array}{cc}=\frac{1}{{.Math.H^{\left(1\right)}.Math.}^2+{.Math.H^{\left(2\right)}.Math.}^2}.Math.H^H.Math.y=\left[\begin{array}{c}{s}_1\\ s_2^{*}\end{array}\right]+\frac{1}{{.Math.H^{\left(1\right)}.Math.}^2+{.Math.H^{\left(2\right)}.Math.}^2}.Math.H^H.Math..& \left(17\right)\end{array}$

[0097] It is noted that the outcomes are estimates .sub.1 and .sub.2 of the complex valued virtual symbols s.sub.1 and s.sub.2 that are real-valued desired signal plus intrinsic interference. Thus, the real-valued desired signals are recovered from the complex estimates as

.sub.1=Re{.sub.1} and

.sub.2=Re{.sub.2}.(18)

[0098] To elaborate in detail further, when applying the precoding symbols x.sub.1 and x.sub.2, and when considering the ambiguity functions shown in FIG. 7 that reflect the interference from neighbouring transmission resources, (16) may be rewritten as:

y.sub.m.sub.0.sub.,n.sub.0=H.sup.(1)(s.sub.1.sup.R+j(w.sub.1x.sub.1+I.sub.m.sub.0.sub.,n.sub.0.sup.(1)))H.sup.(2)(s.sub.2.sup.Rj(w.sub.1x.sub.2+I.sub.m.sub.0.sub.,n.sub.0.sup.(2)))+.sub.m.sub.0.sub.,n.sub.0

y.sub.m.sub.0.sub.+1,n.sub.0=H.sup.(1)(s.sub.2.sup.R+j(w.sub.3x.sub.1I.sub.m.sub.0.sub.+1,n.sub.0.sup.(1)))+H.sup.(2)(s.sub.1.sup.R+j(w.sub.3x.sub.2+I.sub.m.sub.0.sub.+1,n.sub.0.sup.(2)+.sub.m.sub.0.sub.+1,n.sub.0(19)

where

I.sub.m.sub.0.sub.,n.sub.0.sup.(1)=I.sub.m.sub.0.sub.,n.sub.0.sup.(1)w.sub.1x.sub.1

I.sub.m.sub.0.sub.,n.sub.0.sup.(2)=I.sub.m.sub.0.sub.,n.sub.0.sup.(2)w.sub.1x.sub.2

I.sub.m.sub.0.sub.+1,n.sub.0.sup.(1)=I.sub.m.sub.0.sub.+1,n.sub.0.sup.(1)w.sub.3x.sub.1

I.sub.m.sub.0.sub.+1,n.sub.0.sup.(2)=I.sub.m.sub.0.sub.+1,n.sub.0.sup.(2)w.sub.3x.sub.2(20)

[0099] Then, the receive signals can be further rewritten as

y.sub.m.sub.0.sub.,n.sub.0=H.sup.(1)s.sub.1H.sup.(2)(s*.sub.2+jI.sub.1)+.sub.m.sub.0.sub.,n.sub.0

y.sub.m.sub.0.sub.+1,n.sub.0=H.sup.(1)s.sub.2+H.sup.(2)(s*.sub.1+jI.sub.2)+.sub.m.sub.0.sub.+1,n.sub.0(21)

where s.sub.1 and s.sub.1 are defined as

s.sub.1=s.sub.1.sup.R+j(w.sub.1x.sub.1+I.sub.m.sub.0.sub.,n.sub.0.sup.(1))

s.sub.2=s.sub.2.sup.R+j(w.sub.3x.sub.1+I.sub.m.sub.0.sub.+1,n.sub.0.sup.(1))(22)

and also

I.sub.1=I.sub.m.sub.0.sub.+1,n.sub.0.sup.(1)I.sub.m.sub.0.sub.,n.sub.0.sup.(2)=I.sub.m.sub.0.sub.,n.sub.0.sup.(1)I.sub.m.sub.0.sub.,n.sub.0.sup.(2)w.sub.1x.sub.1+w.sub.1x.sub.2

I.sub.2=I.sub.m.sub.0.sub.,n.sub.0.sup.(1)+I.sub.m.sub.0.sub.+1,n.sub.0.sup.(2)=I.sub.m.sub.0.sub.+1,n.sub.0.sup.(1)+I.sub.m.sub.0.sub.+1,n.sub.0.sup.(2)w.sub.3x.sub.1w.sub.3x.sub.2 (23)

[0100] The constraints are then I.sub.1=I.sub.2=0, which can be written as

[00013]$\begin{array}{cc}\left[\begin{array}{cc}{w}_1& -w_1\\ w_3& w_3\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]=\left[\begin{array}{c}{I}_{m_0,n_0}^{\left(1\right)}-I_{m_0,n_0}^{\left(2\right)}\\ I_{m_0+1,n_0}^{\left(1\right)}+I_{m_0+1,n_0}^{\left(2\right)}\end{array}\right]& \left(24\right)\end{array}$

[0101] This equation system can be easily solved to get the desired precoding symbols x.sub.1 and x.sub.2 that satisfy the constraints. And it reduces to the equivalent Alamouti system in (1) and (2). Then, with the additional steps in (17) and (18) the desired signals can be demodulated.

[0102] The advantage of the technology according to the embodiments presented herein is the ability to realize transmit diversity from the orthogonal design with full diversity, i.e. diversity order of 2 for two transmit antennas. The embodiments differ e.g. In their effectiveness to exploit available channel resources for the transmission of data symbols (rate loss).

[0103] It will be readily apparent to the skilled person that the methods, the elements, units and apparatuses described in connection with embodiments of the invention may be Implemented in hardware, in software, or as a combination of both. In particular it will be appreciated that the embodiments of the invention and the elements of modules described in connection therewith may be implemented by a computer program or computer programs running on a computer or being executed by a microprocessor. Any apparatus implementing the invention may in particular take the form of a computing device acting as a network entity.