Transmitting and receiving methods

• US 7,773,685 B2
• Filed: 01/23/2003
• Issued: 08/10/2010
• Est. Priority Date: 05/27/2002
• Status: Active Grant

• Current Assignee: Nokia Technologies Oy (Nokia Corporation)
• Original Assignee: Nokia Corporation
• Inventors: Kallojarvi, Kari, Kashaev, Rinat, Tirkkonen, Olav, Kokkonen, Mikko
• Primary Examiner(s): Fan; Chieh M
• Assistant Examiner(s): Ghulamali; Qutbuddin
• Application Number:
  US10/349,168
• Publication Number:
  US 20040002364A1
• Time in Patent Office: 2,756 Days
• Field of Search: 375/267, 375/260, 375/233, 375/347, 375/144, 375/299, 375/268, 375/295, 375/259, 375/285, 375/220, 375/348, 375/349, 370/334, 370/310, 370/464, 370/208, 455/69, 455/562.1
• US Class Current: 375/267
• CPC Class Codes: H04L 1/0009 by adapting the channel coding H04L1/1812 takes precedence
• CPC Class Codes: H04L 1/0042 Encoding specially adapted to other signal generation operation, e.g. in order to reduce transmit distortions, jitter, or to improve signal shape H04L1/0067 takes precedence
• CPC Class Codes: H04L 1/0048 in conjunction with detection of multiuser or interfering signals, e.g. iteration between CDMA or MIMO detector and FEC decoder for spatial equalizer H04L25/03286
• CPC Class Codes: H04L 1/0069 Puncturing patterns
• CPC Class Codes: H04L 1/0618 Space-time coding
• CPC Class Codes: H04L 1/0662 Limited orthogonality systems
• CPC Class Codes: H04L 5/0023 Time-frequency-space
• CPC Class Codes: H04L 5/0044 allocation of payload
• CPC Class Codes: H04L 5/0048 Allocation of pilot signals, i.e. of signals known to the receiver
• CPC Class Codes: H04L 5/0058 Allocation criteria

Abstract

This invention describes a wireless system comprising a plurality of transmitters and receivers, wherein each transmitter has between 1 and n antennas and each receiver has between 1 and m antennas wherein one of said transmitter is arranged to transmit to one of the receivers, said one transmitter is controlled in dependence on at least one of at least one parameter of said transmitters, at least one parameter of said receiver, and at least one parameter of a wireless environment between said transmitter and said receiver.

Claims

1. A system comprising:

a plurality of transmitters and receivers, wherein each transmitter comprises at least one transmitter element and each receiver comprises at least one receiver element and wherein one of said plurality of transmitters is configured to transmit to one of said plurality of receivers, said one of said plurality of transmitters further comprising

data transmitting circuitry,

determining circuitry configured to determine an estimated value based on at least one parameter of said one of said plurality of transmitters, at least one parameter of said one of said plurality of receivers, and at least one parameter of a wireless environment between said one of said plurality of transmitters and said one of said plurality of receivers, and

controller circuitry configured to control said data transmitting circuitry and said at least one transmitter element in accordance with said estimated value,

wherein said estimated value is a practical rank number, wherein said practical rank number is defined as the number of singular values of a matrix H above a threshold value, where H is a channel transfer matrix, and said practical rank number is no greater than the smallest of the number of said transmitter elements and the number of receiver elements of said one of said plurality of receivers.

2. A system as claimed in claim 1, wherein said system is a cellular communication system.

3. A system as claimed in claim 1, wherein said one of said plurality of transmitters comprises one of a base station and a mobile station and/or said one of said plurality of receivers comprises one of a base station and a mobile station.

4. A system as claimed in claim 1, wherein said at least one parameter of said one of said plurality of transmitters comprises at least one of:

number of antennas;

number of substantially orthogonal transmission resources;

available antenna polarisations;

or

modulation scheme.

5. A system as claimed in claim 1, wherein said at least one parameter of said one of said plurality of receivers comprises at least one of:

number of antennas;

service required by said receiver;

one or more parameters of said service required by said receiver;

computational capacity of said receiver;

quality of service required by said receiver;

or

data rate required by said receiver.

6. An apparatus, comprising:

a plurality of transmitter elements;

a data transmitter; and

a processor configured to determine an estimated value based on at least one parameter of said apparatus, at least one parameter of a receiver to which said apparatus is configured to transmit, and at least one parameter of a wireless environment between said apparatus and said receiver comprising a plurality of receiver elements, and to control said data transmitter and said transmitter elements in accordance with said estimated value,

wherein said estimated value is a practical rank number, wherein said practical rank number is defined as the number of singular values of a matrix H above a threshold value, where H is a channel transfer matrix, and said practical rank number is no greater than the smallest of the number of transmitter elements and the number of receiver elements of said receiver.

7. An apparatus as claimed in claim 6, wherein said at least one parameter of said apparatus comprises at least one of:

number of transmitter elements;

available time slots;

available frequency;

available frequency subcarrier;

available codes;

or

transmitter element polarization.

8. An apparatus as claimed in claim 6, wherein said at least one parameter of said receiver comprises:

number of receiver elements;

computational capacity of said receiver;

service required by said receiver;

one or more parameters of a service required by said receiver;

quality of service required by said receiver; and

data rate required by said receiver.

9. An apparatus as claimed in claim 6, wherein said at least one parameter of said wireless environment comprises:

propagation characteristics of said wireless environment.

10. An apparatus as claimed in claim 6, wherein said data transmitter is configured to send a signal to said receiver, said processor being configured to estimate said practical rank number using said signal.

11. An apparatus as claimed in claim 6, wherein said processor is configured to estimate said practical rank number from a signal sent from said receiver.

12. An apparatus as claimed in claim 11, wherein said sent signal is a reference signal.

13. An apparatus according to claim 6, wherein said practical rank number is defined with reference to at least one of a relative threshold, an absolute threshold.

14. An apparatus according to claim 13 wherein said relative threshold is defined by a constant times the average value of all of the singular values.

15. An apparatus according to claim 13, wherein said absolute threshold is defined by the signal to noise interference ratio.

16. An apparatus as claimed in claim 6, wherein said practical rank number is used by said processor in determining at least one of coding, modulation, power, beam forming, interleaving, error correction, or antenna arrangement of said apparatus.

17. An apparatus as claimed in claim 6, wherein the number of different parallel channels transmitted on the same set of orthogonal transmission resources is less than or equal to said practical rank number.

18. An apparatus as claimed in claim 17, wherein said set of orthogonal transmission resources comprises at least one of frequency, frequency sub-carrier, code, spreading code, time, time slot and direction.

19. An apparatus as claimed in claim 6, further comprising:

a beam transmitter, wherein said beam transmitter is configured to generate at least one beam to be transmitted by said transmitter elements.

20. An apparatus as claimed in claim 19, wherein said beam transmitter is configured to weight signals to be transmitted by different transmitter elements.

21. An apparatus as claimed in claim 20, wherein said signals are weighted in accordance with the wireless environment between said apparatus and receiver.

22. An apparatus as claimed in claim 6, wherein said processor is configured to control a scalable space time code.

23. An apparatus as claimed in claim 22, wherein said scalable space time code is in the form:

C₂n(S<sub>1−

2</sub>x2n)=[C_n(S<sub>1−

2</sub>n)C_n(S<sub>(2n+1)−

2x2n</sub>)],

where C_2n is a space-time coding matrix for 2n transmitter elements, C_n a space-time matrix for n transmitter elements and S₁ to S_2n, S_n+1 to S_2x2n are the encoded symbols, wherein

$C_1=\left[\begin{array}{cc}{S}_1& S_2\\ -S_2^{*}& S_1^{*}\end{array}\right]$ $<br><br>\mathrm{and}$ $C_2<br><br>\left({\stackrel{\rightharpoonup <br><br>}{s}}_{1-4}\right)=\left[\begin{array}{cc}{S}_1& S_2\\ -S_2^{*}& S_1^{*}\end{array}\right]+U<br><br>\left[\begin{array}{cc}{S}_3& S_4\\ S_4^{*}& -S_3^{*}\end{array}\right]$

and U is a unitary 2×

2 matrix with determinant=1.

24. The apparatus as claimed in claim 6, further comprising:

a beam transmitter configured to transmit a plurality of beams to said receiver,

wherein said processor is configured to multiply a stream of symbols to be transmitted by a first number (n) of transforms to generate a resultant transformation used in the generation of said beams, and

wherein said first number (n) of transforms used are selected in dependence on said practical rank number.

25. An apparatus as claimed in claim 24, wherein said processor is configured to select said first number (n) of transforms from a set of a second number (in) of transforms, where said second number (in) is greater than or equal to said first number (n).

26. An apparatus as claimed in claim 25, wherein a plurality of sets of said transforms are provided, and wherein said processor is configured to select the set of the second number (in) of transforms dependent on at least said practical rank number.

27. An apparatus as claimed in claim 26, wherein said set of the second number (in) of transforms form a basis set of transforms.

28. An apparatus as claimed in claim 27, wherein said sets of transforms are created from at least one of:

Weyl basis sets;

Hadamard basis sets;

Clifford basis sets;

or

Alamouti basis sets.

29. An apparatus as claimed in claim 24 wherein said processor is configured to select said first number (n) of transforms in dependence of the capacity of said first number (n) of selected transforms.

30. An apparatus as claimed in claim 29, wherein the capacity of said first number (n) of selected transforms is inversely related to a self-interference between the transforms.

31. An apparatus as claimed in claim 24, wherein at least one of said transforms, and said resultant transformation is represented as a matrix with r rows and c columns.

32. An apparatus as claimed in claim 31, wherein said one of the number of rows and columns is equal to a number of substantially orthogonal transmission resources and the other of the number of said rows and columns is equal to a number of the plurality of beams used to transmit said stream of symbols.

33. An apparatus as claimed in claim 24, wherein said processor is configured to multiply said stream of symbols by said first number (n) of transforms to provide the first number (n) of results, and further configured to combine said first number (n) of results to provide said resultant transform.

34. An apparatus as claimed in claim 33, wherein said apparatus is configured to transmit said symbol stream at a rate defined by the number of complex symbols transmitted per substantially orthogonal transmission resource.

35. An apparatus as claimed in claim 24, wherein said apparatus is configured to transmit the symbol stream comprising the real and imaginary parts of a series of complex symbols.

36. An apparatus as claimed in claim 24, wherein five groups of sets are defined as, {tilde over (B)}₁={β

₀₀,β

₀₁,β

₀₂,jβ

₁₃,β

₂₃,β

₃₃}{tilde over (B)}₂={jβ

₀₀,jβ

₀₃,jβ

₀₂,β

₁₁,jβ

₂₁,jβ

₃₁}{tilde over (B)}₃32 {β

₁₀,β

₁₂,β

₁₃,β

₂₁,β

₃₁,jβ

₀₁}{tilde over (B)}₄={β

₀₃,jβ

₁₀,jβ

₁₁,jβ

₁₂,jβ

₂₃,jβ

₃₃}{tilde over (B)}₅={β

₂₀,β

₃₀,β

₃₂,jβ

₃₂,jβ

₂₂,jβ

₂₀,jβ

₃₀,β

₂₂}

where β

<sub>μ

ν</sub>

=τ

_μ

{circumflex over (x)}τ

_ν

,μ

,ν

ε

{0,1,2,3}

and

${\mathrm{\tau <br><br>}}_0=I_2=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right];<br><br>{\mathrm{\tau <br><br>}}_1=\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right];<br><br>{\mathrm{\tau <br><br>}}_2=\left[\begin{array}{cc}0& j\\ j& 0\end{array}\right];<br><br>{\mathrm{\tau <br><br>}}_3=\left[\begin{array}{cc}j& 0\\ 0& -j\end{array}\right].$

37. An apparatus as claimed in claim 24, wherein said apparatus is configured to transmit a symbol stream at a rate of one and a half, the first number (n) off transforms selected being defined as B^{3/2, subopt}={tilde over (B)}₁∪

{tilde over (B)}₂.

38. An apparatus as claimed in claim 24, wherein said apparatus is configured to transmit a symbol stream at a rate of two, the first number (n) of transforms selected being defined as B^{2, subopt}={tilde over (B)}₁∪

{tilde over (B)}₂∪

{β

<sub>10,β

12</sub>}∪

{jβ

₁₀,jβ

₁₂}.

39. An apparatus as claimed in claim 24, wherein said apparatus is configured to transmit a symbol stream at a rate of three, the first number (n) of transforms selected being defined as

B^3,subopt={tilde over (B)}₁∪

{tilde over (B)}₂∪

{tilde over (B)}₃∪

{β

₂₀,β

₃₀,β

₃₂,jβ

₃₂,jβ

₂₂,jβ

₂₀}.

40. An apparatus as claimed in claim 24, wherein said apparatus is configured to transmit 4 beams, over four substantially orthogonal transmission resources using a set of transforms determined by the Weil basis set comprising 32 elements.

41. An apparatus as claimed in claim 40, wherein four groups of sets are defined as

$B_1^W=\{{\beta }_{}^{}$

11 W , β

21 W , β

12 W , β

22 W } , B 2 W = { β

31 W , β

41 W , β

32 W , β

42 W } , ⁢

B 3 W = { β

13 W , β

23 W , β

14 W , β

24 W } , B 4 W = { β

33 W , β

43 W , β

34 W , β

44 W } , ⁢

where ⁢

⁢

β

k1 W = D k - 1 ⁢

Π

l - 1 , for ⁢

⁢

k = 1 , …

⁢

, 4 ;

l = 1 , …

⁢

, 4 ⁢

⁢

and $D=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& {\mathrm{e<br><br>}}^{\mathrm{j\pi <br><br>}/2}& 0& 0\\ 0& 0& {\mathrm{e<br><br>}}^{\mathrm{j\pi <br><br>}}& 0\\ 0& 0& 0& {\mathrm{e<br><br>}}^{\mathrm{j3\pi <br><br>}/2}\end{array}\right],\mathrm{\Pi <br><br>}=\left[\begin{array}{cccc}0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\\ 1& 0& 0& 0\end{array}\right].<br><br>$

42. An apparatus as claimed in claim 41, wherein said apparatus is configured to transmit a symbol stream at a rate of one and a half, the first number (n) of transforms selected being defined as B^{3/2, W}=B₁^W∪

jB₂^W∪

B₃^W.

43. An apparatus as claimed in claim 41, wherein said apparatus is configured to transmit a symbol stream at a rate of two, the first number (n) of transforms selected being defined as B^2,W=B₁^W∪

B₂^W∪

jB₁^W∪

jB₂^W.

44. An apparatus as claimed in claim 41, wherein said apparatus is configured to transmit a symbol stream at a rate of three, the first number (n) of transforms selected being defined as B^3,W=B₁^W∪

B₂^W∪

B₃^W∪

jB₁^W∪

jB₂^W∪

jB₃^W.

45. An apparatus, comprising:

a plurality of transmitter elements;

a processor configured to receive capability information of a receiver to which said apparatus is configured to transmit; and

a beam transmitter configured to transmit a plurality of beams, said receiver being configured to receive said plurality of beams,

wherein the processor is configured to control said transmitter elements in accordance with at least one parameter of said apparatus;

at least one parameter of said receiver;

at least one parameter of a wireless environment between said apparatus and said receiver,

wherein said processor is configured to multiply a stream of symbols (x) to be transmitted by a first number (n) of transforms to generate a resultant transformation used in the generation of said beams,

wherein the first number (n) of transforms used are selected dependent on at least one parameter of said apparatus;

at least one parameter of said receiver;

at least one parameter of a wireless environment between said apparatus and said receiver and the capacity of the first number (n) of selected transforms,

wherein the capacity of the first number (n) of selected transforms is inversely related to the self-interference and the self-interference (SI) of 2KT selected transforms and their symbols is defined by,

$\mathrm{SI}=\underset{i=1}{\overset{i=2<br><br>\mathrm{KT}}{\sum <br><br>}}<br><br>\underset{k=i+1}{\overset{k=2<br><br>\mathrm{KT}}{\sum <br><br>}}<br><br>x_i<br><br>x_k<br><br>{\mathrm{SI}}^{\left(i,k\right)}$

where SI^(i,k)=β

_i*β

_k+β

_k*β

_i and β

is the transform, and

wherein K is a number of independent modulatable data streams, T denotes how many slots of space-time the modulator extends over.

46. An apparatus, comprising:

a plurality of transmitter elements;

a beam transmitter configured to transmit a plurality of beams to a receiver configured to receive said plurality of beams; and

a processor configured to control said transmitter elements in accordance with at least one parameter of said apparatus;

at least one parameter of said receiver; and

at least one parameter of a wireless environment between said apparatus and said receiver,

wherein said processor is configured to multiply a stream of symbols to be transmitted by a first number (n) of transforms to generate a resultant transformation used in the generation of said beams,

wherein said processor is further configured to select the first number (n) of transforms used dependent on said at least one parameter of said apparatus;

said at least one parameter of said receiver; and

said at least one parameter of a wireless environment between said apparatus and said receiver, wherein said apparatus is configured to transmit the symbol stream comprising the real and imaginary parts of a series of complex symbols and said apparatus is configured to transmit four beams, over four substantially orthogonal transmission resources using a set of transforms determined by the Clifford basis set comprising thirty-two elements,

wherein said Clifford basis set is defined as the 16 real tensor products of the Alamouti basis set and 16 imaginary tensor products of the Alamouti basis set, and

wherein the set of transforms used to transmit said four beams, over said four substantially orthogonal transmission resources are defined as,

$\begin{array}{ccccccc}{B}_0={\left\{{\mathrm{\beta <br><br>}}_{0<br><br>v}\right\}}_{v<br><br>{=}_0^3},& & B_1={\left\{{\mathrm{\beta <br><br>}}_{1<br><br>v}\right\}}_{v<br><br>{=}_0^3}& & B_2={\left\{{\mathrm{\beta <br><br>}}_{2<br><br>v}\right\}}_{v<br><br>{=}_0^3},& & B_3={\left\{{\mathrm{\beta <br><br>}}_{3<br><br>v}\right\}}_{v<br><br>{=}_0^3}\end{array}$
where β

<sub>μ

ν</sub>

=τ

_μ

{circumflex over (x)}τ

_ν

,μ

,ν

ε

{0,1,2,3}

and

${\mathrm{\tau <br><br>}}_0=I_2=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right];<br><br>{\mathrm{\tau <br><br>}}_1=\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right];<br><br>{\mathrm{\tau <br><br>}}_2=\left[\begin{array}{cc}0& j\\ j& 0\end{array}\right];<br><br>{\mathrm{\tau <br><br>}}_3=\left[\begin{array}{cc}j& 0\\ 0& -j\end{array}\right].$

47. An apparatus as claimed in claim 46, wherein said apparatus is configured to transmit a symbol stream at a rate of one, the first number (n) of transforms selected being defined as B¹=B₀∪

B₂.

48. An apparatus as claimed in claim 46, wherein said apparatus is configured to transmit a symbol stream at a rate of one and a half, the first number (n) of transforms selected being defined as B^3/2=B₀∪

e<sup>jπ

/3</sup>B₁∪

e<sup>−

jπ

/3</sup>B₃.

49. An apparatus as claimed in claim 46, wherein said apparatus is configured to transmit a symbol stream at a rate of two, the first number (n) of transforms selected being defined as B²=B₀∪

B₁∪

B₂∪

B₃.

50. An apparatus as claimed in claim 46, wherein said apparatus is configured to transmit a symbol stream at a rate of two, the first number (n) of transforms selected being defined as B^{{tilde over (2)}}=B₀∪

{tilde over (B)}₁∪

{tilde over (B)}₂∪

B₃ where

${\tilde{B}}_k=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& j& 0\\ 0& 0& 0& j\end{array}\right]<br><br>B_k.$

51. An apparatus as claimed in claim 46, wherein said apparatus is configured to transmit a symbol stream at a rate of two and a half, the first number (n) of transforms selected being defined as B^5/2=B₀∪

{tilde over (B)}₁∪

{tilde over (B)}₂∪

B₃∪

jB₀ where

${\tilde{B}}_k=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& j& 0\\ 0& 0& 0& j\end{array}\right]<br><br>B_k.$

52. An apparatus as claimed in claim 46, wherein said apparatus is configured to transmit a symbol stream at a rate of three, the first number (n) of transforms selected being defined as

$B^3=B_0\bigcup$

B ~ 2 ⋃

j ⁢

⁢

B 0 ⋃

j ⁢

⁢

B ~ 2 ⋃

N r 2 ⁢

N r - 1 ⁢

( B ~ 1 + j ⁢

⁢

B 3 ) ⋃

N r 2 ⁢

N r - 1 ⁢

( j ⁢

⁢

B ~ 1 + B 3 ) $\mathrm{where}$ ${\tilde{B}}_k=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& j& 0\\ 0& 0& 0& j\end{array}\right]<br><br>B_k.$

53. An apparatus as claimed in claim 46, wherein said apparatus is configured to transmit a symbol stream at a rate of four, the first number (n) of transforms selected being defined as B⁴=B₀∪

B₁∪

B₂∪

B₃∪

jB₀∪

jB₁∪

jB₂∪

jB₃.

54. An apparatus as claimed in claim 46, wherein said apparatus is configured to transmit a symbol stream at a rate of four, the first number (n) of transforms selected being defined as B^{{tilde over (4)}}=B₀∪

{tilde over (B)}₁∪

{tilde over (B)}₂∪

B₃∪

jB₀∪

j{tilde over (B)}₁∪

j{tilde over (B)}₂∪

jB₃ where

${\tilde{B}}_k=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& j& 0\\ 0& 0& 0& j\end{array}\right]<br><br>B_k.$

55. A method, comprising:

receiving a stream of symbols (x) to be transmitted;

selecting a first number (n) of transforms in dependence on at least one of a wireless radio environment between a transmitter configured to transmit a plurality of beams and a receiver configured to receive said plurality of beams, at least one receiver characteristic, at least one transmitter characteristic; and

the capacity of the first number (n) of transforms;

multiplying said stream of symbols to be transmitted by said n transforms to generate a resultant transformation used in the generation of said beams; and

determining the capacity of the first number (n) of the transforms,

wherein determining the capacity of the first number (n) of transforms comprises

determining the self-interference (SI) of 2KT selected transforms and their symbols is defined by,

$\mathrm{SI}=\underset{i=1}{\overset{i=2<br><br>\mathrm{KT}}{\sum <br><br>}}<br><br><br><br>\underset{k=i+1}{\overset{k=2<br><br>\mathrm{KT}}{\sum <br><br>}}<br><br>x_i<br><br>x_k<br><br>{\mathrm{SI}}^{\left(i,k\right)}$

where SI^(i,k)=β

_i*β

_k+β

_k*β

_i and β

is the transform, and

wherein K is a number of independent modulatable data streams, and T denotes how many slots of space-time the modulator extends over.

56. A method, comprising:

determining an estimated value based on at least one parameter of a transmitter, at least one parameter of a receiver to which said transmitter is to transmit, and/or at least one parameter of a wireless environment between said transmitter and said receiver, wherein each transmitter comprises one or more transmitter elements and each receiver comprises one or more receiver elements; and

controlling said one or more transmitter elements to transmit to said receiver dependent on said estimated value, wherein said estimated value is a practical rank number no greater than the smallest of the number of transmitter elements of said transmitter and the number of receiver elements of said receiver to which said transmitter is transmitting, and wherein said practical rank number is defined as the number of singular values of a matrix H above a threshold value, where H is a channel transfer matrix.

57. A method as claimed in claim 56, wherein determining comprises determining the number of transmitter elements of said transmitter and the number of receiving elements of said receiver to which said transmitter is transmitting.

58. A method as claimed in claim 57, further comprising:

providing scalable space time codes C₁ and C₂;

determining space time codes C_n for said transmission in accordance with the number of transmitter elements; and

transmitting to said receiver in accordance with the determined space time codes, wherein

$C_1=\left[\begin{array}{cc}{S}_1& S_2\\ -S_2^{*}& S_1^{*}\end{array}\right]$ $<br><br>\mathrm{and}$ $C_2<br><br>\left({\stackrel{\rightharpoonup <br><br>}{s}}_{1-4}\right)=\left[\begin{array}{cc}{S}_1& S_2\\ -S_2^{*}& S_1^{*}\end{array}\right]+U<br><br>\left[\begin{array}{cc}{S}_3& S_4\\ S_4^{*}& -S_3^{*}\end{array}\right]$

and U is a unitary 2×

2 matrix with determinant=1.

59. A method as claimed in claim 56, wherein said transmitter is configured to transmit a plurality of beams to said receiver, said method further comprising:

receiving a stream of symbols to be transmitted;

selecting a first number (n) of transforms dependent on said practical rank number; and

multiplying said stream of symbols to be transmitted by the first number (n) of transforms to generate a resultant transformation used in the generation of said beams.

60. A method as claimed in claim 59, wherein the selecting a first number (n) of transforms further comprises selecting said first number (n) of transforms from a set of a second number (in) of transforms, where the second number (m) is greater than or equal to the first number (n).

61. A method as claimed in claim 60, further comprising:

selecting said set of second number (in) of transforms from a plurality of sets of said transforms dependent on said practical rank number value.

62. A method as claimed in claim 60, further comprising:

determining the capacity of the first number (n) of selected transforms.

63. A method as claimed in claim 62, wherein determining the capacity of the first number (n) of selected transforms comprises:

determining the self-interference (SI) of 2KT selected transforms and their symbols (x) by,

$\mathrm{SI}=\underset{i=1}{\overset{i=2<br><br>\mathrm{KT}}{\sum <br><br>}}<br><br><br><br>\underset{k=i+1}{\overset{k=2<br><br>\mathrm{KT}}{\sum <br><br>}}<br><br>x_i<br><br>x_k<br><br>{\mathrm{SI}}^{\left(i,k\right)}$

where SI^(i,k)=β

_i*β

_k+β

_k*β

_i and β

is the transform,

wherein K is a number of independent modulatable data streams, and T denotes how many slots of space-time the modulator extends over.