Radio transmitter for distortion mitigation

1. A transmitter for radio transmission to one or more receivers over a channel described at least in part by a channel matrix H, the transmitter comprising:

a pre-coder connected to an antenna array via a transmit unit;

wherein the antenna array comprises a number M of antenna elements a m , m=1, 2, . . . , M, each antenna element a m being configured to receive a respective transmit signal component x m from the pre-coder via the transmit unit;

wherein the pre-coder is configured to:

receive a number K<M of data streams s k , k=1, 2, . . . , K; and

generate the M transmit signal components by adding M shaping components e m , m=1, 2, . . . , M, to respective transmit signal components x m ; and

wherein the shaping components e m are determined based on a null-space of the channel matrix H and on one or more properties of the transmit unit.

2. The transmitter of claim 1 , wherein the shaping components e m are determined by projection of a shaping vector 6 onto the null-space of the channel matrix H.

3. The transmitter of claim 2 , wherein the projection comprises multiplication by an orthogonal projection matrix P H ⊥ =I−H(H H H) −1 H H , where:

I denotes the identity matrix;

(⋅) −1 denotes matrix inverse; and

H H denotes Hermitian transpose of the channel matrix H.

4. The transmitter of claim 1 , wherein the one or more properties of the transmit unit comprise addition of distortion components d m to the respective transmit signal components x m , the distortion components d m being dependent on the shaping components e m of corresponding transmit signal components x m .

5. The transmitter of claim 4 , wherein:

the transmit unit comprises one or more digital to analog converters (DACs);

the distortion components d m comprise quantization errors due to the DACs;

the shaping components e m comprise independent dithering components determined based on a least significant bit (LSB) signal magnitude of the one or more DACs; and

the dithering components comprise a random signal for de-correlating parts of the transmit signal components.

6. The transmitter of claim 5 , wherein the dithering components constitute a vector of independent identically distributed elements, statistically distributed between −LSB/2 and LSB/2, and projected onto the null-space of the channel matrix H.

7. The transmitter of claim 1 , wherein:

a performance metric of the transmit unit is dependent on one or more characteristics of the transmit signal components x m ; and

the respective shaping components e m have an impact on the characteristics of the transmit signal components x m .

8. The transmitter of claim 7 , wherein:

the performance metric of the transmit unit comprises a power efficiency of a power amplifier comprised in the transmit unit; and

the one or more characteristics of the transmit signal components x m comprise a signal variance of the transmit signal components x m .

9. The transmitter of claim 7 :

wherein the performance metric comprises a measure of non-linear distortion on the transmit signal components x m by the transmit unit; and

wherein the one or more characteristics of the transmit signal components x m comprise a peak-to-average power ratio or a cubic metric of the transmit signal components x m .

10. The transmitter of claim 7 :

wherein the performance metric comprises a dynamic range of the transmit unit or of a component comprised in the transmit unit; and

wherein the one or more characteristics of the transmit signal components x m comprises a peak amplitude of the transmit signal components x m .

11. A network node comprising:

a transmitter for radio transmission to one or more receivers over a channel described at least in part by a channel matrix H, the transmitter comprising:

a pre-coder connected to an antenna array via a transmit unit;

wherein the antenna array comprises a number M of antenna elements a m , m=1, 2, . . . , M, each antenna element a m being configured to receive a respective transmit signal component x m from the pre-coder via the transmit unit;

wherein the pre-coder is configured to:

receive a number K<M of data streams s k , k=1, 2, . . . , K; and

generate the M transmit signal components by adding M shaping components e m , m=1, 2, . . . , M, to respective transmit signal components x m ; and

wherein the shaping components e m are determined based on a null-space of the channel matrix H and on one or more properties of the transmit unit.

12. A radar transceiver comprising:

a transmitter for radio transmission to one or more receivers over a channel described at least in part by a channel matrix H, the transmitter comprising:

a pre-coder connected to an antenna array via a transmit unit;

wherein the antenna array comprises a number M of antenna elements a m , m=1, 2, . . . , M, each antenna element a m being configured to receive a respective transmit signal component x m from the pre-coder via the transmit unit;

wherein the pre-coder is configured to:

receive a number K<M of data streams s k , k=1, 2, . . . , K; and

generate the M transmit signal components by adding M shaping components e m , m=1, 2, . . . , M, to respective transmit signal components x m ; and

wherein the shaping components e m are determined based on a null-space of the channel matrix H and on one or more properties of the transmit unit.

13. A method for radio transmission to one or more receivers over a channel described at least in part by a channel matrix H, performed in a transmitter comprising a transmit unit connected to an antenna array having a number M of antenna elements a m , m=1, 2, . . . , M, the method comprising;

receiving a number K<M of data streams s k , k=1, 2, . . . , K;

determining M shaping components e m based on a null-space of the channel matrix H and on one or more properties of the transmit unit;

generating M transmit signal components x m from the K data streams, the generating comprising adding the M shaping components e m to respective transmit signal components x m ; and

transmitting the M transmit signal components x m from respective antenna elements a m .

14. The method of claim 13 , wherein the determining comprises determining the shaping components e m by projecting a shaping vector ε onto the null-space of the channel matrix H.

15. The method of claim 14 , the projecting comprising multiplying by an orthogonal projection matrix P H ⊥ =I−H(H H H) −1 H H , where:

I denotes the identity matrix;

(⋅) −1 denotes matrix inverse; and

H H denotes Hermitian transpose of the channel matrix H.

16. The method of claim 13 , wherein the one or more properties of the transmit unit comprise addition of distortion components d m to the respective transmit signal components x m , the distortion components d m being dependent on the shaping components e m of corresponding the transmit signal components x m .

17. The method of claim 16 , wherein:

the transmit unit comprises one or more digital to analog converters (DACs);

the distortion components d m comprise quantization errors due to the DACs;

the determining comprises determining the shaping components e m as independent dithering components generated based on a least significant bit (LSB) signal magnitude of the one or more DACs;

the dithering components comprise a random signal for de-correlating parts of the transmit signal components.

18. The method of claim 17 , wherein the determining comprises determining the shaping components e m as a vector of independent identically distributed elements, statistically distributed between −LSB/2 and LSB/2, and projected onto the null-space of the channel matrix H.

19. The method of claim 13 , wherein:

a performance metric of the transmit unit is dependent on one or more characteristics of the transmit signal components x m ; and

the respective shaping components e m have an impact on the characteristics of the transmit signal components x m .

20. The method of claim 19 , wherein:

the performance metric of the transmit unit comprises a power efficiency of a power amplifier comprised in the transmit unit; and

the one or more characteristics of the transmit signal components x m comprise a signal variance of the transmit signal components x m .

21. The method of claim 19 , wherein:

the performance metric comprises a measure of non-linear distortion on the transmit signal components x m by the transmit unit; and

the one or more characteristics of the transmit signal components x m comprises a peak-to-average power ratio or a cubic metric of the transmit signal components x m .

22. The method of claim 19 , wherein:

the performance metric comprises a dynamic range of the transmit unit, or of a component comprised in the transmit unit; and

the one or more characteristics of the transmit signal components x m comprise a peak amplitude of the transmit signal components x m .

23. The method of claim 13 , wherein the determining comprises determining the shaping components e m as a vector which optimizes a performance metric of the transmit unit.

24. A non-transitory computer readable recording medium storing a computer program product for controlling a transmitter's radio transmission to one or more receivers over a channel described at least in part by a channel matrix H; the transmitter comprising a transmit unit connected to an antenna array having a number M of antenna elements a m , m=1, 2, . . . , M; the computer program product comprising software instructions which, when run on processing circuitry of the transmitter, causes the transmitter to:

receive a number K<M of data streams s k , k=1, 2, . . . , K;

determine M shaping components e m based on a null-space of the channel matrix H and on one or more properties of the transmit unit;

generate M transmit signal components x m from the K data streams, the generating comprising adding the M shaping components e m to respective transmit signal components x m ; and

transmit the M transmit signal components x m from respective antenna elements a m .