Linear Minimum Mean Squared Error (MMSE) Multiple Input Multiple Output (MIMO) detector for RISC-V with support for "V" Vector Extension based on Cholesky decomposition. Supports ARA and baremetal. Implements fixed- and floating-point solutions (LDL and LL Cholesky decompositions respectively). Vectorizes along the subcarriers dimension.

Multiple user antennas transmit data (x) to a base station equiped with multiple receiving antennas. Application of a multiplexing channel H and noise n yields a received signal vector y. Channel and noise estimators support with the channel matrix H and a noise covariance matrix R. This program implements a detector that approximates x from y, H and R.

• NUM_RX - number of receiving antennas.
• NUM_TX - number of transmitting antennas.
• NUM_SC - number of subcarriers.
• x - transmitted signal.
• y - received signal.
• H - multiplexing channel matrix.
• n - noise vector on the receiving antennas.
• R - noise covariance matrix.

Find such x that x = G^{-1} H^H y where G is a Gram matrix defined as G = (H^H H + R) and H^H is a Hermittian transpose of H. This is done in 5 steps:

• cmatgram: Calculate G = H^H H + R
• ccholesky: Perform Cholesky decomposition (G=LL^H or G=LDL^H)
• cmatvecmul: Multiply H^H and y (HHy=H^H y)
• cforwardsub: Perform forward substitution to find such z that Lz=HHy
• cbackwardsub: Perform backward substitution to find such x that z=L^H x (or D^{-1} z = L^H x in case of LDL Cholesky)

The following data flow diagrams demonstrate element-wise formulas for both LL and LDL based detection:

Each of the five operations is implemented in its source file in src. main.c contains memory intialization and cycles measurments for each function.

scripts/gen_data.py generates x, H, R and n in data directory. re and im in the names mean real and imaginary parts. Then the data is loaded diectly into the program memory compile-time in main.c (thanks to ChaN for sharing the macro).

Compile by passing configuration parameters to make:

$ make help

Usage:
  make [ARCH=<arch>] [DATA_TYPE=<type>] [PLATFORM=<platform>] [NUM_RX=<num_rx>] [NUM_TX=<num_tx>] [NUM_SC=<num_sc>]

Supported ARCH values:
  - x86 (default)
  - rv
  - rvv

Supported DATA_TYPE values:
  - float (default)
  - fixed

Supported PLATFORM values:
  - linux (default)
  - ara
  - baremetal

Supported NUM_RX values: integers > 0 (default = 4)
Supported NUM_TX values: integers > 0 (default = 4)
Supported NUM_SC values: integers > 0 (default = 1024)

Debug mode:
  - DEBUG=0 (default, optimized with -O1)
  - DEBUG=1 (debug mode with -g -O0)

• ARCH:
  • x86 - (x86-64) for testing purposes. Sequential solution, no vectorization.
  • rv - RISC-V 64 (rv64) without "V" extension. Sequential solution, no vectorization.
  • rvv - rv64v. Vectorized solution.
• DATA_TYPE:
  • float - all the data and computation is done with float. Requires "F" extension. Uses LL Cholesky.
  • fixed - Q31 fixed-point. Uses LDL Cholesky.
• PLATFORM - this parameter currently only affects printf:
  • linux - printf from <stdio.h>
  • ara - ARA's printf from apps/common. Assumes the repository is in the apps directory`.
  • baremental - simple UART printf strictly to output the cycles as used in main.c. NOT IMPLEMENTED YET.

Running make with the given parameters will create build directory and an .elf with the parameters in its name.