1. A method for Soft-output Fixed-complexity Sphere Decoding (SFSD) detection, comprising: performing QR decomposition on a channel response matrix to acquire a Q matrix and an R matrix; multiplying a conjugate transpose of the Q matrix by a received signal to acquire an equalized signal of the received signal; performing path extension starting from a top layer of the R matrix, which is a layer having only one non-zero element, to a bottom layer of the R matrix; reserving all nodes of the top layer of the R matrix; decreasing, layer by layer, reserved nodes in layers below the top layer of the R matrix to acquire Euclidean distances of respective branches; selecting a branch having a minimum Euclidean distance as a Maximum Likelihood (ML) path, and reserving branches as many as iterations; performing path extension starting from a top layer of acquired complementary set layers of respective reserved branches to corresponding bottom layer of the acquired complementary set layers; reserving all nodes of the top layer of the acquired complementary set layers; decreasing, layer by layer, reserved nodes in layers below the top layer of the acquired complementary set layers to acquire Euclidean distances of respective branches; selecting, layer by layer, starting from the top layer of the acquired complementary set layers, a branch having a minimum Euclidean distance as an ML complementary set path of each layer; and acquiring Likelihood Ratio (LLR) information of each bit of each symbol of each layer according to the ML path and the ML complementary set path.