Beam Raster a Practical Fast Massive MU-MIMO System with PreComputed Pre coders
Abstract: In order to achieve more dramatic spatial multiplexing gains, both industry and academia have pushed towards the massive Multi-User Multi-Input and MultiOutput (MU-MIMO) systems. However, traditional linear pre coding techniques do not scale up well with the number of antennas, i.e., they either have high implementation difficulties (zero-forcing) or sacrifice wireless capacity as a price (conjugate or codebook-based pre coding). In this paper, we present a novel pre coding scheme, Beam Raster, which is a fast and high efficient scheme for massive MU-MIMO system. Inspired from the codebook-based pre coding, Beam Raster pre-computes a set of angle-domain beam filters that divide the channel into directional subspaces. Unlike previous work, Beam Raster carefully manages the cross-interference using (1) a grating table to track the correlation among beams in real-time, (2) an interference-aware user-beam selection, and (3) a pre-distortion method to cancel the residual interference because of side-lobes. We implement and evaluate the Beam Raster using FPGA and software defined radio platform. On one hand, Beam Raster is easy to implement in hardware, i.e., it can realize the pre coding for a 64-antenna MU-MIMO system in real time with a single Altera
Stratix V FPGA. On the other hand, both the experiments with medium-scale antennas and simulations with large-scale antennas show that Beam Raster can achieve high capacity gain. Existing system: Although they avoid to exhaustively searching all possible combinations of mobile users, searching a minimum SINR in each iteration still costs much. In, the AP beam forms probing signal of existing selected users and other candidate clients report feedback to the AP if its channel state is orthogonal to the existing selected users. Then the AP adds the client with feedback into the selected user. Meanwhile, SIEVE leverages the idea of branch and- bound and provides a scalable user selection module for large-scale MU-MIMO systems. In contrast, Beam Raster establishes a grating table to track the correlation among the precompiled beams, so that it can leverage a rather Light weight score-board algorithm to select proper user beam pairs. Proposed system: Previously, many works also exploit other pre coding methods with lower complexity. One predominate method is called conjugate precoding. In this scheme, the precoder is directly chosen as the conjugate transpose of the channel vector, i.e., W = HH. Intuitively, conjugate precoding form beams towards the direction of each mobile client and therefore maximize the signal strength at each individual client. A similar design is also proposed in LTE Advanced (LTE-A) with limited channel feedback as codebook-based precoding. Basically, codebookbased precoding precomputes a set of beam filters, each of which points to an identical direction. This set of beams is called codebook and shared between the base station and the mobile clients. So based on the CSI, the client can independently choose a beam that maximizes its signal strength, i.e., the one closest to the conjugate transpose of the channel, and feedback the index of the filter to the base station. Advantages:
Codebook-based precoding, however, manages cross interference among clients by selecting concurrent users only in orthogonal subspaces as determined by the pre computed filters. However, in the next section, we will show that in practice all subspaces could have cross-talks, even though they are designed to be orthogonal in theory. Without well managing these cross-talks, the performance of codebook-based precoding is still much inferior compared to ZF. Disadvantages: With the channel response information stored in the grating table, the user-beam selection algorithm focuses on finding a group of K users to maximize the sumrate. Thus, the user-beam selection problem can be formalized as integer programming. Let Ik,i be an integer variable which indicates that the user k is assigned to beam f(i). Then, the problem is to select a group G to maximize the following objective function. Modules: Signal Pre-distortion: The aforementioned interference-aware user-beam selection algorithm effectively avoids strong cross-interference among concurrent users – predominately by multipath fading. However, there are still weak energy leakages due to side-lobes. Since there could be multiple concurrent users, the aggregated energy leakage from others may still cause significant interference to one user. We develop a predistortion technique to combat this side-lobe interference. The basic idea is illustrated. Data Partitioning and Processing Pipeline: In this section, we will illustrate how the workload of Beam Raster is balanced between the FPGA and the host PC. As discussed earlier, most of processing in BeamRaster is the multiplication of matrix and vector, i.e., calculating the grating table, pre-distorting the symbols and precoding. All these modules consist of mere adding, multiplication operations and thus can be fully parallelized. In our
implementation, all these matrix multiplication tasks are done in the FPGA. However, FPGA is known to be inefficient for division implementation. So the calculation of pre-distortion matrix A which requires division operation is implemented on the host PC. At the same time, as the pre-distortion matrix relies on the data in grating table, we also have grating table maintained in the host PC. The related user beam selection algorithm is also implemented on the host PC. Overhead Evaluation: We have already shown that the resource in one FPGA chip can support a MUMIMO system with up to 64 antennas. In this section, we will evaluate the system overhead with antenna number ranges from 12 to 64. As we analyzed in §4.4.2, Beam Raster transfers the grating table calculation to the channel measurement period. Therefore, unlike other precoding technique simply computing the channel state of each antenna, Beam Raster also requires to decompose the channel state into different beams (i.e., computing the grating table). We first evaluate the time overhead of grating table calculation. The sounding frame for channel measurement in 802.11 standard starts with 10 STS(short training sequence) and 2 LTS(long training sequence), and the total frame lasts for 40Οs. We measure the time needed for the grating table calculation in different scenarios. Multi – User Mimo: THE rapid growth of mobile devices and data-driven applications creates a tremendous demand for high-speed wireless networks. Multi-User MIMO (MUMIMO) technology, however, holds the promise to significantly increase the wireless channel capacity. In a MU-MIMO system, an access point (AP) equipped with multiple antennas can transmit multiple data frames simultaneously to multiple clients, and therefore may increase the capacity linearly with the number of antennas of the AP. Consequently, many recent MU-MIMO systems have been built to incorporate as many antennas as possible to provide high wireless data rate to multiple devices simultaneously. To transmit multiple data frames to different clients, the AP is required to pre code the frames of each antenna, so that when the emitted wireless waves arrive at clients, the strength of the desired frame remains strong, while all interference is suppressed at a low level. Singular Value Decomposition:
While ZF precoding effectively exploits spatial diversity to boost channel capacity, generating precoders, however, is computationally intensive. Essentially, the ZF precoder requires to compute an inverse of the channel matrix, which takes O (K2N) operations, where K is the number of concurrently served clients and N is the number of antennas on the AP. The value of K and N are usually large in a massive MIMO system. Therefore, the computational complexity of the matrix inverse grows quickly. The inverse of a matrix can be computed using many methods, such as Gauss-Jordan elimination, LU decomposition, Singular Value Decomposition (SVD), and QR decomposition. However, the processes of all those methods are basically sequential. Take the Gauss-Jordan method for example. The basic procedure is as follows: First, we augment the matrix A with an identity matrix I of the same order into an extended matrix